
MARCO GIBERTINI
Professore Associato Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede exFisica

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2023
 Accurate Prediction of Hall Mobilities in TwoDimensional Materials through GaugeCovariant Quadrupolar Contributions
[Articolo su rivista]
Ponce, S.; Royo, M.; Gibertini, M.; Marzari, N.; Stengel, M.
abstract
Despite considerable efforts, accurate computations of electronphonon and carrier transport properties of lowdimensional materials from first principles have remained elusive. By building on recent advances in the description of longrange electrostatics, we develop a general approach to the calculation of electronphonon couplings in twodimensional materials. We show that the nonanalytic behavior of the electronphonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS2 monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the roomtemperature electron and hole Hall mobilities, respectively.
2023
 Electronic Structure of FewLayer Black Phosphorus from μARPES
[Articolo su rivista]
Margot, F.; Lisi, S.; Cucchi, I.; Cappelli, E.; Hunter, A.; GutiérrezLezama, I.; Ma, K. Y.; von Rohr, F.; Berthod, C.; Petocchi, F.; Poncé, S.; Marzari, N.; Gibertini, M.; Tamai, A.; Morpurgo, A. F.; Baumberger, F.
abstract
: Black phosphorus (BP) stands out among twodimensional (2D) semiconductors because of its high mobility and thickness dependent direct band gap. However, the quasiparticle band structure of ultrathin BP has remained inaccessible to experiment thus far. Here we use a recently developed laserbased microfocus angle resolved photoemission (μARPES) system to establish the electronic structure of 29 layer BP from experiment. Our measurements unveil ladders of anisotropic, quantized subbands at energies that deviate from the scaling observed in conventional semiconductor quantum wells. We quantify the anisotropy of the effective masses and determine universal tightbinding parameters, which provide an accurate description of the electronic structure for all thicknesses.
2023
 Expansion of the Materials Cloud 2D Database
[Articolo su rivista]
Campi, D.; Mounet, N.; Gibertini, M.; Pizzi, G.; Marzari, N.
abstract
Twodimensional (2D) materials are among the most promising candidates for beyondsilicon electronic, optoelectronic, and quantum computing applications. Recently, their recognized importance sparked a push to discover and characterize novel 2D materials. Within a few years, the number of experimentally exfoliated or synthesized 2D materials went from a few to more than a hundred, with the number of theoretically predicted compounds reaching a few thousand. In 2018 we first contributed to this effort with the identification of 1825 compounds that are either easily (1036) or potentially (789) exfoliable from experimentally known 3D compounds. Here, we report on a major expansion of this 2D portfolio thanks to the extension of the screening protocol to an additional experimental database (MPDS) as well as the updated versions of the two databases (ICSD and COD) used in our previous work. This expansion leads to the discovery of an additional 1252 monolayers, bringing the total to 3077 compounds and, notably, almost doubling the number of easily exfoliable materials to 2004. We optimize the structural properties of all these monolayers and explore their electronic structure with a particular emphasis on those rare largebandgap 2D materials that could be precious in isolating 2D fieldeffecttransistor channels. Finally, for each material containing up to 6 atoms per unit cell, we identify the best candidates to form commensurate heterostructures, balancing requirements on supercell size and minimal strain.
2023
 GateControlled Magnetotransport and Electrostatic Modulation of Magnetism in 2D Magnetic Semiconductor CrPS4
[Articolo su rivista]
Wu, F.; Gibertini, M.; Watanabe, K.; Taniguchi, T.; GutierrezLezama, I.; Ubrig, N.; Morpurgo, A. F.
abstract
Using fieldeffect transistors (FETs) to explore atomically thin magnetic semiconductors with transport measurements is difficult, because the very narrow bands of most 2D magnetic semiconductors cause carrier localization, preventing transistor operation. Here, it is shown that exfoliated layers of CrPS4—a 2D layered antiferromagnetic semiconductor whose bandwidth approaches 1 eV—allow the realization of FETs that operate properly down to cryogenic temperature. Using these devices, conductance measurements as a function of temperature and magnetic field are performed to determine the full magnetic phase diagram, which includes a spinflop and a spinflip phase. The magnetoconductance, which depends strongly on gate voltage, is determined. reaching values as high as 5000% near the threshold for electron conduction. The gate voltage also allows the magnetic states to be tuned, despite the relatively large thickness of the CrPS4 multilayers employed in the study. The results show the need to employ 2D magnetic semiconductors with sufficiently large bandwidth to realize properly functioning transistors, and identify a candidate material to realize a fully gatetunable halfmetallic conductor.
2023
 Longrange electrostatic contribution to electronphonon couplings and mobilities of twodimensional and bulk materials
[Articolo su rivista]
Ponce, S; Royo, M; Stengel, M; Marzari, N; Gibertini, M
abstract
Charge transport plays a crucial role in manifold potential applications of twodimensional materials, including fieldeffect transistors, solar cells, and transparent conductors. At most operating temperatures, charge transport is hindered by scattering of carriers by lattice vibrations. Assessing the intrinsic phononlimited carrier mobility is thus of paramount importance to identify promising candidates for nextgeneration devices. Here we provide a framework to efficiently compute the drift and Hall carrier mobility of twodimensional materials through the Boltzmann transport equation by relying on a FourierWannier interpolation. Building on a recent formulation of longrange contributions to dynamical matrices and phonon dispersions [Phys. Rev. X 11, 041027 (2021)], we extend the approach to electronphonon coupling including the effect of dynamical dipoles and quadrupoles. We identify an unprecedented contribution associated with the Berry connection that is crucial to preserve the Wanniergauge covariance of the theory. This contribution is not specific to twodimensional crystals, but also concerns the threedimensional case, as we demonstrate via an application to bulk SrO. We showcase our method on a wide selection of relevant monolayers ranging from SnS2 to MoS2, graphene, BN, InSe, and phosphorene. We also discover a nontrivial temperature evolution of the Hall hole mobility in InSe whereby the mobility increases with temperature above 150 K due to the Mexicanhat electronic structure of the InSe valence bands. Overall, we find that dynamical quadrupoles are essential and can impact the carrier mobility in excess of 75%.
2023
 MagnetismInduced BandEdge Shift as the Mechanism for Magnetoconductance in CrPS4 Transistors
[Articolo su rivista]
Wu, F.; Gibertini, M.; Watanabe, K.; Taniguchi, T.; GutierrezLezama, I.; Ubrig, N.; Morpurgo, A. F.
abstract
Transistors realized on the 2D antiferromagnetic semiconductor CrPS4 exhibit large magnetoconductance due to magneticfieldinduced changes in the magnetic state. The microscopic mechanism coupling the conductance and magnetic state is not understood. We identify it by analyzing the evolution of the parameters determining the transistor behavior─carrier mobility and threshold voltage─with temperature and magnetic field. For temperatures T near the Néel temperature TN, the magnetoconductance originates from a mobility increase due to the applied magnetic field that reduces spin fluctuation induced disorder. For T ≪ TN, instead, what changes is the threshold voltage, so that increasing the field at fixed gate voltage increases the density of accumulated electrons. The phenomenon is explained by a conduction bandedge shift correctly predicted by the ab initio calculations. Our results demonstrate that the band structure of CrPS4 depends on its magnetic state and reveal a mechanism for magnetoconductance that had not been identified earlier.
2023
 Multiple antiferromagnetic phases and magnetic anisotropy in exfoliated CrBr3 multilayers
[Articolo su rivista]
Yao, F.; Multian, V.; Wang, Z.; Ubrig, N.; Teyssier, J.; Wu, F.; Giannini, E.; Gibertini, M.; GutierrezLezama, I.; Morpurgo, A. F.
abstract
In twisted twodimensional (2D) magnets, the stacking dependence of the magnetic exchange interaction can lead to regions of ferromagnetic and antiferromagnetic interlayer order, separated by noncollinear, skyrmionlike spin textures. Recent experimental searches for these textures have focused on CrI3, known to exhibit either ferromagnetic or antiferromagnetic interlayer order, depending on layer stacking. However, the very strong uniaxial anisotropy of CrI3 disfavors smooth noncollinear phases in twisted bilayers. Here, we report the experimental observation of three distinct magnetic phases—one ferromagnetic and two antiferromagnetic—in exfoliated CrBr3 multilayers, and reveal that the uniaxial anisotropy is significantly smaller than in CrI3. These results are obtained by magnetoconductance measurements on CrBr3 tunnel barriers and Raman spectroscopy, in conjunction with density functional theory calculations, which enable us to identify the stackings responsible for the different interlayer magnetic couplings. The detection of all locally stable magnetic states predicted to exist in CrBr3 and the excellent agreement found between theory and experiments, provide complete information on the stackingdependent interlayer exchange energy and establish twisted bilayer CrBr3 as an ideal system to deterministically create noncollinear magnetic phases.
2022
 Quasi1D Electronic Transport in a 2D Magnetic Semiconductor
[Articolo su rivista]
Wu, F.; GutierrezLezama, I.; LopezPaz, S. A.; Gibertini, M.; Watanabe, K.; Taniguchi, T.; von Rohr, F. O.; Ubrig, N.; Morpurgo, A. F.
abstract
Electronic transport through exfoliated multilayers of CrSBr, a 2D semiconductor of interest because of its magnetic properties, is investigated. An extremely pronounced anisotropy manifesting itself in qualitative and quantitative differences of all quantities measured along the inplane a and b crystallographic directions is found. In particular, a qualitatively different dependence of the conductivities σa and σb on temperature and gate voltage, accompanied by orders of magnitude differences in their values (σb/σa ≈ 3 × 102 to 105 at low temperature and negative gate voltage) are observed, together with a different behavior of the longitudinal magnetoresistance in the two directions and the complete absence of the Hall effect in transverse resistance measurements. These observations appear not to be compatible with a description in terms of conventional band transport of a 2D doped semiconductor. The observed phenomenology—and unambiguous signatures of a 1D van Hove singularity detected in energyresolved photocurrent measurements—indicate that electronic transport through CrSBr multilayers is better interpreted by considering the system as formed by weakly and incoherently coupled 1D wires, than by conventional 2D band transport. It is concluded that CrSBr is the first 2D semiconductor to show distinctly quasi1D electronic transport properties.
2022
 Quenching the bandgap of twodimensional semiconductors with a perpendicular electric field
[Articolo su rivista]
Domaretskiy, D.; Philippi, M.; Gibertini, M.; Ubrig, N.; GutierrezLezama, I.; Morpurgo, A. F.
abstract
Perpendicular electric fields can tune the electronic band structure of atomically thin semiconductors. In bilayer graphene, which is an intrinsic zerogap semiconductor, a perpendicular electric field opens a finite bandgap. So far, however, the same principle could not be applied to control the properties of a broader class of 2D materials because the required electric fields are beyond reach in current devices. To overcome this limitation, we design double ionic gated transistors that enable the application of large electric fields of up to 3 V nm−1. Using such devices, we continuously suppress the bandgap of fewlayer semiconducting transition metal dichalcogenides (that is, bilayer to heptalayer WSe2) from 1.6 V to zero. Our results illustrate an excellent level of control of the band structure of 2D semiconductors.
2022
 Twistresilient and robust ferroelectric quantum spin Hall insulators driven by van der Waals interactions
[Articolo su rivista]
Marrazzo, A.; Gibertini, M.
abstract
Quantum spin Hall insulators (QSHI) have been proposed to power several applications, many of which rely on the possibility to switch on and off the nontrivial topology. Typically this control is achieved through strain or electric fields, which require energy consumption to be maintained. On the contrary, a nonvolatile mechanism would be highly beneficial and could be realized through ferroelectricity if opposite polarization states are associated with different topological phases. While this is not possible in a single ferroelectric material where the two polarization states are related by inversion, the necessary asymmetry could be introduced by combining a ferroelectric layer with another twodimensional (2D) trivial insulator. Here, by means of firstprinciples simulations, not only we propose that this is a promising strategy to engineer nonvolatile ferroelectric control of topological order in 2D heterostructures, but also that the effect is robust and can survive up to room temperature, irrespective of the weak van der Waals coupling between the layers. We illustrate the general idea by considering a heterostructure made of a wellknown ferroelectric material, In2Se3, and a suitably chosen, easily exfoliable trivial insulator, CuI. In one polarization state the system is trivial, while it becomes a QSHI with a sizable band gap upon polarization reversal. Remarkably, the topological band gap is mediated by the interlayer hybridization and allows to maximize the effect of intralayer spinorbit coupling, promoting a robust ferroelectric topological phase that could not exist in monolayer materials and is resilient against relative orientation and lattice matching between the layers.
2021
 Gatetunable imbalanced KaneMele model in encapsulated bilayer jacutingaite
[Articolo su rivista]
Rademaker, L.; Gibertini, M.
abstract
We study free, capped, and encapsulated bilayer jacutingaite (Pt2HgSe3) from first principles. While the freestanding bilayer is a largegap trivial insulator, we find that the encapsulated structure has a small trivial gap due to the competition between sublattice symmetry breaking and sublatticedependent nextnearestneighbor hopping. Upon the application of a small perpendicular electric field, the encapsulated bilayer undergoes a topological transition towards a quantum spin Hall insulator. We find that this topological transition can be qualitatively understood by modeling the two layers as uncoupled and can be described by an imbalanced KaneMele model that takes into account the sublattice imbalance and the corresponding inversionsymmetry breaking in each layer. Within this picture, bilayer jacutingaite undergoes a transition from a 0+0 state, where each layer is trivial, to a 0+1 state, where an unusual topological state relying on Rashbalike spin orbit coupling emerges in only one of the layers.
2021
 Magnetism and stability of all primitive stacking patterns in bilayer chromium trihalides
[Articolo su rivista]
Gibertini, M.
abstract
Chromium trihalides, CrX3 (with X = Cl, Br, I), are a family of layered magnetic materials that can be easily exfoliated to provide ferromagnetic monolayers. When two layers are stacked together to form a bilayer the interlayer exchange coupling can be either ferromagnetic or antiferromagnetic depending on the stacking sequence. Here we combine crystallographic arguments based on the closepacking condition with firstprinciples simulations to enumerate all possible stacking patterns in CrX3 bilayers that preserve the spatial periodicity of each layer. We recover all configurations observed in bulk crystals and disclose stacking sequences with no bulk counterpart where the two layers have opposite chirality. Stacking sequences are ranked according to their relative stability and a preferential interlayer magnetic ordering is assigned to each of them. Simulations provide a consistent picture to frame all current experimental observations on bulk and exfoliated CrX3 crystals, with interesting implications for future measurements, including synthetic bilayers with nonstandard stacking patterns.
2021
 Magnetization dependent tunneling conductance of ferromagnetic barriers
[Articolo su rivista]
Wang, Z.; GutierrezLezama, I.; Dumcenco, D.; Ubrig, N.; Taniguchi, T.; Watanabe, K.; Giannini, E.; Gibertini, M.; Morpurgo, A. F.
abstract
Recent experiments on van der Waals antiferromagnets have shown that measuring the temperature (T) and magnetic field (H) dependence of the conductance allows their magnetic phase diagram to be mapped. Similarly, experiments on ferromagnetic CrBr3 barriers enabled the Curie temperature to be determined at H = 0, but a precise interpretation of the magnetoconductance data at H ≠ 0 is conceptually more complex, because at finite H there is no welldefined phase boundary. Here we perform systematic transport measurements on CrBr3 barriers and show that the tunneling magnetoconductance depends on H and T exclusively through the magnetization M(H, T) over the entire temperature range investigated. The phenomenon is reproduced by the spindependent Fowler–Nordheim model for tunneling, and is a direct manifestation of the spin splitting of the CrBr3 conduction band. Our analysis unveils a new approach to probe quantitatively different properties of atomically thin ferromagnetic insulators related to their magnetization by performing simple conductance measurements.
2021
 Remote freecarrier screening to boost the mobility of Fröhlichlimited twodimensional semiconductors
[Articolo su rivista]
Sohier, T.; Gibertini, M.; Verstraete, M. J.
abstract
Van der Waals heterostructures provide a versatile tool to not only protect or control, but also enhance the properties of a 2D material. We use ab initio calculations and semianalytical models to find strategies which boost the mobility of a currentcarrying twodimensional (2D) semiconductor within a heterostructure. Freecarrier screening from a metallic "screener"layer remotely suppresses electronphonon interactions in the currentcarrying layer. This concept is most effective in 2D semiconductors whose scattering is dominated by screenable electronphonon interactions, and in particular, the Fröhlich coupling to polaroptical phonons. Such materials are common and characterized by overall low mobilities in the small doping limit and much higher ones when the 2D material is doped enough for electronphonon interactions to be screened by its own free carriers. We use GaSe as a prototype and place it in a heterostructure with doped graphene as the "screener"layer and boron nitride as a separator. We develop an approach to determine the electrostatic response of any heterostructure by combining the responses of the individual layers computed within density functional perturbation theory. Remote screening from graphene can suppress the longwavelength Fröhlich interaction, leading to a consistently high mobility around 500600cm2/V s for carrier densities in GaSe from 1011 to 1013cm2. Notably, the lowdoping mobility is enhanced by a factor 2.5. This remote freecarrier screening is more efficient than more conventional manipulation of the dielectric environment, and it is most effective when the separator (boron nitride) is thin.
2021
 Shear and Breathing Modes of Layered Materials
[Articolo su rivista]
Pizzi, G.; Milana, S.; Ferrari, A. C.; Marzari, N.; Gibertini, M.
abstract
Layered materials (LMs), such as graphite, hexagonal boron nitride, and transitionmetal dichalcogenides, are at the center of an everincreasing research effort, due to their scientific and technological relevance. Raman and infrared spectroscopies are accurate, nondestructive approaches to determine a wide range of properties, including the number of layers, N, and the strength of the interlayer interactions. We present a general approach to predict the complete spectroscopic fan diagrams, i.e., the relations between frequencies and N for the optically active shear and layerbreathing modes of any multilayer comprising N ≥ 2 identical layers. In order to achieve this, we combine a description of the normal modes in terms of a onedimensional mechanical model, with symmetry arguments that describe the evolution of the point group as a function of N. Group theory is then used to identify which modes are Raman and/or infraredactive, and to provide diagrams of the optically active modes for any stack composed of identical layers. We implement the method and algorithms in an opensource tool to assist researchers in the prediction and interpretation of such diagrams. Our work will underpin future efforts on Raman and infrared characterization of known, and yet not investigated, LMs.
2020
 Bulk and Surface Electronic Structure of the DualTopology Semimetal Pt2HgSe3
[Articolo su rivista]
Cucchi, I.; Marrazzo, A.; Cappelli, E.; Ricco, S.; Bruno, F. Y.; Lisi, S.; Hoesch, M.; Kim, T. K.; Cacho, C.; Besnard, C.; Giannini, E.; Marzari, N.; Gibertini, M.; Baumberger, F.; Tamai, A.
abstract
We report highresolution angleresolved photoemission measurements on single crystals of Pt_{2}HgSe_{3} grown by highpressure synthesis. Our data reveal a gapped Dirac nodal line whose (001) projection separates the surface Brillouin zone in topological and trivial areas. In the nontrivial kspace range, we find surface states with multiple saddle points in the dispersion, resulting in two van Hove singularities in the surface density of states. Based on densityfunctional theory calculations, we identify these surface states as signatures of a topological crystalline state, which coexists with a weak topological phase.
2020
 Emergent dual topology in the threedimensional KaneMele Pt2HgSe3
[Articolo su rivista]
Marrazzo, Antimo; Marzari, Nicola; Gibertini, Marco
abstract
Recently, the very first largegap KaneMele quantum spin Hall insulator was predicted to be monolayer jacutingaite (Pt2HgSe3), a naturally occurring exfoliable mineral discovered in Brazil in 2008. The stacking of quantum spin Hall monolayers into a vanderWaals layered crystal typically leads to a (0;001) weak topological phase, which does not protect the existence of surface states on the (001) surface. Unexpectedly, recent angleresolved photoemission spectroscopy experiments revealed the presence of surface states dispersing over large areas of the 001surface Brillouin zone of jacutingaite single crystals. The 001surface states have been shown to be topologically protected by a mirror Chern number CM = 2, associated with a nodal line gapped by spinorbit interactions. Here, we extend the twodimensional KaneMele model to bulk jacutingaite and unveil the microscopic origin of the gapped nodal line and the emerging crystalline topological order. By using maximally localized Wannier functions, we identify a large nontrivial second nearestlayer hopping term that breaks the standard paradigm of weak topological insulators. Complemented by this term, the predictions of the KaneMele model are in remarkable agreement with recent experiments and firstprinciples simulations, providing an appealing conceptual framework also relevant for other layered materials made of stacked honeycomb lattices.
2020
 Intrinsic edge excitons in twodimensional MoS2
[Articolo su rivista]
D'Amico, P.; Gibertini, M.; Prezzi, D.; Varsano, D.; Ferretti, A.; Marzari, N.; Molinari, E.
abstract
Using accurate firstprinciples calculations based on manybody perturbation theory, we predict that twodimensional MoS2 hosts edge excitons with universal character, intrinsic to the existence of edges and lying well below the onset of bulk features. These excitons are largely insensitive to edge terminations or orientation, persisting even in the presence of metallic screening at zigzag edges, with large binding energies of ∼0.4 eV. Additional excitons can also emerge in ultranarrow ribbons or as a function of the chemical nature of the termination. The chemical, structural, and electronic similarities with Se or Wbased transitionmetal dichalcogenides suggest that these optical features could be common in this class of materials.
2020
 Lowtemperature monoclinic layer stacking in atomically thin CrI3 crystals
[Articolo su rivista]
Ubrig, N.; Wang, Z.; Teyssier, J.; Taniguchi, T.; Watanabe, K.; Giannini, E.; Morpurgo, A. F.; Gibertini, M.
abstract
Chromium triiodide, CrI3, is emerging as a promising magnetic twodimensional semiconductor where spins are ferromagnetically aligned within a single layer. Potential applications in spintronics arise from an antiferromagnetic ordering between adjacent layers that gives rise to spin filtering and a large magnetoresistance in tunnelling devices. This key feature appears only in thin multilayers and it is not inherited from bulk crystals, where instead neighbouring layers share the same ferromagnetic spin orientation. This discrepancy between bulk and thin samples is unexpected, as magnetic ordering between layers arises from exchange interactions that are local in nature and should not depend strongly on thickness. Here we solve this controversy and show through polarization resolved Raman spectroscopy that thin multilayers do not undergo a structural phase transition typical of bulk crystals. As a consequence, a different stacking pattern is present in thin and bulk samples at the temperatures at which magnetism sets in and, according to previous firstprinciples simulations, this results in a different interlayer magnetic ordering. Our experimental findings provide evidence for the strong interplay between stacking order and magnetism in CrI3, opening interesting perspectives to design the magnetic state of van der Waals multilayers.
2020
 Multifrequency Shubnikovde Haas oscillations in topological semimetal Pt2HgSe3
[Articolo su rivista]
Mauro, D.; Henck, H.; Gibertini, M.; Filippone, M.; Giannini, E.; GutierrezLezama, I.; F Morpurgo, A.
abstract
Monolayer jacutingaite (Pt2HgSe3) has been recently identified as a candidate quantum spin Hall system with a 0.5 eV band gap, but no transport measurements have been performed so far on this material, neither in monolayer nor in the bulk. By using a dedicated highpressure technique, we grow crystals enabling the exfoliation of 50100 nm thick layers and the realization of devices for controlled transport experiments. Magnetoresistance measurements indicate that jacutingaite is a semimetal, exhibiting Shubnikovde Haas (SdH) resistance oscillations with a multifrequency spectrum. We adapt the LifshitzKosevich formula to analyze quantitatively the SdH resistance oscillations in the presence of multiple frequencies, and find that the experimental observations are overall reproduced well by band structure abinitio calculations for bulk jacutingaite. Together with the relatively high electron mobility extracted from the experiments (≈ 2000 cm2/V1s1, comparable to what is observed in WTe2 crystals of the same thickness), our results indicate that monolayer jacutingaite should provide an excellent platform to investigate transport in 2D quantum spin Hall systems.
2020
 Persistence of Magnetism in Atomically Thin MnPS3 Crystals
[Articolo su rivista]
Long, G.; Henck, H.; Gibertini, M.; Dumcenco, D.; Wang, Z.; Taniguchi, T.; Watanabe, K.; Giannini, E.; Morpurgo, A. F.
abstract
The magnetic state of atomically thin semiconducting layered antiferromagnets such as CrI3 and CrCl3 can be probed by forming tunnel barriers and measuring their resistance as a function of magnetic field (H) and temperature (T). This is possible because the spins within each individual layer are ferromagnetically aligned and the tunneling magnetoresistance depends on the relative orientation of the magnetization in adjacent layers. The situation is different for systems that are antiferromagnetic within the layers in which case it is unclear whether magnetoresistance measurements can provide information about the magnetic state. Here, we address this issue by investigating tunnel transport through atomically thin crystals of MnPS3, a van der Waals semiconductor that in the bulk exhibits easyaxis antiferromagnetic order within the layers. For thick multilayers below T ∼78 K, a Tdependent magnetoresistance sets in at μ0H ∼5 T and is found to track the boundary between the antiferromagnetic and the spinflop phases known from bulk measurements. We show that the magnetoresistance persists as thickness is reduced with nearly unchanged characteristic temperature and magnetic field scales, albeit with a different dependence on H, indicating the persistence of magnetism in the ultimate limit of individual monolayers.
2020
 Production and processing of graphene and related materials
[Articolo su rivista]
Backes, C.; Abdelkader, A. M.; Alonso, C.; AndrieuxLedier, A.; Arenal, R.; Azpeitia, J.; Balakrishnan, N.; Banszerus, L.; Barjon, J.; Bartali, R.; Bellani, S.; Berger, C.; Berger, R.; Ortega, M. M. B.; Bernard, C.; Beton, P. H.; Beyer, A.; Bianco, A.; Boggild, P.; Bonaccorso, F.; Barin, G. B.; Botas, C.; Bueno, R. A.; Carriazo, D.; CastellanosGomez, A.; Christian, M.; Ciesielski, A.; Ciuk, T.; Cole, M. T.; Coleman, J.; Coletti, C.; Crema, L.; Cun, H.; Dasler, D.; De Fazio, D.; Diez, N.; Drieschner, S.; Duesberg, G. S.; Fasel, R.; Feng, X.; Fina, A.; Forti, S.; Galiotis, C.; Garberoglio, G.; Garcia, J. M.; Garrido, J. A.; Gibertini, M.; Golzhauser, A.; Gomez, J.; Greber, T.; Hauke, F.; Hemmi, A.; HernandezRodriguez, I.; Hirsch, A.; Hodge, S. A.; Huttel, Y.; Jepsen, P. U.; Jimenez, I.; Kaiser, U.; Kaplas, T.; Kim, H.; Kis, A.; Papagelis, K.; Kostarelos, K.; Krajewska, A.; Lee, K.; Li, C.; Lipsanen, H.; Liscio, A.; Lohe, M. R.; Loiseau, A.; Lombardi, L.; Lopez, M. F.; Martin, O.; Martin, C.; Martinez, L.; MartinGago, J. A.; Martinez, J. I.; Marzari, N.; Mayoral, A.; Mcmanus, J.; Melucci, M.; Mendez, J.; Merino, C.; Merino, P.; Meyer, A. P.; Miniussi, E.; Miseikis, V.; Mishra, N.; Morandi, V.; Munuera, C.; Munoz, R.; Nolan, H.; Ortolani, L.; Ott, A. K.; Palacio, I.; Palermo, V.; Parthenios, J.; Pasternak, I.; Patane, A.; Prato, M.; Prevost, H.; Prudkovskiy, V.; Pugno, N.; Rojo, T.; Rossi, A.; Ruffieux, P.; Samori, P.; Schue, L.; Setijadi, E.; Seyller, T.; Speranza, G.; Stampfer, C.; Stenger, I.; Strupinski, W.; Svirko, Y.; Taioli, S.; Teo, K. B. K.; Testi, M.; Tomarchio, F.; Tortello, M.; Treossi, E.; Turchanin, A.; Vazquez, E.; Villaro, E.; Whelan, P. R.; Xia, Z.; Yakimova, R.; Yang, S.; Yazdi, G. R.; Yim, C.; Yoon, D.; Zhang, X.; Zhuang, X.; Colombo, L.; Ferrari, A. C.; GarciaHernandez, M.
abstract
We present an overview of the main techniques for production and processing of graphene and related materials (GRMs), as well as the key characterization procedures. We adopt a 'handson' approach, providing practical details and procedures as derived from literature as well as from the authors' experience, in order to enable the reader to reproduce the results. Section I is devoted to 'bottom up' approaches, whereby individual constituents are pieced together into more complex structures. We consider graphene nanoribbons (GNRs) produced either by solution processing or by onsurface synthesis in ultra high vacuum (UHV), as well carbon nanomembranes (CNM). Production of a variety of GNRs with tailored band gaps and edge shapes is now possible. CNMs can be tuned in terms of porosity, crystallinity and electronic behaviour. Section II covers 'top down' techniques. These rely on breaking down of a layered precursor, in the graphene case usually natural crystals like graphite or artificially synthesized materials, such as highly oriented pyrolythic graphite, monolayers or few layers (FL) flakes. The main focus of this section is on various exfoliation techniques in a liquid media, either intercalation or liquid phase exfoliation (LPE). The choice of precursor, exfoliation method, medium as well as the control of parameters such as time or temperature are crucial. A definite choice of parameters and conditions yields a particular material with specific properties that makes it more suitable for a targeted application. We cover protocols for the graphitic precursors to graphene oxide (GO). This is an important material for a range of applications in biomedicine, energy storage, nanocomposites, etc. Hummers' and modified Hummers' methods are used to make GO that subsequently can be reduced to obtain reduced graphene oxide (RGO) with a variety of strategies. GO flakes are also employed to prepare threedimensional (3d) low density structures, such as sponges, foams, hydro or aerogels. The assembly of flakes into 3d structures can provide improved mechanical properties. Aerogels with a highly open structure, with interconnected hierarchical pores, can enhance the accessibility to the whole surface area, as relevant for a number of applications, such as energy storage. The main recipes to yield graphite intercalation compounds (GICs) are also discussed. GICs are suitable precursors for covalent functionalization of graphene, but can also be used for the synthesis of uncharged graphene in solution. Degradation of the molecules intercalated in GICs can be triggered by high temperature treatment or microwave irradiation, creating a gas pressure surge in graphite and exfoliation. Electrochemical exfoliation by applying a voltage in an electrolyte to a graphite electrode can be tuned by varying precursors, electrolytes and potential. Graphite electrodes can be either negatively or positively intercalated to obtain GICs that are subsequently exfoliated. We also discuss the materials that can be amenable to exfoliation, by employing a theoretical datamining approach. The exfoliation of LMs usually results in a heterogeneous dispersion of flakes with different lateral size and thickness. This is a critical bottleneck for applications, and hinders the full exploitation of GRMs produced by solution processing. The establishment of procedures to control the morphological properties of exfoliated GRMs, which also need to be industrially scalable, is one of the key needs. Section III deals with the processing of flakes. (Ultra)centrifugation techniques have thus far been the most investigated to sort GRMs following ultrasonication, shear mixing, ball milling, microfluidization, and wetjet milling. It allows sorting by size and thickness. Inks formulated from GRM dispersions can be printed using a number of processes, from inkjet to screen printing. Each technique has specific rheological requirements, as well as geometrical constraints. The solve
2020
 Profiling novel highconductivity 2D semiconductors
[Articolo su rivista]
Sohier, T.; Gibertini, M.; Marzari, N.
abstract
When complex mechanisms are involved, pinpointing highperformance materials within large databases is a major challenge in materials discovery. We focus here on phononlimited conductivities, and study 2D semiconductors doped by field effects. Using stateoftheart densityfunctional perturbation theory and Boltzmann transport equation, we discuss 11 monolayers with outstanding transport properties. These materials are selected from a computational database of exfoliable materials providing monolayers that are dynamically stable and that do not have more than six atoms per unit cell. We first analyze electronphonon scattering in two wellknown systems: electrondoped InSe and holedoped phosphorene. Both are singlevalley systems with weak electronphonon interactions, but they represent two distinct pathways to fast transport: a steep and deep isotropic valley for the former and strongly anisotropic electronphonon physics for the latter. We identify similar features in the database and compute the conductivities of the relevant monolayers. This process yields several highconductivity materials, some of them only very recently emerging in the literature (GaSe, Bi2SeTe2, Bi2Se3, Sb2SeTe2), others never discussed in this context (AlLiTe2, BiClTe, ClGaTe, AuI). Comparing these 11 monolayers in detail, we discuss how the strength and angular dependency of the electronphonon scattering drives key differences in the transport performance of materials despite similar valley structure. We also discuss the high conductivity of holedoped WSe2, and how this case study shows the limitations of a selection process that would be based on band properties alone.
2020
 Wannier90 as a community code: New features and applications
[Articolo su rivista]
Pizzi, G.; Vitale, V.; Arita, R.; Blugel, S.; Freimuth, F.; Geranton, G.; Gibertini, M.; Gresch, D.; Johnson, C.; Koretsune, T.; IbañezAzpiroz, J.; Lee, H.; Lihm, J. M.; Marchand, D.; Marrazzo, A.; Mokrousov, Y.; Mustafa, J. I.; Nohara, Y.; Nomura, Y.; Paulatto, L.; Ponce, S.; Ponweiser, T.; Qiao, J.; Thole, F.; Tsirkin, S. S.; Wierzbowska, M.; Marzari, N.; Vanderbilt, D.; Souza, I.; Mostofi, A. A.; Yates, J. R.
abstract
Wannier90 is an opensource computer program for calculating maximallylocalised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronicstructure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a communitydriven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetryadapted Wannier functions, selectivelylocalised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berrycurvature dipole, and a new interface to manybody perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinorvalued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with highthroughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic sourcecode documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.
2019
 Determining the phase diagram of atomically thin layered antiferromagnet CrCl3
[Articolo su rivista]
Wang, Z.; Gibertini, M.; Dumcenco, D.; Taniguchi, T.; Watanabe, K.; Giannini, E.; Morpurgo, A. F.
abstract
Changes in the spin configuration of atomically thin, magnetic van der Waals multilayers can cause drastic modifications in their optoelectronic properties. Conversely, the optoelectronic response of these systems provides information about the magnetic state, which is very difficult to obtain otherwise. Here, we show that in CrCl3 multilayers, the dependence of the tunnelling conductance on applied magnetic field, temperature and number of layers tracks the evolution of the magnetic state, enabling the magnetic phase diagram to be determined experimentally. Besides a highfield spinflip transition occurring for all thicknesses, the inplane magnetoconductance exhibits an even–odd effect due to a lowfield spinflop transition. Through a quantitative analysis of the phenomena, we determine the interlayer exchange coupling as well as the layer magnetization and show that in CrCl3 shape anisotropy dominates. Our results reveal the rich behaviour of atomically thin layered antiferromagnets with weak magnetic anisotropy.
2019
 Enhanced ElectronPhonon Interaction in Multivalley Materials
[Articolo su rivista]
Sohier, T.; Ponomarev, E.; Gibertini, M.; Berger, H.; Marzari, N.; Ubrig, N.; Morpurgo, A. F.
abstract
We report a combined experimental and theoretical investigation that reveals a new mechanism responsible for the enhancement of electronphonon coupling in doped semiconductors in which multiple inequivalent valleys are simultaneously populated. Using Raman spectroscopy on ionicliquidgated monolayer and bilayer MoS2, WS2, and WSe2 over a wide range of electron and hole densities, we find that phonons with a dominant outofplane character exhibit strong softening upon electron accumulation while remaining unaffected upon hole doping. This unexpectedbut very pronouncedelectronhole asymmetry is systematically observed in all monolayers and bilayers. By performing firstprinciples simulations, we show that the phonon softening occurs when multiple inequivalent valleys are populated simultaneously. Accordingly, the observed electronhole asymmetry originates from the much larger energy separation between valleys in the valence bandsas compared to the conduction bandthat prevents the population of multiple valleys upon hole accumulation. We infer that the enhancement of the electronphonon coupling occurs because the population of multiple valleys acts to strongly reduce the efficiency of electrostatic screening for those phonon modes that cause the energy of the inequivalent valleys to oscillate out of phase. This robust mechanism is likely to play an important role in several physical phenomena, possibly including the occurrence of superconductivity in different transition metal dichalcogenides.
2019
 Magnetic 2D materials and heterostructures
[Articolo su rivista]
Gibertini, M.; Koperski, M.; Morpurgo, A. F.; Novoselov, K. S.
abstract
The family of twodimensional (2D) materials grows day by day, hugely expanding the scope of possible phenomena to be explored in two dimensions, as well as the possible van der Waals (vdW) heterostructures that one can create. Such 2D materials currently cover a vast range of properties. Until recently, this family has been missing one crucial member: 2D magnets. The situation has changed over the past 2 years with the introduction of a variety of atomically thin magnetic crystals. Here we will discuss the difference between magnetic states in 2D materials and in bulk crystals and present an overview of the 2D magnets that have been explored recently. We will focus on the case of the two most studied systems—semiconducting CrI 3 and metallic Fe 3 GeTe 2 —and illustrate the physical phenomena that have been observed. Special attention will be given to the range of new van der Waals heterostructures that became possible with the appearance of 2D magnets, offering new perspectives in this rapidly expanding field.
2019
 Microfocus LaserAngleResolved Photoemission on Encapsulated Mono, Bi, and FewLayer 1T′WTe 2
[Articolo su rivista]
Cucchi, I.; GutierrezLezama, I.; Cappelli, E.; Walker, S. M.; Bruno, F. Y.; Tenasini, G.; Wang, L.; Ubrig, N.; Barreteau, C.; Giannini, E.; Gibertini, M.; Tamai, A.; Morpurgo, A. F.; Baumberger, F.
abstract
Twodimensional crystals of semimetallic van der Waals materials hold much potential for the realization of novel phases, as exemplified by the recent discoveries of a polar metal in fewlayer 1T′WTe 2 and of a quantum spin Hall state in monolayers of the same material. Understanding these phases is particularly challenging because little is known from experiments about the momentum space electronic structure of ultrathin crystals. Here, we report direct electronic structure measurements of exfoliated mono, bi, and fewlayer 1T′WTe 2 by laserbased microfocus angleresolved photoemission. This is achieved by encapsulating with monolayer graphene a flake of WTe 2 comprising regions of different thickness. Our data support the recent identification of a quantum spin Hall state in monolayer 1T′WTe 2 and reveal strong signatures of the broken inversion symmetry in the bilayer. We finally discuss the sensitivity of encapsulated samples to contaminants following exposure to ambient atmosphere.
2019
 Probing magnetism in 2D materials at the nanoscale with singlespin microscopy
[Articolo su rivista]
Thiel, L.; Wang, Z.; Tschudin, M. A.; Rohner, D.; GutierrezLezama, I.; Ubrig, N.; Gibertini, M.; Giannini, E.; Morpurgo, A. F.; Maletinsky, P.
abstract
The discovery of ferromagnetism in twodimensional (2D) van der Waals (vdW) crystals has generated widespread interest. Making further progress in this area requires quantitative knowledge of the magnetic properties of vdWmagnets at the nanoscale.We used scanning singlespin magnetometry based on diamond nitrogenvacancy centers to image the magnetization, localized defects, and magnetic domains of atomically thin crystals of the vdW magnet chromium(III) iodide (CrI3).We determined themagnetization of CrI3 monolayers to be ∼16 Bohr magnetons per square nanometer, with comparable values in samples with odd numbers of layers; however, the magnetization vanishes when the number of layers is even.We also found that structural modifications can induce switching between ferromagnetic and antiferromagnetic interlayer ordering.These results demonstrate the benefit of using singlespin scanning magnetometry to study the magnetism of 2D vdW magnets.
2019
 Relative Abundance of Z2 Topological Order in Exfoliable TwoDimensional Insulators
[Articolo su rivista]
Marrazzo, A.; Gibertini, M.; Campi, D.; Mounet, N.; Marzari, N.
abstract
Quantum spin Hall insulators make up a class of twodimensional materials with a finite electronic band gap in the bulk and gapless helical edge states. In the presence of timereversal symmetry, Z2 topological order distinguishes the topological phase from the ordinary insulating one. Some of the phenomena that can be hosted in these materials, from onedimensional lowdissipation electronic transport to spin filtering, could be promising for many technological applications in the fields of electronics, spintronics, and topological quantum computing. Nevertheless, the rarity of twodimensional materials that can exhibit nontrivial Z2 topological order at room temperature hinders development. Here, we screen a comprehensive database we recently identified of 1825 monolayers that can be exfoliated from experimentally known compounds to search for novel quantum spin Hall insulators. Using densityfunctional and manybody perturbation theory simulations, we identify 13 monolayers that are candidates for quantum spin Hall insulators including highperforming materials such as AsCuLi2 and (platinum) jacutingaite (Pt2HgSe3). We also identify monolayer Pd2HgSe3 (palladium jacutingaite) as a novel KaneMele quantum spin Hall insulator and compare it with platinum jacutingaite. A handful of promising materials are mechanically stable and exhibit Z2 topological order, either unperturbed or driven by small amounts of strain. Such screening highlights a relative abundance of Z2 topological order of around 1% and provides an optimal set of candidates for experimental efforts.
2019
 ValleyEngineering Mobilities in TwoDimensional Materials
[Articolo su rivista]
Sohier, T.; Gibertini, M.; Campi, D.; Pizzi, G.; Marzari, N.
abstract
Twodimensional materials are emerging as a promising platform for ultrathin channels in fieldeffect transistors. To this aim, novel highmobility semiconductors need to be found or engineered. Although extrinsic mechanisms can in general be minimized by improving fabrication processes, the suppression of intrinsic scattering (driven, for example, by electronphonon interactions) requires modification of the electronic or vibrational properties of the material. Because intervalley scattering critically affects mobilities, a powerful approach to enhance transport performance relies on engineering the valley structure. We show here the power of this strategy using uniaxial strain to lift degeneracies and suppress scattering into entire valleys, dramatically improving performance. This is shown in detail for arsenene, where a 2% strain stops scattering into four of the six valleys and leads to a 600% increase in mobility. The mechanism is general and can be applied to many other materials, including in particular the isostructural antimonene and blue phosphorene.
2018
 Mobility of twodimensional materials from first principles in an accurate and automated framework
[Articolo su rivista]
Sohier, T.; Campi, D.; Marzari, N.; Gibertini, M.
abstract
We present a firstprinciples approach to compute the transport properties of 2D materials in an accurate and automated framework. We use densityfunctional perturbation theory in the appropriate bidimensional setup with openboundary conditions in the third direction. The materials are charged by field effect via planar countercharges. In this approach, we obtain electronphonon matrix elements in which dimensionality and doping effects are inherently accounted for, without the need for postprocessing corrections. This treatment highlights some unexpected consequences, such as an increase of electronphonon coupling with doping in transitionmetal dichalcogenides. We use symmetries extensively and identify pockets of relevant electronic states to minimize the number of electronphonon interactions to compute; the integrodifferential Boltzmann transport equation is then linearized and solved beyond the relaxationtime approximation. We apply the entire protocol to a set of much studied materials with diverse electronic and vibrational band structures: electrondoped MoS2,WS2,WSe2, phosphorene, arsenene, and holedoped phosphorene. Among these, holedoped phosphorene is found to have the highest mobility, with a room temperature value around 600cm2V1s1. Last, we identify the factors that affect most phononlimited mobilities, such as the number and the anisotropy of electron and hole pockets, to provide a broader understanding of the driving forces behind high mobilities in twodimensional materials.
2018
 Prediction of a LargeGap and Switchable KaneMele Quantum Spin Hall Insulator
[Articolo su rivista]
Marrazzo, A.; Gibertini, M.; Campi, D.; Mounet, N.; Marzari, N.
abstract
Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically nontrivial phase, especially in two dimensions. Here, by means of extensive firstprinciples calculations, we propose a novel quantum spin Hall insulator with a sizable band gap of ∼0.5 eV that is a monolayer of jacutingaite, a naturally occurring layered mineral first discovered in 2008 in Brazil and recently synthesized. This system realizes the paradigmatic KaneMele model for quantum spin Hall insulators in a potentially exfoliable twodimensional monolayer, with helical edge states that are robust and that can be manipulated exploiting a unique strong interplay between spinorbit coupling, crystalsymmetry breaking, and dielectric response.
2018
 Twodimensional materials from highthroughput computational exfoliation of experimentally known compounds
[Articolo su rivista]
Mounet, N.; Gibertini, M.; Schwaller, P.; Campi, D.; Merkys, A.; Marrazzo, A.; Sohier, T.; Castelli, I. E.; Cepellotti, A.; Pizzi, G.; Marzari, N.
abstract
Twodimensional (2D) materials have emerged as promising candidates for nextgeneration electronic and optoelectronic applications. Yet, only a few dozen 2D materials have been successfully synthesized or exfoliated. Here, we search for 2D materials that can be easily exfoliated from their parent compounds. Starting from 108,423 unique, experimentally known 3D compounds, we identify a subset of 5,619 compounds that appear layered according to robust geometric and bonding criteria. Highthroughput calculations using van der Waals density functional theory, validated against experimental structural data and calculated random phase approximation binding energies, further allowed the identification of 1,825 compounds that are either easily or potentially exfoliable. In particular, the subset of 1,036 easily exfoliable cases provides novel structural prototypes and simple ternary compounds as well as a large portfolio of materials to search from for optimal properties. For a subset of 258 compounds, we explore vibrational, electronic, magnetic and topological properties, identifying 56 ferromagnetic and antiferromagnetic systems, including halfmetals and halfsemiconductors.
2018
 Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3
[Articolo su rivista]
Wang, Z.; GutierrezLezama, I.; Ubrig, N.; Kroner, M.; Gibertini, M.; Taniguchi, T.; Watanabe, K.; Imamoglu, A.; Giannini, E.; Morpurgo, A. F.
abstract
Magnetic layered van der Waals crystals are an emerging class of materials giving access to new physical phenomena, as illustrated by the recent observation of 2D ferromagnetism in Cr2Ge2Te6 and CrI3. Of particular interest in semiconductors is the interplay between magnetism and transport, which has remained unexplored. Here we report magnetotransport measurements on exfoliated CrI3 crystals. We find that tunneling conduction in the direction perpendicular to the crystalline planes exhibits a magnetoresistance as large as 10,000%. The evolution of the magnetoresistance with magnetic field and temperature reveals that the phenomenon originates from multiple transitions to different magnetic states, whose possible microscopic nature is discussed on the basis of all existing experimental observations. This observed dependence of the conductance of a tunnel barrier on its magnetic state is a phenomenon that demonstrates the presence of a strong coupling between transport and magnetism in magnetic van der Waals semiconductors.
2017
 Breakdown of Optical Phonons' Splitting in TwoDimensional Materials
[Articolo su rivista]
Sohier, T.; Gibertini, M.; Calandra, M.; Mauri, F.; Marzari, N.
abstract
We investigate the longwavelength dispersion of longitudinal and transverse optical phonon modes in polar twodimensional materials, multilayers, and their heterostructures. Using analytical models and densityfunctional perturbation theory in a twodimensional framework, we show that at variance with the threedimensional case these modes are degenerate at the zone center but the macroscopic electric field associated with the longitudinaloptical modes gives rise to a finite slope at the zone center in their corresponding phonon dispersions. This slope increases linearly with the number of layers and it is determined solely by the Born effective charges of the material and the dielectric properties of the surrounding media. Screening from the environment can greatly reduce the slope splitting between the longitudinal and transverse optical modes and can be seen in the experimentally relevant case of boron nitridegraphene heterostructures. As the phonon momentum increases, the intrinsic screening properties of the twodimensional material dictate the transition to a momentumindependent splitting similar to that of threedimensional materials. These considerations are essential to understand electrical transport and optical coupling in twodimensional systems.
2017
 Straininduced polar discontinuities in twodimensional materials from combined firstprinciples and SchrödingerPoisson simulations
[Articolo su rivista]
Bussy, A.; Pizzi, G.; Gibertini, M.
abstract
The local application of mechanical stress in piezoelectric materials gives rise to boundaries across which the electric polarization changes. Polarization charges appear along such polar discontinuities and the ensuing electric fields drive a charge reconstruction with the accumulation of free carriers at the boundaries. This is particularly relevant for twodimensional materials that can sustain very large strains and display record piezoelectric responses. Here we show by firstprinciples simulations the emergence of onedimensional wires of free electrons and holes along strain interfaces, taking SnSe as a paradigmatic material. We complement this by developing a SchrödingerPoisson approach specifically designed for twodimensional materials that is able to reproduce the ab initio results and also to extend them to regimes of parameters and system sizes that would be unaffordable in firstprinciples calculations. This model allows us to assess the degree of tunability for the free charge in the wires coming from strain values and profiles, and to obtain the critical size at which the interfaces start to be metallic.
2016
 Performance of arsenene and antimonene doublegate MOSFETs from first principles
[Articolo su rivista]
Pizzi, G.; Gibertini, M.; Dib, E.; Marzari, N.; Iannaccone, G.; Fiori, G.
abstract
In the race towards highperformance ultrascaled devices, twodimensional materials offer an alternative paradigm thanks to their atomic thickness suppressing shortchannel effects. It is thus urgent to study the most promising candidates in realistic configurations, and here we present detailed multiscale simulations of fieldeffect transistors based on arsenene and antimonene monolayers as channels. The accuracy of firstprinciples approaches in describing electronic properties is combined with the efficiency of tightbinding Hamiltonians based on maximally localized Wannier functions to compute the transport properties of the devices. These simulations provide for the first time estimates on the upper limits for the electron and hole mobilities in the Takagi's approximation, including spinorbit and multivalley effects, and demonstrate that ultrascaled devices in the sub10nm scale show a performance that is compliant with industry requirements.
2015
 BandLike electron transport with recordhigh mobility in the TCNQ family
[Articolo su rivista]
Krupskaya, Y.; Gibertini, M.; Marzari, N.; Morpurgo, A. F.
abstract
The occurrence of extremely pronounced bandlike transport with very high electron mobility in fluorinated tetracyanoquinodimethane (F2TCNQ) singlecrystal fieldeffect transistors is discovered. This finding identifies the FxTCNQ family as a paradigm to investigate the fundamental aspects of electronic transport in organic crystals.
2015
 Emergence of OneDimensional Wires of Free Carriers in TransitionMetalDichalcogenide Nanostructures
[Articolo su rivista]
Gibertini, M.; Marzari, N.
abstract
We highlight the emergence of metallic states in twodimensional transitionmetaldichalcogenide nanostructuresnanoribbons, islands, and inversion domain boundariesas a widespread and universal phenomenon driven by the polar discontinuities occurring at their edges or boundaries. We show that such metallic states form onedimensional wires of electrons or holes, with a free charge density that increases with the system size, up to complete screening of the polarization charge, and can also be controlled by the specific edge or boundary configurations, e.g., through chemisorption of hydrogen or sulfur atoms at the edges. For triangular islands, local polar discontinuities occur even in the absence of a total dipole moment for the island and lead to an accumulation of free carriers close to the edges, providing a consistent explanation of previous experimental observations. To further stress the universal character of these mechanisms, we show that polar discontinuities give rise to metallic states also at inversion domain boundaries. These findings underscore the potential of engineering transitionmetaldichalcogenide nanostructures for manifold applications in nano and optoelectronics, spintronics, catalysis, and solarenergy harvesting.
2015
 Largearea epitaxial monolayer MoS2
[Articolo su rivista]
Dumcenco, D.; Ovchinnikov, D.; Marinov, K.; Lazic, P.; Gibertini, M.; Marzari, N.; Sanchez, O. L.; Kung, Y. C.; Krasnozhon, D.; Chen, M. W.; Bertolazzi, S.; Gillet, P.; Fontcuberta I Morral, A.; Radenovic, A.; Kis, A.
abstract
Twodimensional semiconductors such as MoS2 are an emerging material family with wideranging potential applications in electronics, optoelectronics, and energy harvesting. Largearea growth methods are needed to open the way to applications. Control over lattice orientation during growth remains a challenge. This is needed to minimize or even avoid the formation of grain boundaries, detrimental to electrical, optical, and mechanical properties of MoS2 and other 2D semiconductors. Here, we report on the growth of highquality monolayer MoS2 with control over lattice orientation. We show that the monolayer film is composed of coalescing single islands with limited numbers of lattice orientation due to an epitaxial growth mechanism. Optical absorbance spectra acquired over large areas show significant absorbance in the highenergy part of the spectrum, indicating that MoS2 could also be interesting for harvesting this region of the solar spectrum and fabrication of UVsensitive photodetectors. Even though the interaction between the growth substrate and MoS2 is strong enough to induce lattice alignment via van der Waals interaction, we can easily transfer the grown material and fabricate devices. Local potential mapping along channels in fieldeffect transistors shows that the singlecrystal MoS2 grains in our film are well connected, with interfaces that do not degrade the electrical conductivity. This is also confirmed by the relatively large and lengthindependent mobility in devices with a channel length reaching 80um.
2014
 Engineering polar discontinuities in honeycomb lattices
[Articolo su rivista]
Gibertini, M.; Pizzi, G.; Marzari, N.
abstract
Unprecedented and fascinating phenomena have been recently observed at oxide interfaces between centrosymmetric cubic materials, where polar discontinuities can give rise to polarization charges and electric fields that drive a metalinsulator transition and the appearance of a twodimensional electron gas. Lowerdimensional analogues are possible, and honeycomb lattices offer a fertile playground, thanks to their versatility and the extensive ongoing experimental efforts in graphene and related materials. Here we suggest different realistic pathways to engineer polar discontinuities in honeycomb lattices and support these suggestions with extensive firstprinciples calculations. Several approaches are discussed, based on (i) nanoribbons, where a polar discontinuity against the vacuum emerges, and (ii) functionalizations, where covalent ligands are used to engineer polar discontinuities by selective or total functionalization of the parent systems. All the cases considered have the potential to deliver innovative applications in ultrathin and flexible solarenergy devices and in micro and nanoelectronics.
2014
 Spinresolved optical conductivity of twodimensional groupVIB transitionmetal dichalcogenides
[Articolo su rivista]
Gibertini, M.; Pellegrino, F. M. D.; Marzari, N.; Polini, M.
abstract
We present an ab initio study of the spinresolved optical conductivity of twodimensional (2D) groupVIB transitionmetal dichalcogenides (TMDs). We carry out fully relativistic densityfunctionaltheory calculations combined with maximally localized Wannier functions to obtain band manifolds at extremely high resolutions and focus on the photoresponse of 2D TMDs to circularly polarized light in a wide frequency range. We present extensive numerical results for monolayer TMDs involving molybdenum and tungsten combined with sulfur and selenium. Our numerical approach allows us to locate with a high degree of accuracy the positions of the points in the Brillouin zone that are responsible for Van Hove singularities in the optical response. Surprisingly, some of the saddle points do not occur exactly along highsymmetry directions in the Brillouin zone, although they happen to be in their close proximity.
2013
 JosephsonMajorana cycle in topological singleelectron hybrid transistors
[Articolo su rivista]
Didier, N.; Gibertini, M.; Moghaddam, A. G.; Konig, J.; Fazio, R.
abstract
Charge transport through a small topological superconducting island in contact with a normal and a superconducting electrode occurs through a cycle that involves coherent oscillations of Cooper pairs and tunneling in/out the normal electrode through a Majorana bound state, the JosephsonMajorana cycle. We illustrate this mechanism by studying the currentvoltage characteristics of a superconductortopological superconductornormal metal singleelectron transistor. At low bias and temperature the JosephsonMajorana cycle is the dominant mechanism for transport. We discuss a threeterminal configuration where the nonlocal character of the Majorana bound states is emergent. © 2013 American Physical Society.
2013
 Topological pumping in classD superconducting wires
[Articolo su rivista]
Gibertini, M.; Fazio, R.; Polini, M.; Taddei, F.
abstract
We study adiabatic pumping at a normal metal/classD superconductor hybrid interface when superconductivity is induced through the proximity effect in a spinorbit coupled nanowire in the presence of a tilted Zeeman field. When the induced order parameter in the nanowire is nonuniform, the phase diagram has isolated trivial regions surrounded by topological ones. We show that in this case the pumped charge is quantized in units of the elementary charge e and has a topological nature. © 2013 American Physical Society.
2013
 Topological pumping in the onedimensional BoseHubbard model
[Articolo su rivista]
Rossini, D.; Gibertini, M.; Giovannetti, V.; Fazio, R.
abstract
By means of timedependent densitymatrix renormalizationgroup calculations, we study topological quantum pumping in a strongly interacting system. The system under consideration is described by the Hamiltonian of a onedimensional extended BoseHubbard model in the presence of a correlated hopping which breaks lattice inversion symmetry. This model has been predicted to support topological pumping. The pumped charge is quantized and of a topological nature. We provide a detailed analysis of the finitesize scaling behavior of the pumped charge and its deviations from the quantized value. Furthermore, we also analyze the nonadiabatic corrections due to the finite frequency of the modulation. We consider two configurations: a closed ring where the time dependence of the parameter induces a circulating current and a finite openended chain where particles are dragged from one edge to the opposite edge, due to the pumping mechanism induced by the bulk. © 2013 American Physical Society.
2012
 Electronhole puddles in the absence of charged impurities
[Articolo su rivista]
Gibertini, M.; Tomadin, A.; Guinea, F.; Katsnelson, M. I.; Polini, M.
abstract
It is widely believed that carrierdensity inhomogeneities ("electronhole puddles") in singlelayer graphene on a substrate such as quartz are due to charged impurities located close to the graphene sheet. Here we demonstrate by using a KohnShamDirac densityfunctional scheme that corrugations in a real sample are sufficient to determine electronhole puddles on length scales that are larger than the spatial resolution of stateoftheart scanning tunneling microscopy. © 2012 American Physical Society.
2012
 Local density of states in metaltopological superconductor hybrid systems
[Articolo su rivista]
Gibertini, M.; Taddei, F.; Polini, M.; Fazio, R.
abstract
We study by means of the recursive Green's function technique the local density of states of (finite and semiinfinite) multiband spinorbitcoupled semiconducting nanowires in proximity to an swave superconductor and attached to normalmetal electrodes. When the nanowire is coupled to a normal electrode, the zeroenergy peak, corresponding to the Majorana state in the topological phase, broadens with increasing transmission between the wire and the leads, eventually disappearing for ideal interfaces. Interestingly, for a finite transmission a peak is present also in the normal electrode, even though it has a smaller amplitude and broadens more rapidly with the strength of the coupling. Unpaired Majorana states can survive close to a topological phase transition even when the number of open channels (defined in the absence of superconductivity) is even. We finally study the Andreevboundstate spectrum in superconductornormal metalsuperconductor junctions and find that in multiband nanowires the distinction between topologically trivial and nontrivial systems based on the number of zeroenergy crossings is preserved. © 2012 American Physical Society.
2012
 Scattering theory of topological invariants in nodal superconductors
[Articolo su rivista]
Dahlhaus, J. P.; Gibertini, M.; Beenakker, C. W. J.
abstract
Timereversal invariant superconductors having nodes of vanishing excitation gap support zeroenergy boundary states with topological protection. Existing expressions for the topological invariant are given in terms of the Hamiltonian of an infinite system. We give an alternative formulation in terms of the Andreev reflection matrix of a normalmetalsuperconductor interface. This allows us to relate the topological invariant to the angleresolved Andreev conductance also when the boundary state in the superconductor has merged with the continuum of states in the normal metal. A variety of symmetry classes is obtained, depending on additional unitary symmetries of the reflection matrix. We derive conditions for the quantization of the conductance in each symmetry class and test these on a model for a two or threedimensional superconductor with spinsinglet and spintriplet pairing, mixed by Rashba spinorbit interaction. © 2012 American Physical Society.
2011
 Josephson current in a fourterminal superconductor/excitoncondensate/ superconductor system
[Articolo su rivista]
Peotta, S.; Gibertini, M.; Dolcini, F.; Taddei, F.; Polini, M.; Ioffe, L. B.; Fazio, R.; Macdonald, A. H.
abstract
We investigate the transport properties of a bilayer exciton condensate that is contacted by four superconducting leads. We focus on the equilibrium regime and investigate how the Josephson currents induced in the bilayer by phase biases applied to the superconducting electrodes are affected by the presence of an exciton condensate in the bulk of the system. As long as the distance between the superconducting electrodes is much larger than the exciton coherence length, the Josephson current depends only on the difference between the phase biases in the two layers. This result holds true in both short and longjunction limits. We relate it to a new correlated fourparticle Andreev process, which occurs at the superconductor/excitoncondensate interface. The system we investigate provides an implementation of the supercurrent mirror proposed by Kitaev as a viable way to realize topologically protected qubits. © 2011 American Physical Society.
2011
 Twodimensional MottHubbard electrons in an artificial honeycomb lattice
[Articolo su rivista]
Singha, A.; Gibertini, M.; Karmakar, B.; Yuan, S.; Polini, M.; Vignale, G.; Katsnelson, M. I.; Pinczuk, A.; Pfeiffer, L. N.; West, K. W.; Pellegrini, V.
abstract
Artificial crystal lattices can be used to tune repulsive Coulomb interactions between electrons. We trapped electrons, confined as a twodimensional gas in a gallium arsenide quantum well, in a nanofabricated lattice with honeycomb geometry. We probed the excitation spectrum in a magnetic field, identifying collective modes that emerged from the Coulomb interaction in the artificial lattice, as predicted by the MottHubbard model. These observations allow us to determine the Hubbard gap and suggest the existence of a Coulombdriven ground state.
2010
 Delocalizedlocalized transition in a semiconductor twodimensional honeycomb lattice
[Articolo su rivista]
De Simoni, G.; Singha, A.; Gibertini, M.; Karmakar, B.; Polini, M.; Piazza, V.; Pfeiffer, L. N.; West, K. W.; Beltram, F.; Pellegrini, V.
abstract
We report the magnetotransport properties of a twodimensional electron gas in a modulationdoped AlGaAs/GaAs heterostructure subjected to a lateral potential with honeycomb geometry. Periodic oscillations of the magnetoresistance and a delocalizedlocalized transition are shown by applying a gate voltage. We argue that electrons in such artificialgraphene lattices offer a promising approach for the simulation of quantum phases dictated by Coulomb interactions. © 2010 American Institute of Physics.
2010
 Electron density distribution and screening in rippled graphene sheets
[Articolo su rivista]
Gibertini, M.; Tomadin, A.; Polini, M.; Fasolino, A.; Katsnelson, M. I.
abstract
Singlelayer graphene sheets are typically characterized by longwavelength corrugations (ripples) which can be shown to be at the origin of rather strong potentials with both scalar and vector components. We present an extensive microscopic study, based on a selfconsistent KohnShamDirac densityfunctional method, of the carrierdensity distribution in the presence of these rippleinduced external fields. We find that spatial density fluctuations are essentially controlled by the scalar component, especially in nearly neutral graphene sheets, and that inplane atomic displacements are as important as outofplane ones. The latter fact is at the origin of a complicated spatial distribution of electronhole puddles which has no evident correlation with the outofplane topographic corrugations. In the range of parameters we have explored, exchange and correlation contributions to the KohnSham potential seem to play a minor role. © 2010 The American Physical Society.
2009
 Engineering artificial graphene in a twodimensional electron gas
[Articolo su rivista]
Gibertini, M.; Singha, A.; Pellegrini, V.; Polini, M.; Vignale, G.; Pinczuk, A.; Pfeiffer, L. N.; West, K. W.
abstract
At low energy, electrons in doped graphene sheets behave like massless Dirac fermions with a Fermi velocity, which does not depend on carrier density. Here we show that modulating a twodimensional electron gas with a longwavelength periodic potential with honeycomb symmetry can lead to the creation of isolated massless Dirac points with tunable Fermi velocity. We provide detailed theoretical estimates to realize such artificial graphenelike system and discuss an experimental realization in a modulationdoped GaAs quantum well. Ultrahighmobility electrons with linearly dispersing bands might open new venues for the studies of Diracfermion physics in semiconductors. © 2009 The American Physical Society.