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RAFFAELLO BIANCO

Ricercatore t.d. art. 24 c. 3 lett. B
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Fisica

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Pubblicazioni

2021 - Anomalous High-Temperature Superconductivity in YH6 [Articolo su rivista]
Troyan, Ia; Semenok, Dv; Kvashnin, Ag; Sadakov, Av; Sobolevskiy, Oa; Pudalov, Vm; Ivanova, Ag; Prakapenka, Vb; Greenberg, E; Gavriliuk, Ag; Lyubutin, Is; Struzhkin, Vv; Bergara, A; Errea, I; Bianco, R; Calandra, M; Mauri, F; Monacelli, L; Akashi, R; Oganov, Ar
abstract

Pressure-stabilized hydrides are a new rapidly growing class of high-temperature superconductors, which is believed to be described within the conventional phonon-mediated mechanism of coupling. Here, the synthesis of one of the best-known high-T-C superconductors-yttrium hexahydride Im3 over bar m-YH6 is reported, which displays a superconducting transition at approximate to 224 K at 166 GPa. The extrapolated upper critical magnetic field B-c2(0) of YH6 is surprisingly high: 116-158 T, which is 2-2.5 times larger than the calculated value. A pronounced shift of T-C in yttrium deuteride YD6 with the isotope coefficient 0.4 supports the phonon-assisted superconductivity. Current-voltage measurements show that the critical current I-C and its density J(C) may exceed 1.75 A and 3500 A mm(-2) at 4 K, respectively, which is higher than that of the commercial superconductors, such as NbTi and YBCO. The results of superconducting density functional theory (SCDFT) and anharmonic calculations, together with anomalously high critical magnetic field, suggest notable departures of the superconducting properties from the conventional Migdal-Eliashberg and Bardeen-Cooper-Schrieffer theories, and presence of an additional mechanism of superconductivity.

2021 - Dominant Role of Quantum Anharmonicity in the Stability and Optical Properties of Infinite Linear Acetylenic Carbon Chains [Articolo su rivista]
Romanin, D; Monacelli, L; Bianco, R; Errea, I; Mauri, F; Calandra, M
abstract

Carbyne, an infinite-length straight chain of carbon atoms, is supposed to undergo a second order phase transition from the metallic bond-symmetric cumulene (=C=C=)(infinity), toward the distorted insulating polyyne chain (-C C-)(infinity), displaying bond-length alternation. However, recent synthesis of ultra long carbon chains (similar to 6000 atoms, [Nat. Mater., 2016, 15, 634]) did not show any phase transition and detected only the polyyne phase, in agreement with previous experiments on capped finite carbon chains. Here, by performing first-principles calculations, we show that quantum-anharmonicity reduces the energy gain of the polyyne phase with respect to the cumulene one by 71%. The magnitude of the bond-length alternation increases by increasing temperature, in stark contrast with a second order phase transition, confining the cumulene-to-polyyne transition to extremely high and unphysical temperatures. Finally, we predict that a high temperature insulator-to-metal transition occurs in the polyyne phase confined in insulating nanotubes with sufficiently large dielectric constant due to a giant quantum-anharmonic bandgap renormalization.

2021 - Quantum anharmonic enhancement of superconductivity in P6(3)/mmc ScH6 at high pressures: A first-principles study [Articolo su rivista]
Hou, Pg; Belli, F; Bianco, R; Errea, I
abstract

Making use of first-principles calculations, we analyze the effect of quantum ionic fluctuations and lattice anharmonicity on the crystal structure and superconductivity of P6 3/mmc ScH 6 in the 100-160 GPa pressure range within the stochastic self-consistent harmonic approximation. We predict a strong correction to the crystal structure, the phonon spectra, and the superconducting critical temperatures, which have been estimated in previous calculations without considering ionic fluctuations on the crystal structure and assuming the harmonic approximation for the lattice dynamics. Quantum ionic fluctuations have a large impact on the H 2 molecular-like units present in the crystal by increasing the hydrogen-hydrogen distance about a 5%. According to our anharmonic phonon spectra, this structure will be dynamically stable at least above 85 GPa, which is 45 GPa lower than the pressure given by the harmonic approximation. Contrary to many superconducting hydrogen-rich compounds, where quantum ionic effects and the consequent anharmonicity tend to lower the superconducting critical temperature, our results show that it can be enhanced in P6 3/mmc ScH 6 by approximately 15%. We attribute the enhancement of the critical temperature to the stretching of the H 2 molecular-like units and the associated increase of the electron-phonon interaction. Our results suggest that quantum ionic effects increase the superconducting critical temperature in hydrogen-rich materials with H 2 units by increasing the hydrogen-hydrogen distance and, consequently, the electron-phonon interaction.

2021 - Strong anharmonic and quantum effects in Pm(3)over-barn AIH(3) under high pressure: A first-principles study [Articolo su rivista]
Hou, Pg; Belli, F; Bianco, R; Errea, I
abstract

Motivated by the absence of experimental superconductivity in the metallic Pm (3) over barn phase of A1H(3) despite the predictions, we reanalyze its vibrational and superconducting properties at pressures P >= 99 GPa making use of first-principles techniques. In our calculations based on the self-consistent harmonic approximation method that treats anharmonicity beyond perturbation theory, we predict a strong anharmonic correction to the phonon spectra and demonstrate that the superconducting critical temperatures predicted in previous calculations based on the harmonic approximation are strongly suppressed by anharmonicity. The electron-phonon coupling concentrates on the lowest-energy hydrogen-character optical modes at the X point of the Brillouin zone. As a consequence of the strong anharmonic enhancement of their frequency, the electron-phonon coupling is suppressed by at least 30%. The suppression in lambda makes T-c smaller than 4.2 K above 120 GPa, which is well consistent with the experimental evidence. Our results underline that metal hydrides with hydrogen atoms in interstitial sites are subject to huge anharmonic effects.

2021 - The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects [Articolo su rivista]
Monacelli, L; Bianco, R; Cherubini, M; Calandra, M; Errea, I; Mauri, F
abstract

The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation (SSCHA) method. This technique rigorously describes the full thermodynamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles density-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at finite temperature. It enables the calculation of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions. We review the theoretical framework of the SSCHA and its dynamical extension, making particular emphasis on the physical inter pretation of the variables present in the theory that can enlighten the comparison with any other anharmonic theory. A modular and flexible Python environment is used for the implementation, which allows for a clean interaction with other packages. We briefly present a toy-model calculation to illustrate the potential of the code. Several applications of the method in superconducting hydrides, charge-density-wave materials, and thermoelectric compounds are also reviewed.

2021 - van der Waals driven anharmonic melting of the 3D charge density wave in VSe2 [Articolo su rivista]
Diego, J; Said, Ah; Mahatha, Sk; Bianco, R; Monacelli, L; Calandra, M; Mauri, F; Rossnagel, K; Errea, I; Blanco-Canosa, S
abstract

Understanding of charge-density wave (CDW) phases is a main challenge in condensed matter due to their presence in high-Tc superconductors or transition metal dichalcogenides (TMDs). Among TMDs, the origin of the CDW in VSe2 remains highly debated. Here, by means of inelastic x-ray scattering and first-principles calculations, we show that the CDW transition is driven by the collapse at 110 K of an acoustic mode at q(CDW) = (2.25 0 0.7) r.l.u. The softening starts below 225 K and expands over a wide region of the Brillouin zone, identifying the electron-phonon interaction as the driving force of the CDW. This is supported by our calculations that determine a large momentum-dependence of the electron-phonon matrix-elements that peak at the CDW wave vector. Our first-principles anharmonic calculations reproduce the temperature dependence of the soft mode and the T-CDW onset only when considering the out-of-plane van der Waals interactions, which reveal crucial for the melting of the CDW phase. The nature of the charge density wave transition in VSe2 is still debated. Here, the authors demonstrate that the transition is mainly driven by electron-phonon interactions, despite the presence of the Fermi-surface nesting, and that Wan-der-Waals forces are responsible for melting of the charge density wave order.

2020 - Anharmonicity and Doping Melt the Charge Density Wave in Single-Layer TiSe2 [Articolo su rivista]
Zhou, Jqs; Monacelli, L; Bianco, R; Errea, I; Mauri, F; Calandra, M
abstract

Low-dimensional systems with a vanishing band gap and a large electron-hole interaction have been proposed to be unstable toward exciton formation. As the exciton binding energy increases in low dimension, conventional wisdom suggests that excitonic insulators should be more stable in 2D than in 3D. Here we study the effects of the electron-hole interaction and anharmonicity in single-layer TiSe2. We find that, contrary to the bulk case and to the generally accepted picture, in single-layer TiSe2, the electron-hole exchange interaction is much smaller in 2D than in 3D and it has weak effects on phonon spectra. By calculating anharmonic phonon spectra within the stochastic self-consistent harmonic approximation, we obtain T-CDW approximate to 440 K for an isolated and undoped single layer and T-CDW approximate to 364 K for an electron-doping n = 4.6 x 10(13) cm(-2), close to the experimental result of 200-280 K on supported samples. Our work demonstrates that anharmonicity and doping melt the charge density wave in single-layer TiSe2.

2020 - Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride [Articolo su rivista]
Errea, I; Belli, F; Monacelli, L; Sanna, A; Koretsune, T; Tadano, T; Bianco, R; Calandra, M; Arita, R; Mauri, F; Flores-Livas, Ja
abstract

The discovery of superconductivity at 200 kelvin in the hydrogen sulfide system at high pressures(1) demonstrated the potential of hydrogen-rich materials as high-temperature superconductors. Recent theoretical predictions of rare-earth hydrides with hydrogen cages(2,3) and the subsequent synthesis of LaH10 with a superconducting critical temperature (T-c) of 250 kelvin(4,5) have placed these materials on the verge of achieving the long-standing goal of room-temperature superconductivity. Electrical and X-ray diffraction measurements have revealed a weakly pressure-dependent T-c for LaH10 between 137 and 218 gigapascals in a structure that has a face-centred cubic arrangement of lanthanum atoms(5). Here we show that quantum atomic fluctuations stabilize a highly symmetrical Fm (3) over barm crystal structure over this pressure range. The structure is consistent with experimental findings and has a very large electron-phonon coupling constant of 3.5. Although ab initio classical calculations predict that this Fm (3) over barm structure undergoes distortion at pressures below 230 gigapascals(2,3,) yielding a complex energy landscape, the inclusion of quantum effects suggests that it is the true ground-state structure. The agreement between the calculated and experimental Tc values further indicates that this phase is responsible for the superconductivity observed at 250 kelvin. The relevance of quantum fluctuations calls into question many of the crystal structure predictions that have been made for hydrides within a classical approach and that currently guide the experimental quest for room-temperature superconductivity(6-8). Furthermore, we find that quantum effects are crucial for the stabilization of solids with high electron-phonon coupling constants that could otherwise be destabilized by the large electron-phonon interaction(9), thus reducing the pressures required for their synthesis.

2020 - Theory of the thickness dependence of the charge density wave transition in 1 T-TiTe2 [Articolo su rivista]
Zhou, Js; Bianco, R; Monacelli, L; Errea, I; Mauri, F; Calandra, M
abstract

Most metallic transition metal dichalcogenides undergo charge density wave (CDW) instabilities with similar or identical ordering vectors in bulk and in single layer, albeit with different critical temperatures. Metallic 1 T-TiTe(2)is a remarkable exception as it shows no evidence of charge density wave formation in bulk, but it displays a stable 2 x 2 reconstruction in single-layer form. The mechanism for this 3D-2D crossover of the transition is still unclear, although strain from the substrate and the exchange interaction have been pointed out as possible formation mechanisms. Here, by performing non-perturbative anharmonic calculations with gradient corrected and hybrid functionals, we explain the thickness behaviour of the transition in 1 T-TiTe. We demonstrate that the CDW in single-layer TiTe(2)occurs from the interplay of non-perturbative anharmonicity and an exchange enhancement of the electron-phonon interaction, larger in the single layer than in the bulk. Finally, we study the electronic and structural properties of the single-layer CDW phase and provide a complete description of its electronic structure, phonon dispersion as well as infrared and Raman active phonon modes.

2020 - Weak Dimensionality Dependence and Dominant Role of Ionic Fluctuations in the Charge-Density-Wave Transition of NbSe2 [Articolo su rivista]
Bianco, R; Monacelli, L; Calandra, M; Mauri, F; Errea, I
abstract

Contradictory experiments have been reported about the dimensionality effect on the charge-density-wave transition in 2H NbSe2. While scanning tunneling experiments on single layers grown by molecular beam epitaxy measure a charge-density-wave transition temperature in the monolayer similar to the bulk, around 33 K, Raman experiments on exfoliated samples observe a large enhancement of the transition temperature up to 145 K. By employing a nonperturbative approach to deal with anharmonicity, we calculate from first principles the temperature dependence of the phonon spectra both for bulk and monolayer. In both cases, the charge-density-wave transition temperature is estimated as the temperature at which the phonon energy of the mode driving the structural instability vanishes. The obtained transition temperature in the bulk is around 59 K, in rather good agreement with experiments, and it is just slightly increased in the single-layer limit to 73 K, showing the weak dependence of the transition on dimensionality. Environmental factors could motivate the disagreement between the transition temperatures reported by experiments. Our analysis also demonstrates the predominance of ionic fluctuations over electronic ones in the melting of the charge-density-wave order.

2019 - Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe [Articolo su rivista]
Aseginolaza, U; Bianco, R; Monacelli, L; Paulatto, L; Calandra, M; Mauri, F; Bergara, A; Errea, I
abstract

Since 2014 the layered semiconductor SnSe in the high-temperature Cmcm phase is known to be the most efficient intrinsic thermoelectric material. Making use of first-principles calculations we show that its vibrational and thermal transport properties are determined by huge nonperturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry Prima is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temperature. Our calculations show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. WC calculate the lattice thermal conductivity obtaining good agreement with experiments only when nonperturbative anharmonic scattering is included. Our results suggest that the good thermoelectric efficiency of SnSe is strongly affected by the nonperturbative anharmonicity.

2019 - Quantum Enhancement of Charge Density Wave in NbS2 in the Two-Dimensional Limit [Articolo su rivista]
Bianco, R; Errea, I; Monacelli, L; Calandra, M; Mauri, F
abstract

At ambient pressure, bulk 2H-NbS2 displays no charge density wave instability, which is at odds with the isostructural and isoelectronic compounds 2H-NbSe2, 2H-TaS2, and 2H-TaSe2, and in disagreement with harmonic calculations. Contradictory experimental results have been reported in supported single layers, as 1H-NbS2 on Au(111) does not display a charge density wave, whereas 1H-NbS2 on 6H-SiC(0001) endures a 3 x 3 reconstruction. Here, by carrying out quantum anharmonic calculations from first-principles, we evaluate the temperature dependence of phonon spectra in NbS2 bulk and single layer as a function of pressure/strain. For bulk 2H-NbS2, we find excellent agreement with inelastic X-ray spectra and demonstrate the removal of charge ordering due to anharmonicity. In the two-dimensional limit, we find an enhanced tendency toward charge density wave order. Freestanding 1H-NbS2 undergoes a 3 x 3 reconstruction, in agreement with data on 6H-SiC(0001) supported samples. Moreover, as strains smaller than 0.5% in the lattice parameter are enough to completely remove the 3 x 3 superstructure, deposition of 1H-NbS2 on flexible substrates or a small charge transfer via field-effect could lead to devices with dynamical switching on/off of charge order.

2019 - Strong anharmonicity and high thermoelectric efficiency in high-temperature SnS from first principles [Articolo su rivista]
Aseginolaza, U; Bianco, R; Monacelli, L; Paulatto, L; Calandra, M; Mauri, F; Bergara, A; Errea, I
abstract

SnS and SnSe are isoelectronic materials with a common phase diagram. Recently, SnSe was found to be the most efficient intrinsic thermoelectric material in its high-temperature Cmcm phase above 800 K. Making use of first-principles calculations, here we show that the electronic and vibrational properties of both materials are very similar in this phase and, consequently, SnS is also expected to have a high thermoelectric figure of merit at high temperature in its Cmcm phase. In fact, the electronic power factor and lattice thermal conductivity are comparable for both materials, which ensures a similar figure of merit. As in the case of SnSe, the vibrational properties of SnS in the Cmcm phase are far from trivial and are dominated by huge anharmonic effects. Its phonon spectra are strongly renormalized by anharmonicity and the spectral functions of some particular in-plane modes depict anomalous non-Lorentzian profiles. Finally, we show that nonperturbative anharmonic effects in the third-order force-constants are crucial in the calculation of the lattice thermal conductivity. Our results motivate new experiments in the high-temperature regime to measure the figure of merit of SnS.

2018 - High-pressure phase diagram of hydrogen and deuterium sulfides from first principles: Structural and vibrational properties including quantum and anharmonic effects [Articolo su rivista]
Bianco, R; Errea, I; Calandra, M; Mauri, F
abstract

We study the structural and vibrational properties of the high-temperature superconducting sulfur trihydride and trideuteride in the high-pressure Im (3) over barm and R3m phases by first-principles density-functional-theory calculations. On lowering pressure, the rhombohedral transition Im (3) over barm -> R3m is expected, with hydrogen-bond desymmetrization and occurrence of trigonal lattice distortion. With both Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, in hydrostatic conditions we find that, contrary to what is suggested in some recent experiments, if the rhombohedral distortion exists it affects mainly the hydrogen bonds, whereas the resulting cell distortion is minimal. We estimate that the occurrence of a stress anisotropy of approximately 10% could explain this discrepancy. Assuming hydrostatic conditions, we calculate the critical pressure at which the rhombohedral transition occurs. Quantum and anharmonic effects, which are relevant in this system, are included at nonperturbative level with the stochastic self-consistent harmonic approximation. Within this approach, we determine the transition pressure by calculating the free-energy Hessian, a method that allows to estimate the critical pressure with much higher precision (and much lower computational cost) compared with the free-energy "finite-difference" approach previously used. Using PBE and BLYP, we find that quantum anharmonic effects are responsible for a strong reduction of the critical pressure with respect to the one obtained with the classical harmonic approach. Interestingly, for the two functionals, even if the transition pressures at classical harmonic level differ by 83 GPa, the transition pressures including quantum anharmonic effects differ only by 23 GPa. Moreover, we observe a prominent isotope effect, as we estimate higher transition pressure for D3S than for H3S. Finally, within the stochastic self-consistent harmonic approximation, with PBE we calculate the anharmonic phonon spectral functions in the Im (3) over barm phase. The strong anharmonicity of the system is confirmed by the occurrence of very large anharmonic broadenings leading to complex non-Lorentzian line shapes. Generally, for the high-energy hydrogen bond-stretching modes, the anharmonic phonon broadening is of the same magnitude of the electron-phonon one. However, for the vibrational spectra at zone center, accessible, e.g., by infrared spectroscopy, the broadenings are very small (linewidth at most around 2 meV) and anharmonic phonon quasiparticles are well defined.

2018 - Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles [Articolo su rivista]
Ribeiro, Gas; Paulatto, L; Bianco, R; Errea, I; Mauri, F; Calandra, M
abstract

At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depend on the approximation used for the exchange-correlation kernel in density-functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the phonon frequencies as obtained from the diagonalization of the free-energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe we evaluate the linear thermal expansion coefficient gamma = 2.3x10(-5) K-1, finding it to be in good agreement with experimental value of gamma = 2.04x10(-5) K-1. Furthermore, we study the phonon spectrum and we do reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the Gamma X direction. The phonon satellite becomes broader at high temperatures but its energy is essentially temperature independent, in agreement with experiments. We decompose the selfconsistent harmonic free energy in second-, third-, and fourth-order anharmonic terms. We find that the thirdand fourth-order terms are small. However, treating the third-order term perturbatively on top of the second-order self-consistent harmonic free energy overestimates the energy of the satellite associated with the transverse optical mode. On the contrary, a perturbative treatment on top of the harmonic Hamiltonian breaks down and leads to imaginary phonon frequencies already at 300 K. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high-temperatureFm3mstructure to the low-temperature R3mone. The transition temperature is, however, underestimated with respect to the experimental one. No satellites are present in the SnTe phonon spectra despite a not negligible anharmonic broadening of the zone-center TO mode.

2017 - Critical Role of the Exchange Interaction for the Electronic Structure and Charge-Density-Wave Formation in TiSe2 [Articolo su rivista]
Hellgren, M; Baima, J; Bianco, R; Calandra, M; Mauri, F; Wirtz, L
abstract

We show that the inclusion of screened exchange via hybrid functionals provides a unified description of the electronic and vibrational properties of TiSe2. In contrast to local approximations in density functional theory, the explicit inclusion of exact, nonlocal exchange captures the effects of the electron-electron interaction needed to both separate the Ti-d states from the Se-p states and stabilize the charge-density-wave (CDW) (or low-T) phase through the formation of a p-d hybridized state. We further show that this leads to an enhanced electron-phonon coupling that can drive the transition even if a small gap opens in the high-T phase. Finally, we demonstrate that the hybrid functionals can generate a CDW phase where the electronic bands, the geometry, and the phonon frequencies are in agreement with experiments.

2017 - Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation [Articolo su rivista]
Bianco, R; Errea, I; Paulatto, L; Calandra, M; Mauri, F
abstract

The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study, from first-principles, the anharmonic properties of solids. The free energy as a function of average atomic positions (centroids) can be used to study quantum or thermal lattice instability. In particular the centroids are order parameters in second-order structural phase transitions such as, e.g., charge-density-waves or ferroelectric instabilities. According to Landau's theory, the knowledge of the second derivative of the free energy (i.e., the curvature) with respect to the centroids in a high-symmetry configuration allows the identification of the phase-transition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the self-consistent harmonic approximation for a generic atomic configuration. The analytic derivative is expressed in terms of the atomic displacements and forces in a form that can be evaluated by a stochastic technique using importance sampling. Our approach is particularly suitable for applications based on first-principles density-functional-theory calculations, where the forces on atoms can be obtained with a negligible computational effort compared to total energy determination. Finally, we propose a dynamical extension of the theory to calculate spectral properties of strongly anharmonic phonons, as probed by inelastic scattering processes. We illustrate our method with a numerical application on a toy model that mimics the ferroelectric transition in rock-salt crystals such as SnTe or GeTe.

2016 - Orbital magnetization in insulators: Bulk versus surface [Articolo su rivista]
Bianco, R; Resta, R
abstract

The orbital magnetic moment of a finite piece of matter is expressed in terms of the one-body density matrix as a simple trace. We address a macroscopic system, insulating in the bulk, and we show that its orbital moment is the sum of a bulk term and a surface term, both extensive. The latter only occurs when the transverse conductivity is nonzero and it is due to conducting surface states. Simulations on a model Hamiltonian validate our theory.

2015 - Electronic and vibrational properties of TiSe2 in the charge-density-wave phase from first principles [Articolo su rivista]
Bianco, R; Calandra, M; Mauri, F
abstract

We study the charge-density-wave phase in TiSe2 by using first-principles density functional theory calculations with the harmonic approximation for the electron-phonon coupling. We consider several local functionals and both experimental and theoretical cell parameters. The results obtained are very sensitive to the cell parameters used. However, we show that, if the experimental cell is used, harmonic calculations are able to reproduce not only the structural instability of TiSe2 but also the effective distortion observed in the experiments, irrespective of the local functional used. If the experimental cell is used, the energy profile obtained by displacing the atoms is independent of the local functional considered too. With the semiempirical functional Grimme B97-D, aimed at describing better the van der Waals forces coupling the TiSe2 layers, the theoretical cell is in agreement with the experimental one and the structural analysis gives results analogous to the ones obtained with the experimental cell. We also present a study of the electronic structure evolution under the charge-density-wave deformation. In particular, we apply the unfolding technique in order to compare the calculated energy bands for the distorted structure with angle-resolved photoemission spectroscopy (ARPES) data taken at low temperature. In order to obtain a better agreement between ARPES and the calculated bands, both at high and low temperature, we investigate the effect of the correlation on the electrons of the localized Ti-3d orbitals by using the LDA + U method. We show that within this approximation the electronic bands for both the undistorted and distorted structure are in good agreement with ARPES. On the other hand, U eliminates the phonon instability of the system. A possible explanation for this counterintuitive result is proposed. Particularly, the possibility of taking into account the dependence of the parameter U on the atomic positions is suggested.

2014 - How disorder affects the Berry-phase anomalous Hall conductivity: A reciprocal-space analysis [Articolo su rivista]
Bianco, R; Resta, R; Souza, I
abstract

The anomalous Hall conductivity of "dirty" ferromagnetic metals is dominated by a Berry-phase contribution which is usually interpreted as an intrinsic property of the Bloch electrons in the pristine crystal. In this work we evaluate the geometric Hall current directly from the electronic ground state with disorder and then recast it as an integral over the crystalline Brillouin zone. The integrand is an effective k-space Berry curvature, obtained by unfolding the Berry curvature from the small Brillouin zone of a large supercell. Therein, disorder yields a net extrinsic Hall contribution, which we argue is related to the elusive side-jump effect. As an example, we unfold the first-principles Berry curvature of an ordered Fe3Co alloy from the original fcc-lattice Brillouin zone onto a bcc-lattice zone with four times the volume. Comparison with the virtual-crystal Berry curvature clearly reveals the symmetry-breaking effects of the substitutional Co atoms.

2013 - Orbital Magnetization as a Local Property [Articolo su rivista]
Bianco, R; Resta, R
abstract

The modern expressions for polarization P and orbital magnetization M are k-space integrals. But a genuine bulk property should also be expressible in r space, as an unambiguous function of the ground-state density matrix, "nearsighted'' in insulators, independently of the boundary conditions-either periodic or open. While P-owing to its "quantum'' indeterminacy-is not a bulk property in this sense, M is. We provide its r-space expression for any insulator, even with a nonzero Chern invariant. Simulations on a model Hamiltonian validate our theory. DOI: 10.1103/PhysRevLett.110.087202

2011 - Mapping topological order in coordinate space [Articolo su rivista]
Bianco, R; Resta, R
abstract

The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wave function. Here we address the Chern number of a two-dimensional insulator and we show that the corresponding topological order can be mapped by means of a "topological marker," defined in r space, and which may vary in different regions of the same sample. Notably, this applies equally well to periodic and open boundary conditions. Simulations over a model Hamiltonian validate our theory.