
RAFFAELLO BIANCO
Ricercatore t.d. art. 24 c. 3 lett. B Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede exFisica

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2024
 Electronic structure and lattice dynamics of 1TVSe2:Origin of the threedimensional charge density wave
[Articolo su rivista]
Diego, Josu; Subires, D.; Said, A. H.; Chaney, D. A.; Korshunov, A.; Garbarino, G.; Diekmann, F.; Mahatha, S. K.; Pardo, V.; Wilkinson, J. M.; Lord, J. S.; Strempfer, J.; Perez, Pablo J. Bereciartua; Francoual, S.; Popescu, C.; Tallarida, M.; Dai, J.; Bianco, Raffaello; Monacelli, Lorenzo; Calandra, Matteo; Bosak, A.; Mauri, Francesco; Rossnagel, K.; Fumega, Adolfo O.; Errea, Ion; BlancoCanosa, S.
abstract
To characterize in detail the charge density wave (CDW) transition of 1TVSe2, its electronic structure and lattice dynamics are comprehensively studied by means of xray diffraction, muon spectroscopy, angle resolved photoemission (ARPES), diffuse and inelastic xray scattering, and stateoftheart firstprinciples density functional theory calculations. Resonant elastic xray scattering does not show any resonant enhancement at either V or Se, indicating that the CDW peak at the K edges describes a purely structural modulation of the electronic ordering. ARPES experiments identify (i) a pseudogap at T>TCDW, which leads to a depletion of the density of states in the MLM'L' plane at T
2021
 Anomalous HighTemperature 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
Pressurestabilized hydrides are a new rapidly growing class of hightemperature superconductors, which is believed to be described within the conventional phononmediated mechanism of coupling. Here, the synthesis of one of the bestknown highTC superconductorsyttrium hexahydride Im3 over bar mYH6 is reported, which displays a superconducting transition at approximate to 224 K at 166 GPa. The extrapolated upper critical magnetic field Bc2(0) of YH6 is surprisingly high: 116158 T, which is 22.5 times larger than the calculated value. A pronounced shift of TC in yttrium deuteride YD6 with the isotope coefficient 0.4 supports the phononassisted superconductivity. Currentvoltage measurements show that the critical current IC 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 MigdalEliashberg and BardeenCooperSchrieffer 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 infinitelength straight chain of carbon atoms, is supposed to undergo a second order phase transition from the metallic bondsymmetric cumulene (=C=C=)(infinity), toward the distorted insulating polyyne chain (C C)(infinity), displaying bondlength 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 firstprinciples calculations, we show that quantumanharmonicity reduces the energy gain of the polyyne phase with respect to the cumulene one by 71%. The magnitude of the bondlength alternation increases by increasing temperature, in stark contrast with a second order phase transition, confining the cumulenetopolyyne transition to extremely high and unphysical temperatures. Finally, we predict that a high temperature insulatortometal transition occurs in the polyyne phase confined in insulating nanotubes with sufficiently large dielectric constant due to a giant quantumanharmonic bandgap renormalization.
2021
 Quantum anharmonic enhancement of superconductivity in P6(3)/mmc ScH6 at high pressures: A firstprinciples study
[Articolo su rivista]
Hou, Pg; Belli, F; Bianco, R; Errea, I
abstract
Making use of firstprinciples 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 100160 GPa pressure range within the stochastic selfconsistent 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 molecularlike units present in the crystal by increasing the hydrogenhydrogen 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 hydrogenrich 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 molecularlike units and the associated increase of the electronphonon interaction. Our results suggest that quantum ionic effects increase the superconducting critical temperature in hydrogenrich materials with H 2 units by increasing the hydrogenhydrogen distance and, consequently, the electronphonon interaction.
2021
 Strong anharmonic and quantum effects in Pm(3)overbarn AIH(3) under high pressure: A firstprinciples 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 firstprinciples techniques. In our calculations based on the selfconsistent 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 electronphonon coupling concentrates on the lowestenergy hydrogencharacter optical modes at the X point of the Brillouin zone. As a consequence of the strong anharmonic enhancement of their frequency, the electronphonon coupling is suppressed by at least 30%. The suppression in lambda makes Tc 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 selfconsistent 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 selfconsistent 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 BornOppenheimer 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 densityfunctionaltheory 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 firstorder and secondorder 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 toymodel calculation to illustrate the potential of the code. Several applications of the method in superconducting hydrides, chargedensitywave 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; BlancoCanosa, S
abstract
Understanding of chargedensity wave (CDW) phases is a main challenge in condensed matter due to their presence in highTc superconductors or transition metal dichalcogenides (TMDs). Among TMDs, the origin of the CDW in VSe2 remains highly debated. Here, by means of inelastic xray scattering and firstprinciples 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 electronphonon interaction as the driving force of the CDW. This is supported by our calculations that determine a large momentumdependence of the electronphonon matrixelements that peak at the CDW wave vector. Our firstprinciples anharmonic calculations reproduce the temperature dependence of the soft mode and the TCDW onset only when considering the outofplane 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 electronphonon interactions, despite the presence of the Fermisurface nesting, and that WanderWaals forces are responsible for melting of the charge density wave order.
2020
 Anharmonicity and Doping Melt the Charge Density Wave in SingleLayer TiSe2
[Articolo su rivista]
Zhou, Jqs; Monacelli, L; Bianco, R; Errea, I; Mauri, F; Calandra, M
abstract
Lowdimensional systems with a vanishing band gap and a large electronhole 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 electronhole interaction and anharmonicity in singlelayer TiSe2. We find that, contrary to the bulk case and to the generally accepted picture, in singlelayer TiSe2, the electronhole 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 selfconsistent harmonic approximation, we obtain TCDW approximate to 440 K for an isolated and undoped single layer and TCDW approximate to 364 K for an electrondoping n = 4.6 x 10(13) cm(2), close to the experimental result of 200280 K on supported samples. Our work demonstrates that anharmonicity and doping melt the charge density wave in singlelayer TiSe2.
2020
 Quantum crystal structure in the 250kelvin 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; FloresLivas, Ja
abstract
The discovery of superconductivity at 200 kelvin in the hydrogen sulfide system at high pressures(1) demonstrated the potential of hydrogenrich materials as hightemperature superconductors. Recent theoretical predictions of rareearth hydrides with hydrogen cages(2,3) and the subsequent synthesis of LaH10 with a superconducting critical temperature (Tc) of 250 kelvin(4,5) have placed these materials on the verge of achieving the longstanding goal of roomtemperature superconductivity. Electrical and Xray diffraction measurements have revealed a weakly pressuredependent Tc for LaH10 between 137 and 218 gigapascals in a structure that has a facecentred 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 electronphonon 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 groundstate 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 roomtemperature superconductivity(68). Furthermore, we find that quantum effects are crucial for the stabilization of solids with high electronphonon coupling constants that could otherwise be destabilized by the large electronphonon interaction(9), thus reducing the pressures required for their synthesis.
2020
 Theory of the thickness dependence of the charge density wave transition in 1 TTiTe2
[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 TTiTe(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 singlelayer form. The mechanism for this 3D2D 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 nonperturbative anharmonic calculations with gradient corrected and hybrid functionals, we explain the thickness behaviour of the transition in 1 TTiTe. We demonstrate that the CDW in singlelayer TiTe(2)occurs from the interplay of nonperturbative anharmonicity and an exchange enhancement of the electronphonon interaction, larger in the single layer than in the bulk. Finally, we study the electronic and structural properties of the singlelayer 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 ChargeDensityWave 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 chargedensitywave transition in 2H NbSe2. While scanning tunneling experiments on single layers grown by molecular beam epitaxy measure a chargedensitywave 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 chargedensitywave 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 singlelayer 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 chargedensitywave order.
2019
 Phonon Collapse and SecondOrder 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 hightemperature Cmcm phase is known to be the most efficient intrinsic thermoelectric material. Making use of firstprinciples 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 lowsymmetry Prima is a secondorder 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 inplane vibrational modes are strongly anomalous with shoulders and doublepeak 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 TwoDimensional Limit
[Articolo su rivista]
Bianco, R; Errea, I; Monacelli, L; Calandra, M; Mauri, F
abstract
At ambient pressure, bulk 2HNbS2 displays no charge density wave instability, which is at odds with the isostructural and isoelectronic compounds 2HNbSe2, 2HTaS2, and 2HTaSe2, and in disagreement with harmonic calculations. Contradictory experimental results have been reported in supported single layers, as 1HNbS2 on Au(111) does not display a charge density wave, whereas 1HNbS2 on 6HSiC(0001) endures a 3 x 3 reconstruction. Here, by carrying out quantum anharmonic calculations from firstprinciples, we evaluate the temperature dependence of phonon spectra in NbS2 bulk and single layer as a function of pressure/strain. For bulk 2HNbS2, we find excellent agreement with inelastic Xray spectra and demonstrate the removal of charge ordering due to anharmonicity. In the twodimensional limit, we find an enhanced tendency toward charge density wave order. Freestanding 1HNbS2 undergoes a 3 x 3 reconstruction, in agreement with data on 6HSiC(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 1HNbS2 on flexible substrates or a small charge transfer via fieldeffect could lead to devices with dynamical switching on/off of charge order.
2019
 Strong anharmonicity and high thermoelectric efficiency in hightemperature 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 hightemperature Cmcm phase above 800 K. Making use of firstprinciples 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 inplane modes depict anomalous nonLorentzian profiles. Finally, we show that nonperturbative anharmonic effects in the thirdorder forceconstants are crucial in the calculation of the lattice thermal conductivity. Our results motivate new experiments in the hightemperature regime to measure the figure of merit of SnS.
2018
 Highpressure 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 hightemperature superconducting sulfur trihydride and trideuteride in the highpressure Im (3) over barm and R3m phases by firstprinciples densityfunctionaltheory calculations. On lowering pressure, the rhombohedral transition Im (3) over barm > R3m is expected, with hydrogenbond desymmetrization and occurrence of trigonal lattice distortion. With both PerdewBurkeErnzerhof (PBE) and BeckeLeeYangParr (BLYP) exchangecorrelation 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 selfconsistent harmonic approximation. Within this approach, we determine the transition pressure by calculating the freeenergy Hessian, a method that allows to estimate the critical pressure with much higher precision (and much lower computational cost) compared with the freeenergy "finitedifference" 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 selfconsistent 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 nonLorentzian line shapes. Generally, for the highenergy hydrogen bondstretching modes, the anharmonic phonon broadening is of the same magnitude of the electronphonon 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 selfconsistent 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 exchangecorrelation kernel in densityfunctional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the phonon frequencies as obtained from the diagonalization of the freeenergy 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) K1, finding it to be in good agreement with experimental value of gamma = 2.04x10(5) K1. 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 fourthorder anharmonic terms. We find that the thirdand fourthorder terms are small. However, treating the thirdorder term perturbatively on top of the secondorder selfconsistent 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 hightemperatureFm3mstructure to the lowtemperature 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 zonecenter TO mode.
2017
 Critical Role of the Exchange Interaction for the Electronic Structure and ChargeDensityWave 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 electronelectron interaction needed to both separate the Tid states from the Sep states and stabilize the chargedensitywave (CDW) (or lowT) phase through the formation of a pd hybridized state. We further show that this leads to an enhanced electronphonon coupling that can drive the transition even if a small gap opens in the highT 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
 Secondorder structural phase transitions, free energy curvature, and temperaturedependent anharmonic phonons in the selfconsistent harmonic approximation: Theory and stochastic implementation
[Articolo su rivista]
Bianco, R; Errea, I; Paulatto, L; Calandra, M; Mauri, F
abstract
The selfconsistent 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 firstprinciples, 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 secondorder structural phase transitions such as, e.g., chargedensitywaves 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 highsymmetry configuration allows the identification of the phasetransition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the selfconsistent 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 firstprinciples densityfunctionaltheory 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 rocksalt 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 onebody 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 chargedensitywave phase from first principles
[Articolo su rivista]
Bianco, R; Calandra, M; Mauri, F
abstract
We study the chargedensitywave phase in TiSe2 by using firstprinciples density functional theory calculations with the harmonic approximation for the electronphonon 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 B97D, 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 chargedensitywave deformation. In particular, we apply the unfolding technique in order to compare the calculated energy bands for the distorted structure with angleresolved 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 Ti3d 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 Berryphase anomalous Hall conductivity: A reciprocalspace analysis
[Articolo su rivista]
Bianco, R; Resta, R; Souza, I
abstract
The anomalous Hall conductivity of "dirty" ferromagnetic metals is dominated by a Berryphase 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 kspace 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 sidejump effect. As an example, we unfold the firstprinciples Berry curvature of an ordered Fe3Co alloy from the original fcclattice Brillouin zone onto a bcclattice zone with four times the volume. Comparison with the virtualcrystal Berry curvature clearly reveals the symmetrybreaking 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 kspace integrals. But a genuine bulk property should also be expressible in r space, as an unambiguous function of the groundstate density matrix, "nearsighted'' in insulators, independently of the boundary conditionseither periodic or open. While Powing to its "quantum'' indeterminacyis not a bulk property in this sense, M is. We provide its rspace 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 twodimensional 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.