arXiv subjects

Matteo Calandra

Publications and source records attributed to Matteo Calandra.

At least 91 records · Page 5Linked to original sources

arXiv2018

High-pressure phase diagram of hydrogen and deuterium sulfides from first principles: structural and vibrational properties including quantum and anharmonic effects

We study the structural and vibrational properties of the high-temperature superconducting sulfur trihydride and trideuteride in the high-pressure $Im\bar{3}m$ and $R3m$ phases by first-principles density-functional-theory calculations. On lowering pressure, the rhombohedral transition $Im\bar{3}m \rightarrow R3m$ is expected, with hydrogen bond desymmetrization and occurrence of trigonal lattice distortion. In hydrostatic conditions we find that, contrary to what 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 (SSCHA). Within this approach, we determine the transition pressure by calculating the free energy Hessian. 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. Moreover, we observe a prominent isotope effect, as we estimate higher pressure transition for D${}_3$S than for H${}_3$S. Finally, within SSCHA we calculate the anharmonic phonon spectral functions in the $Im\bar{3}m$ phase. The strong anharmonicity of the system is confirmed by the occurrence of very large anharmonic broadenings leading to complex non-Lorentzian line shapes. 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.

cond-mat.mtrl-sci↗

arXiv2017

Exchange Enhancement of the Electron-Phonon Interaction: the Case of Weakly Doped Two-Dimensional Multivalley Semiconductors

The effect of the exchange interaction on the vibrational properties and on the electron-phonon coupling were investigated in several recent works. In most of the case, exchange tends to enhance the electron-phonon interaction, although the motivations for such behaviour are not completely understood. Here we consider the class of weakly doped two-dimensional multivalley semiconductors and we demonstrate that a more global picture emerges. In particular we show that in these systems, at low enough doping, even a moderate electron-electron interaction enhances the response to any perturbation inducing a valley polarization. If the valley polarization is due to the electron-phonon coupling, the electron-electron interaction results in an enhancement of the superconducting critical temperature. We demonstrate the applicability of the theory by performing random phase approximation and first principles calculations in transition metal chloronitrides. We find that exchange is responsible for the enhancement of the superconducting critical temperature in Li$_x$ZrNCl and that much larger T$_c$s could be obtained in intercalated HfNCl if the synthesis of cleaner samples could remove the Anderson insulating state competing with superconductivity.

cond-mat.supr-con↗

arXiv2017

Critical role of the exchange interaction for the electronic structure and charge-density-wave formation in TiSe2

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, non-local 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.

cond-mat.mtrl-sci↗

arXiv2017

Anharmonic phonon spectra of PbTe and SnTe in the self-consistent harmonic approximation

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 depends 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 free energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe, we 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 $Γ$X direction. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high temperature Fm$\overline{3}$m structure to the low temperature R3m one.

cond-mat.mtrl-sci↗

arXiv2017

Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene

The ability to perform first-principles calculations of electronic and vibrational properties of two-dimensional heterostructures in a field-effect setup is crucial for the understanding and design of next-generation devices. We present here an implementation of density functional perturbation theories tailored for the case of two-dimensional heterostructures in field-effect configuration. Key ingredients are the inclusion of a truncated Coulomb interaction in the direction perpendicular to the slab and the possibility of simulating charging of the slab via field-effects. With this implementation we can access total energies, force and stress tensors, the vibrational properties and the electron-phonon interaction. We demonstrate the relevance of the method by studying flexural acoustic phonons and their coupling to electrons in graphene doped by field-effect. In particular, we show that while the electron-phonon coupling to those phonons can be significant in neutral graphene, it is strongly screened and negligible in doped graphene, in disagreement with other recent first-principles reports. Consequently, the gate-induced coupling with flexural acoustic modes would not be detectable in transport measurements on doped graphene.

cond-mat.mtrl-sci↗

arXiv2017

High-$T_c$ superconductivity in weakly electron-doped HfNCl

We investigate the magnetic and superconducting properties in electron-doped Li$_x$HfNCl. HfNCl is a band insulator that undergoes an insulator to superconductor transition upon doping at $x\approx0.13$. The persistence of the insulating state for $x<0.13$ is due to an Anderson transition probably related to Li disorder. In the metallic and superconducting phase, Li$_x$HfNCl is a prototype two-dimensional two-valley electron gas with parabolic bands. By performing a model random phase approximation approach as well as first-principles range-separated Heyd-Scuseria-Ernzerhof (HSE06) calculations, we find that the spin susceptibility $χ_s$ is strongly enhanced in the low doping regime by the electron-electron interaction. Furthermore, in the low doping limit, the exchange interaction renormalizes the intervalley electron-phonon coupling and results in a strong increase of the superconducting critical temperature for $x<0.15$. On the contrary, for $x>0.15$, $T_c$ is approximately constant, in agreement with experiments. At $x=0.055$ we found that $T_c$ can be as large as 40 K, suggesting that the synthesis of cleaner samples of Li$_x$HfNCl could remove the Anderson insulating state competing with superconductivity and generate a high-$T_c$ superconductor.

cond-mat.supr-con↗

arXiv2017

Anharmonicity and the isotope effect in superconducting lithium at high pressures: a first-principles approach

Recent experiments [Schaeffer 2015] have shown that lithium presents an extremely anomalous isotope effect in the 15-25 GPa pressure range. In this article we have calculated the anharmonic phonon dispersion of $\mathrm{^7Li}$ and $\mathrm{^6Li}$ under pressure, their superconducting transition temperatures, and the associated isotope effect. We have found a huge anharmonic renormalization of a transverse acoustic soft mode along $Γ$K in the fcc phase, the expected structure at the pressure range of interest. In fact, the anharmonic correction dynamically stabilizes the fcc phase above 25 GPa. However, we have not found any anomalous scaling of the superconducting temperature with the isotopic mass. Additionally, we have also analyzed whether the two lithium isotopes adopting different structures could explain the observed anomalous behavior. According to our enthalpy calculations including zero-point motion and anharmonicity it would not be possible in a stable regime.

cond-mat.supr-con↗

arXiv2017

Second order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: theory and stochastic implementation

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.

cond-mat.mtrl-sci↗

arXiv2017

The Raman fingerprint of rhombohedral graphite

Multi-layer graphene with rhombohedral stacking is a promising carbon phase possibly displaying correlated states like magnetism or superconductivity due to the occurrence of a flat surface band at the Fermi level. Recently, flakes of thickness up to 17 layers were tentatively attributed ABC sequences although the Raman fingerprint of rhombohedral multilayer graphene is currently unknown and the 2D resonant Raman spectrum of Bernal graphite not understood. We provide a first principles description of the 2D Raman peak in three and four layers graphene (all stackings) as well as in Bernal, rhombohedral and an alternation of Bernal and rhombohedral graphite. We give practical prescriptions to identify long range sequences of ABC multi-layer graphene. Our work is a prerequisite to experimental non-destructive identification and synthesis of rhombohedral graphite.

cond-mat.mtrl-sci↗

arXiv2017

Breakdown of optical phonons' splitting in two-dimensional materials

We investigate the long-wavelength dispersion of longitudinal and transverse optical phonon modes in polar two-dimensional materials, multilayers, and their heterostructures. Using analytical models and density-functional perturbation theory in a two-dimensional framework, we show that, at variance with the three-dimensional case, these modes are degenerate at the zone center but the macroscopic electric field associated with the longitudinal-optical 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 nitride-graphene heterostructures. As the phonon momentum increases, the intrinsic screening properties of the two-dimensional material dictate the transition to a momentum-independent splitting similar to that of three-dimensional materials. These considerations are essential to understand electrical transport and optical coupling in two-dimensional systems.

cond-mat.mtrl-sci↗

arXiv2017

Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles

We investigate the occurrence of magnetic and charge density wave instabilities in rhombohedral-stacked multilayer (three to eight layers) graphene by first principles calculations including exact exchange. Neglecting spin-polarization, an extremely flat surface band centered at the special point ${\bf K}$ of the Brillouin zone occurs at the Fermi level. Spin polarization opens a gap in the surface state by stabilizing an antiferromagnetic state. The top and the bottom surface layers are weakly ferrimagnetic in-plane (net magnetization smaller than $10^{-3}μ_B$), and are antiferromagnetic coupled to each other. This coupling is propagated by the out-of-plane antiferromagnetic coupling between the nearest neighbors. The gap is very small in a spin-polarized generalized gradient approximation, while it is proportional to the amount of exact exchange in hybrid functionals. For trilayer rhombohedral graphene it is $38.6$ meV in PBE0, in agreement with the $42$ meV gap found in experiments. We study the temperature and doping dependence of the magnetic gap. At electron doping of $n \sim 7 \times 10^{11}$ cm$^{-2}$ the gap closes. Charge density wave instabilities with $\sqrt{3}\times\sqrt{3}$ periodicity do not occur.

cond-mat.mtrl-sci↗

arXiv2017

Effect of doping on lattice instabilities of single-layer 1H-TaS2

Recent ARPES measurements of single-layer 1H-TaS2 grown on Au(111) suggest strong electron doping from the substrate. In addition, STM/STS measurements on this system show suppression of the charge-density-wave (CDW) instability that occurs in bulk 2H-TaS2. We present results from ab initio DFT calculations of free-standing single-layer 1H-TaS2 to explore the effects of doping on the CDW. In the harmonic approximation, we find that a lattice instability along the Gamma-M line occurs in the undoped monolayer, consistent with the bulk 3x3 CDW ordering vector. Doping removes the CDW instability, in agreement with the experimental findings. The doping and momentum dependence of both the electron-phonon coupling and of the bare phonon energy (unscreened by metallic electrons) determine the stability of lattice vibrations. Electron doping also causes an expansion of the lattice, so strain is a secondary but also relevant effect.

cond-mat.mtrl-sci↗

arXiv2016

Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: Theoretical modeling and first-principles calculations

We perform ab initio calculations of the coupling between electrons and small-momentum polar-optical phonons in monolayer transition metal dichalcogenides of the 2H type: MoS2, MoSe2, MoTe2, WS2, and WSe2. The so-called Fröhlich interaction is fundamentally affected by the dimensionality of the system. In a plane-wave framework with periodic boundary conditions, this coupling is affected by the spurious interaction between the 2D material and its periodic images. To overcome this, we perform density functional perturbation theory calculations with a truncated Coulomb interaction in the out-of-plane direction. We show that the 2D Fröhlich interaction is much stronger than assumed in previous ab initio studies. We provide analytical models depending on the effective charges and dielectric properties of the materials to interpret our ab initio calculations. Screening is shown to play a fundamental role in the phonon-momentum dependency of the polar-optical coupling, with a crossover between two regimes depending on the dielectric properties of the material relative to its environment. The Fröhlich interaction is screened by the dielectric environment in the limit of small phonon momenta and sharply decreases due to stronger screening by the monolayer at finite momenta. The small-momentum regime of the ab initio Fröhlich interaction is reproduced by a simple analytical model, for which we provide the necessary parameters. At larger momenta, however, direct ab initio calculations of electron-phonon interactions are necessary to capture band-specific effects. We compute and compare the carrier relaxation times associated to the scattering by both LO and A1 phonon modes. While both modes are capable of relaxing carriers on timescales under the picosecond at room temperature, their absolute and relative importance vary strongly depending on the material, the band, and the substrate.

cond-mat.mtrl-sci↗

arXiv2016

Spin susceptibility and electron-phonon coupling of two-dimensional materials by range-separated hybrid density functionals: Case study of Li$_x$ZrNCl

We investigate the capability of density functional theory (DFT) to appropriately describe the spin susceptibility, $χ_s$, and the intervalley electron-phonon coupling in Li$_x$ZrNCl. At low doping, Li$_x$ZrNCl behaves as a two-dimensional two-valley electron gas, with parabolic bands. In such a system, $χ_s$ increases with decreasing doping because of the electron-electron interaction. We show that DFT with local functionals (LDA/GGA) is not capable of reproducing this behavior. The use of exact exchange in Hartree-Fock (HF) or in DFT hybrid functionals enhances $χ_s$. HF, B3LYP, and PBE0 approaches overestimate $χ_s$, whereas the range-separated HSE06 functional leads to results similar to those obtained in the random phase approximation (RPA) applied to a two-valley two-spin electron gas. Within HF, Li$_x$ZrNCl is even unstable towards a ferromagnetic state for $x<0.16$. The intervalley phonons induce an imbalance in the valley occupation that can be viewed as the effect of a pseudomagnetic field. Thus, similarly to what happens for $χ_s$, the electron-phonon coupling of intervalley phonons is enhanced by the electron-electron interaction. Only hybrid DFT functionals capture such an enhancement and the HSE06 functional reproduces the RPA results presented in M. Calandra {\it et al.} [Phys. Rev. Lett. {\bf 114}, 077001 (2015)]. These results imply that the description of the susceptibility and electron-phonon coupling with a range-separated hybrid functional would be important also in other two-dimensional weakly doped semiconductors, such as transition-metal dichalcogenides and graphene.

cond-mat.supr-con↗

arXiv2016

Anharmonic effects in atomic hydrogen: superconductivity and lattice dynamical stability

We present first-principles calculations of metallic atomic hydrogen in the 400-600 GPa pressure range in a tetragonal structure with space group $I4_1/amd$, which is predicted to be its first atomic phase. Our calculations show a band structure close to the free-electron-like limit due to the high electronic kinetic energy induced by pressure. Bands are properly described even in the independent electron approximation fully neglecting the electron-electron interaction. Linear-response harmonic calculations show a dynamically stable phonon spectrum with marked Kohn anomalies. Even if the electron-electron interaction has a minor role in the electronic bands, the inclusion of electronic ex- change and correlation in the density response is essential to obtain a dynamically stable structure. Anharmonic effects, which are calculated within the stochastic self-consistent harmonic approxima- tion, harden high-energy optical modes and soften transverse acoustic modes up to a 20% in energy. Despite a large impact of anharmonicity has been predicted in several high-pressure hydrides, here the superconducting critical temperature is barely affected by anharmonicity, as it is lowered from its harmonic 318 K value only to 300 K at 500 GPa. We atribute the small impact of anharmoncity on superconductivity to the absence of softened optical modes and the fairly uniform distribution of the electron-phonon coupling among the vibrational modes.

cond-mat.supr-con↗

arXiv2016

Determination of scattering time and of valley occupation in transition-metal dichalcogenides doped by field effect

The transition-metal dichalcogenides have attracted a lot of attention as a possible stepping-stone toward atomically thin and flexible field-effect transistors. One key parameter to describe the charge transport is the time between two successive scattering events - the transport scattering time. In a recent report, we have shown that it is possible to use density functional theory to obtain the band structure of two-dimensional semiconductors in presence of field effect doping. Here, we report a simple method to extract the scattering time from the experimental conductivity and from the knowledge of the band structure. We apply our approach to monolayers and multilayers of MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$, and WSe$_2$ in presence of a gate. In WS$_2$, for which accurate measurements of mobility have been published, we find that the scattering time is inversely proportional to the density of states at the Fermi level. Finally, we show that it is possible to identify the critical doping at which different valleys start to be occupied from the doping-dependence of the conductivity.

cond-mat.mes-hall↗

arXiv2015

Quantum Hydrogen-Bond Symmetrization and High-Temperature Superconductivity in Hydrogen Sulfide

Hydrogen compounds are peculiar as the quantum nature of the proton can crucially affect their structural and physical properties. A remarkable example are the high-pressure phases of H$_2$O, where quantum proton fluctuations favor the symmetrization of the H bond and lower by 30 GPa the boundary between the asymmetric structure and the symmetric one. Here we show that an analogous quantum symmetrization occurs in the recently discovered sulfur hydride superconductor with the record superconducting critical temperature $T_c=203$ K at 155 GPa. In this system, according to classical theory, superconductivity occurs via formation of a structure of stoichiometry H$_3$S with S atoms arranged on a body-centered-cubic (bcc) lattice. For $P \gtrsim 175$ GPa, the H atoms are predicted to sit midway between two S atoms, in a structure with $Im\bar3m$ symmetry. At lower pressures the H atoms move to an off-center position forming a short H$-$S covalent bond and a longer H$\cdots$S hydrogen bond, in a structure with $R3m$ symmetry. X-ray diffraction experiments confirmed the H$_3$S stoichiometry and the S lattice sites, but were unable to discriminate between the two phases. Our present ab initio density-functional theory (DFT) calculations show that the quantum nuclear motion lowers the symmetrization pressure by 72 GPa. Consequently, we predict that the $Im\bar3m$ phase is stable over the whole pressure range within which a high $T_c$ was measured. The observed pressure-dependence of $T_c$ is closely reproduced in our calculations for the $Im\bar3m$ phase, but not for the $R3m$ phase. Thus, the quantum nature of the proton completely rules the superconducting phase diagram of H$_3$S.

cond-mat.supr-con↗

arXiv2015

Strong anharmonicity induces quantum melting of charge density wave in 2H-NbSe$\_2$ under pressure

The interplay between charge density wave (CDW) order and superconductivity has attracted much attention. This is the central issue of along standing debate in simple transition metal dichalcogenides without strong electronic correlations, such as 2H-NbSe$\_2$, in which twosuch phases coexist. The importance of anisotropic electron-phonon interaction has been recently highlighted from both theoretical and experimental point of view, and explains some of the key features of the formation of the CDW in this system. On the other hand, other aspects, such as the effects of anharmonicity, remain poorly understood despite their manifest importance in such soft-phonon driven phase transition. At the theoretical level in particular, their prohibitive computational price usually prevents their investigation within conventional perturbative approaches.Here, we address this issue using a combination of high resolution inelastic X-ray scattering measurements of the phonon dispersion, as afunction of temperature and pressure, with state of the art ab initio calculations. By explicitly taking into account anharmonic effects, we obtain an accurate, quantitative, description of the (P,T) dependence of the phonon spectrum, accounting for the rapid destruction of the CDW under pressure by zero mode vibrations - or quantum fluctuations - of the lattice. The low-energy longitudinal acoustic mode that drives the CDW transition barely contributes to superconductivity, explaining the insensitivity of the superconducting critical temperature to the CDW transition.

cond-mat.supr-con↗