Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics

The anharmonic lattice is a representative example of an interacting bosonic many-body system. The self-consistent harmonic approximation has proven versatile for the study of the equilibrium properties of anharmonic lattices. However, the study of dynamical properties therewithin resorts to an ansatz, whose validity has not yet been theoretically proven. Here, we apply the time-dependent variational principle, a recently emerging useful tool for studying the dynamic properties of interacting many-body systems, to the anharmonic lattice Hamiltonian at finite temperature using the Gaussian states as the variational manifold. We derive an analytic formula for the position-position correlation function and the phonon self-energy, proving the dynamical ansatz of the self-consistent harmonic approximation. We establish a fruitful connection between time-dependent variational principle and the anharmonic lattice Hamiltonian, providing insights in both fields. Our work expands the range of applicability of time-dependent variational principle to first-principles lattice Hamiltonians and lays the groundwork for the study of dynamical properties of the anharmonic lattice using a fully variational framework.Comment: v2: Added a citation to L. Monacelli and F. Mauri, "Time-Dependent Self Consistent Harmonic Approximation: Anharmonic nuclear quantum dynamics and time correlation functions," arXiv:2011.14986 and a note on i

General, Strong Impurity-Strength Dependence of Quasiparticle Interference

Quasiparticle interference (QPI) patterns in momentum space are often assumed to be independent of the strength of the impurity potential when compared with other quantities, such as the joint density of states. Here, using the $T$-matrix theory, we show that this assumption breaks down completely even in the simplest case of a single-site impurity on the square lattice with an $s$ orbital per site. Then, we predict from first-principles, a very rich, impurity-strength-dependent structure in the QPI pattern of TaAs, an archetype Weyl semimetal. This study thus demonstrates that the consideration of the details of the scattering impurity including the impurity strength is essential for interpreting Fourier-transform scanning tunneling spectroscopy experiments in general.Comment: main manuscript: 8 pages, 6 figures, Supplementary Information: 3 pages, 6 figure

Phonon-induced renormalization of electron wave functions

The Allen-Heine-Cardona theory allows us to calculate phonon-induced electron self-energies from first principles without resorting to the adiabatic approximation. However, this theory has not been able to account for the change of the electron wave function, which is crucial if interband energy differences are comparable to the phonon-induced electron self-energy as in temperature-driven topological transitions. Furthermore, for materials without inversion symmetry, even the existence of such topological transitions cannot be investigated using the Allen-Heine-Cardona theory. Here, we generalize this theory to the renormalization of both the electron energies and wave functions. Our theory can describe both the diagonal and off-diagonal components of the Debye-Waller self-energy in a simple, unified framework. For demonstration, we calculate the electron-phonon coupling contribution to the temperature-dependent band structure and hidden spin polarization of BiTlSe2 across a topological transition. These quantities can be directly measured. Our theory opens a door for studying temperature-induced topological phase transitions in materials both with and without inversion symmetry

Symmetric improved estimators for multipoint vertex functions

Multipoint vertex functions, and the four-point vertex in particular, are crucial ingredients in many-body theory. Recent years have seen significant algorithmic progress toward numerically computing their dependence on multiple frequency arguments. However, such computations remain challenging and are prone to suffer from numerical artifacts, especially in the real-frequency domain. Here, we derive estimators for multipoint vertices that are numerically more robust than those previously available. We show that the two central steps for extracting vertices from correlators, namely the subtraction of disconnected contributions and the amputation of external legs, can be achieved accurately through repeated application of equations of motion, in a manner that is symmetric with respect to all frequency arguments and involves only fully renormalized objects. The symmetric estimators express the core part of the vertex and all asymptotic contributions through separate expressions that can be computed independently, without subtracting the large-frequency limits of various terms with different asymptotic behaviors. Our strategy is general and applies equally to the Matsubara formalism, the real-frequency zero-temperature formalism, and the Keldysh formalism. We demonstrate the advantages of the symmetric improved estimators by computing the Keldysh four-point vertex of the single-impurity Anderson model using the numerical renormalization group.Comment: 35 pages, 23 figure

Electron-phonon physics from first principles using the EPW code

EPW is an open-source software for $\textit{ab initio}$ calculations of electron-phonon interactions and related materials properties. The code combines density functional perturbation theory and maximally-localized Wannier functions to efficiently compute electron-phonon coupling matrix elements on ultra-fine Brillouin zone grids. This data is employed for predictive calculations of temperature-dependent properties and phonon-assisted quantum processes in bulk solids and low-dimensional materials. Here, we report on significant new developments in the code that occurred during the period 2016-2022, namely: a transport module for the calculation of charge carrier mobility and conductivity under electric and magnetic fields within the $\textit{ab initio}$ Boltzmann transport equation; a superconductivity module for the calculation of critical temperature and gap structure in phonon-mediated superconductors within the $\textit{ab initio}$ anisotropic multi-band Eliashberg theory; an optics module for calculations of phonon-assisted indirect transitions; a module for the calculation of small and large polarons without supercells using the $\textit{ab initio}$ polaron equations; and a module for calculating electron-phonon couplings, band structure renormalization, and temperature-dependent optical spectra using the special displacement method. For each capability, we outline the methodology and implementation, and provide example calculations. We describe recent code refactoring to prepare EPW for exascale architectures, we discuss efficient parallelization strategies, and report on extreme parallel scaling tests.Comment: 61 pages, 9 figure

Wannier90 as a community code: new features and applications

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.The WDG acknowledges financial support from the NCCR MARVEL of the Swiss National Science Foundation, the European Union’s Centre of Excellence E-CAM (Grant No. 676531), and the Thomas Young Centre for Theory and Simulation of Materials (Grant No. TYC-101).Peer reviewe

Comprehensive theory of second-order spin photocurrents

© 2022 American Physical Society.The spin photocurrents, direct currents induced by light, hold great promise for introducing new elements to spintronics. However, a general theory for spin photocurrents in real materials which is applicable to systems with spin-orbit coupling or noncollinear magnetism is absent. Here, we develop such a general theory of second-order spin photocurrents. We find that the second-order spin photocurrents can be classified into Drude, Berry curvature dipole, shift, injection, and rectification currents, which have different physical origins and symmetry properties. Surprisingly, our theory predicts a direct pure spin rectification current in an insulator induced by photons with energies lower than the material band gap. This phenomenon is absent in the case of the charge photocurrent. We find that the pure spin current of BiTeI induced by subgap light is large enough to be observable in experiments. Moreover, the subgap pure spin photocurrent is highly tunable with the polarization of light and the flowing direction of the spin photocurrent. This study lays the groundwork for the study of nonlinear spin photocurrents in real materials and provides a route to engineer light-controlled spin currents.11Nsciescopu

Wannier Function Perturbation Theory: Localized Representation and Interpolation of Wave Function Perturbation

Thanks to the nearsightedness principle, the low-energy electronic structure of solids can be represented by localized states such as the Wannier functions. Wannier functions are actively being applied to a wide range of phenomena in condensed matter systems. However, the Wannier-function-based representation is limited to a small number of bands and thus cannot describe the change of wave functions due to various kinds of perturbations, which require sums over an infinite number of bands. Here, we introduce the concept of the Wannier function perturbation, which provides a localized representation of wave function perturbations. Wannier function perturbation theory allows efficient calculation of numerous quantities involving wave function perturbation, among which we provide three applications. First, we calculate the temperature-dependent indirect optical absorption spectra of silicon near the absorption edge nonadiabatically, i.e., differentiating phonon-absorption and phonon-emission processes, and without arbitrary temperature-dependent shifts in energy. Second, we establish a theory to calculate the shift spin conductivity without any band-truncation error. Unlike the shift charge conductivity, an exact calculation of the shift spin conductivity is not possible within the conventional Wannier function methods because it cannot be obtained from geometric quantities for low-energy bands. We apply the theory to monolayer WTe2. Third, we calculate the spin Hall conductivity of the same material again without any bandtruncation error. Wannier function perturbation theory is a versatile method that can be readily applied to calculate a wide range of quantities related to various kinds of perturbations.11Nsciescopu