We present a workflow of practical calculations of electron-phonon (e-ph) coupling with many-electron correlation effects included using the GW perturbation theory (GWPT). This workflow combines BerkeleyGW, ABINIT, and EPW software packages to enable accurate e-ph calculations at the GW self-energy level, going beyond standard calculations based on density functional theory (DFT) and density-functional perturbation theory (DFPT). This workflow begins with DFT and DFPT calculations (ABINIT) as starting point, followed by GW and GWPT calculations (BerkeleyGW) for the quasiparticle band structures and e-ph matrix elements on coarse electron k- and phonon q-grids, which are then interpolated to finer grids through Wannier interpolation (EPW) for computations of various e-ph coupling determined physical quantities such as the electron self-energies or solutions of anisotropic Eliashberg equations, among others. A gauge-recovering symmetry unfolding technique is developed to reduce the computational cost of GWPT (as well as DFPT) while fulfilling the gauge consistency requirement for Wannier interpolation.

Shift current is a direct current generated from nonlinear light-matter interaction in a noncentrosymmetric crystal and is considered a promising candidate for next-generation photovoltaic devices. The mechanism for shift currents in real materials is, however, still not well understood, especially if electron-hole interactions are included. Here, we employ a first-principles interacting Green's-function approach on the Keldysh contour with real-time propagation to study photocurrents generated by nonlinear optical processes under continuous wave illumination in real materials. We demonstrate a strong direct current shift current at subbandgap excitation frequencies in monolayer GeS due to strongly bound excitons, as well as a giant excitonic enhancement in the shift current coefficients at above bandgap photon frequencies. Our results suggest that atomically thin two-dimensional materials may be promising building blocks for next-generation shift current devices.

Transition metal dichalcogenide (TMD) moiré superlattices provide an emerging platform to explore various light-induced phenomena. Recently, the discoveries of novel moiré excitons have attracted great interest. The nonlinear optical responses of these systems are however still underexplored. Here, we report investigation of light-induced shift currents (a second-order response generating DC current from optical illumination) in the WSe₂/WS₂ moiré superlattice. We identify a striking phenomenon of the formation of shift current vortex crystals-i.e., two-dimensional periodic arrays of moiré-scale current vortices and associated magnetic fields with remarkable intensity under laboratory laser setup. Furthermore, we demonstrate high optical tunability of these current vortices-their location, shape, chirality, and magnitude can be tuned by the frequency, polarization, and intensity of the incident light. Electron-hole interactions (excitonic effects) are found to play a crucial role in the generation and nature of the shift current intensity and distribution. Our findings provide a promising all-optical control route to manipulate nanoscale shift current density distributions and magnetic field patterns, as well as shed light on nonlinear optical responses in moiré quantum matter and their possible applications.

Optical dynamics in van der Waals heterobilayers is of fundamental scientific and practical interest. Based on a time-dependent adiabatic GW approach, we discover a new many-electron (excitonic) channel for converting photoexcited intralayer to interlayer excitations and the associated ultrafast optical responses in heterobilayers, which is conceptually different from the conventional single-particle picture. We find strong electron-hole interactions drive the dynamics and enhance the pump-probe optical responses by an order of magnitude with a rise time of ∼300  fs in MoSe_{2}/WSe_{2} heterobilayers, in agreement with experiment.

Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time-diagonal of such a Green's function or time-dependent physical observables that are functions of one time. In this paper, we discuss the possibility of using dynamic mode decomposition (DMD), a data-driven model order reduction technique, to characterize one-time observables associated with the nonequilibrium dynamics using snapshots computed within a small time window. The DMD method allows us to efficiently predict long time dynamics from a limited number of trajectory samples. We demonstrate the effectiveness of DMD on a model two-band system. We show that, in the equilibrium limit, the DMD analysis yields results that are consistent with those produced from a linear response analysis. In the nonequilibrium case, the extrapolated dynamics produced by DMD is more accurate than a special Fourier extrapolation scheme presented in this paper. We point out a potential pitfall of the standard DMD method caused by insufficient spatial/momentum resolution of the discretization scheme. We show how this problem can be overcome by using a variant of the DMD method known as higher order DMD.

Computing the numerical solution of the Kadanoff–Baym equations, a set of nonlinear integral differential equations satisfied by the two-time Green's functions derived from many-body perturbation theory for a quantum many-body system away from equilibrium, is a challenging task. Recently, we have successfully applied dynamic mode decomposition (DMD) to construct a data driven reduced order model that can be used to extrapolate the time-diagonal of a two-time Green's function from numerical solutions of the KBE within a small time window. In this paper, we extend the previous work and use DMD to predict off-diagonal elements of the two-time Green's function. We partition the two-time Green's function into a number of one-time functions along the diagonal and subdiagonals of the two-time window as well as in horizontal and vertical directions. We use DMD to construct separate reduced order models to predict the dynamics of these one-time functions in a two-step procedure. We extrapolate along diagonal and several subdiagonals within a subdiagonal band of a two-time window in the first step. In the second step, we use DMD to extrapolate the Green's function outside of the sub-diagonal band. We demonstrate the efficiency and accuracy of this approach by applying it to a two-band Hubbard model problem.

Electronic and optical properties of materials are affected by atomic motion through the electron–phonon interaction: not only band gaps change with temperature, but even at absolute zero temperature, zero-point motion causes band-gap renormalization. We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation. For materials with light elements, the band gap renormalization is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if accurate band gaps are sought. For infrared-active materials, global agreement with available experimental data is obtained only when non-adiabatic effects are taken into account. They even dominate zero-point renormalization for many materials, as shown by a generalized Fröhlich model that includes multiple phonon branches, anisotropic and degenerate electronic extrema, whose range of validity is established by comparison with first-principles results.

Stanene (single-layer gray tin), with an electronic structure akin to that of graphene but exhibiting a much larger spin-orbit gap, offers a promising platform for room-temperature electronics based on the quantum spin Hall (QSH) effect. This material has received much theoretical attention, but a suitable substrate for stanene growth that results in an overall gapped electronic structure has been elusive; a sizable gap is necessary for room-temperature applications. Here, we report a study of stanene, epitaxially grown on the (111)B-face of indium antimonide (InSb). Angle-resolved photoemission spectroscopy measurements reveal a gap of 0.44 eV, in agreement with our first-principles calculations. The results indicate that stanene on InSb(111) is a strong contender for electronic QSH applications.

Despite the weak, van der Waals interlayer coupling, photoinduced charge transfer vertically across atomically thin interfaces can occur within surprisingly fast, sub-50 fs time scales. An early theoretical understanding of charge transfer is based on a noninteracting picture, neglecting excitonic effects that dominate optical properties of such materials. We employ an ab initio many-body perturbation theory approach, which explicitly accounts for the excitons and phonons in the heterostructure. Our large-scale first-principles calculations directly probe the role of exciton-phonon coupling in the charge dynamics of the WS₂/MoS₂ heterobilayer. We find that the exciton-phonon interaction induced relaxation time of photoexcited excitons at the K valley of MoS₂ and WS₂ is 67 and 15 fs at 300 K, respectively, which sets a lower bound to the intralayer-to-interlayer exciton transfer time and is consistent with experiment reports. We further show that electron-hole correlations facilitate novel transfer pathways that are otherwise inaccessible to noninteracting electrons and holes.

Three-dimensional (3D) topological Dirac semimetals (TDSs) are rare but important as a versatile platform for exploring exotic electronic properties and topological phase transitions. A quintessential feature of TDSs is 3D Dirac fermions associated with bulk electronic states near the Fermi level. Using angle-resolved photoemission spectroscopy, we have observed such bulk Dirac cones in epitaxially grown α-Sn films on InSb(111), the first such TDS system realized in an elemental form. First-principles calculations confirm that epitaxial strain is key to the formation of the TDS phase. A phase diagram is established that connects the 3D TDS phase through a singular point of a zero-gap semimetal phase to a topological insulator phase. The nature of the Dirac cone crosses over from 3D to 2D as the film thickness is reduced.