Session A20: First-principles Modeling of Excited-state Phenomena in Materials I: Many-body Perturbation Theory (Techniques and Applications)

Accurate Core-Level Spectra from GW

We present an accurate method for computing X-ray photoelectron spectra based on the GW approximation that overcomes the limitations of density functional theory (DFT) approaches. The GW method is routinely used to predict charged valence excitations in molecules and solids. However, GW core-level spectroscopy has thus far been poorly explored. This in parts related to the fact that numerically very efficient techniques such as the analytic continuation, which treat the frequency dependence on the imaginary axis, break down for inner-shell excitations. We implemented a full-frequency approach on the real axis in the all-electron code FHI-aims [1] using a localized basis to enable the treatment of core levels in GW [2]. Our scheme is based on the contour deformation technique and facilitates precise and efficient calculations of the self-energy, which has a complicated pole structure for core states. We present benchmark studies for 1s excitations of small- and medium-sized molecules and discuss the optimization of the starting point as well as self-consistent approaches. We find that the absolute core-level binding energies deviate on average by less than 0.5 eV from experiment outperforming the DFT-based Delta Self-Consistent Field approach. Relative core excitations are also well reproduced with average deviations of less 0.2 eV from the experimental reference. Furthermore, our calculations reveal that the GW excitation spectrum exhibits satellite features in addition to the photoelectric peak, which might provide access to interesting many-body physics.

[1] V. Blum et al., Comput. Phys. Commun. 2009, 180, 2175
[2] D. Golze, J. Wilhelm, M. J. van Setten, P. Rinke, J. Chem. Theory Comput. 2018, 14 (9), 4856   

Time-dependent GW: Progress in Solving Kadanoff-Baym Equations with Dynamic GW Self Energy

The ab initio GW plus Bethe-Salpeter equation (GW-BSE) approach has achieved great success in describing the linear absorption spectra of materials in equilibrium. However, many important photo-processes and experiments of interest that involve ultrafast and high-intensity pulses of light fall well outside the regime of equilibrium and linear responses. One can generalize the Green’s function formalism in many-body perturbation theory to nonequilibrium situations by solving the Kadanoff-Baym equations (KBE), but the presence of two time variables that need to be simultaneously evolved presents a significant computational challenge. In recent years, progress has been made in solving the KBE from ab initio in the static limit of the GW self energy, which greatly simplifies the time evolution. Here, we present progress on solving the KBE including dynamical effects in the self energy. We discuss time-evolution algorithms, memory effects, approximations to the dynamics, and convergence behavior.   

Excitonic effects in shift currents of low dimensional materials from time-dependent GW approach

We present first-principles studies on shift currents with excitonic effects in 2D materials using an adiabatic time-dependent GW approach. Shift current in a noncentrosymmetric semiconductor is a DC current generated by optical excitations from a nonlinear response processes. Using a newly developed real-time simulation method, we are able to include excitonic effects in the nonlinear responses from first principles, treating the complicated electron-hole interaction at the GW plus Bethe-Salpeter equation level for the first time. We applied this method to study shift currents in monolayer GeS and found strongly enhanced responses due to excitonic effects. Most interestingly, the dominant contributions to the shift currents here are generated at in-gap frequencies, which peaked at energies below the quasi-particle band gap by the exciton binding energies.   

Correlation satellites in optical and loss spectra

The coupling of excitations leads to intriguing effects in the spectra of materials. Current approximations to calculate spectra most often describe this coupling insufficiently. We propose a cumulant formulation for neutral electronic excitations which opens the way to describe effects such as double plasmon satellites or exciton-exciton coupling. Our approach starts from the widely used GW plus Bethe-Salpeter approximation to many-body perturbation theory which is based on a quasiparticle picture, and it adds coupling to other excitations through a consistent inclusion of dynamically screened interactions. We show that this requires to consider scattering contributions that are usually neglected. The result is formulated in a way that highlights essential physics, that can be implemented as a post-processing tool in widely used first principles codes, and that suggests which kind of materials and measurements should exhibit strong effects. This is illustrated using a model.   

Faster and more accurate stochastic GW

I will present recent developments in stochastic approach to the GW approximation, which further accelerate the calculation of quasiparticle energies and increase their accuracy. A new concept of sparse stochastic compression is used to speed up stochastic approaches and leads to an overall decrease of statistical errors in large finite and periodic systems. Computation of quasiparticle energies and gaps for systems with up to N_e >10,000 electrons is thus feasible with only small statistical fluctuation (± 0.05 eV) and consuming < 2000 core CPU hours. Further, I will present an efficient scissors-like GW self-consistency approach that can be implemented at zero additional cost. This result is a simple modification of the time-dependent G0W0 and enables an a posteriori self-consistency cycle applicable to large systems.   

Calculations of Multiplet Splittings in Open Shell Systems within the GW approximation

In open shell systems, the coupling of the orbital and spin angular momenta of electrons can result in multiple energy eigenstates of the electronically excited system leading to the characteristic multiplet structures observed in photoemission experiments. While DFT is not capable of determining the resulting multiplet splittings accurately, recent studies have shown that the GW approximation can describe the multiplet structure with reasonable accuracy¹. In this work, we investigate the multiplet splittings for open shell molecules such as NO₂, NF₂, O₂, ClO₂, and single atoms by applying the one-shot GW approximation. We compare predictions obtained with G and W computed with the same hybrid functional starting points containing varying amounts of Fock exchange with those where G is still computed with a hybrid functional starting point but W is computed within PBE. We show that it is possible to achieve excellent agreement with experimental results for molecular systems using both types of approaches, but the amount of exact exchange needed for quantitative accuracy depends on the molecule as well as the choice of the GW method employed.

¹J. Lischner, J. Deslippe, M. Jain, and S. G. Louie, Phys. Rev. Lett. 109, 036406 (2012).   

Electronic structure of 3d-transition-metal oxide clusters with partially filled d shells from GW calculations

The GW approximation using atom-centered localized basis sets is an emerging method for studying the excited properties of confined systems. However, G₀W₀@PBE, which is typically used for simple extended systems, fails to accurately describe the electronic excitations in 3d-transition-metal oxide clusters due to dimensionality and correlation effects, and suffers from exhibiting multiple solutions of the quasiparticle equation due to complex self-energy poles. G₀W₀ on top of exact exchange (EXX) is one way to overcome these problems, but the predictions depend on the amount of EXX and the method suffers from convergence errors in open-shell systems (e.g. due to spin contamination). In our previous work on early and late 3d transition metal oxide clusters, we showed that G_nW₀@PBE addresses all the above issues, and thus is an accurate and efficient GW method for these systems. In this work, we investigate various flavors of the GW method (one-shot, partially self-consistent, quasiparticle self-consistent) with different starting points for 3d transition metal oxide clusters, VO^-, CrO^-, MnO^-, FeO^-, CoO^-, and NiO^-, which display a number of high multiplicity states and exhibit moderate electronic correlation.   

Spin wave spectrum of 3d ferromagnet based on QSGW calculations

We have developed spin wave (SW) spectrum calculation code, combining quasi-particle self-consistent GW(QSGW) and maximum localized Wannier function (MLWF). With MLWF, we can overcome time-consuming calculations for large q-point SW spectrum. Since we adopt the linear response method for dynamical susceptibility^[1], our SW spectrum includes Stoner excitation, which causes the damping of spin SW. Stoner excitation is important in weak ferromagnet such as Fe, while not important in strong ferromagnet such as Ni. In the local density approximation (LDA), our SW energy in Fe is smaller than experimental result or other frozen SW calculation. In the QSGW calculations, due to the corrections of exchange splitting, the calculated SW stiffness constant of Ni (481 meV･Å in average) is in good agreement with inelastic neutron scattering experiment (483 meV･Å), while the LDA result (834 meV･Å) is almost twice as large as experimental one. In the fcc Co, our LDA result corresponds to frozen SW calculation because of weak Stoner excitation coupling in this strong ferromagnet. In the case of cubic FeCo in ordered state, we found acoustic and optical mode in the SW spectrum. [1] C. Friedrich, et al., First Principles Approaches to Spectroscopic Properties of Complex Materials pp 259-301 (2014).   

Tunable Low Temperature Phonon-induced Electronic Bi-stability in Vanadium Dioxide

We use a joint theory and experimental approach to clarify the nature of the Metal-insulator transition in VO₂, by QSGW calculations in the frozen phonon approach, and pump-probe ultra-fast spectroscopy with THz radiation. We first show that the insulating state is induced by a Peierls instability, that is responsible for the orbital selection that drives the material to its insulating state, and is associated with a degenerate two-orbital electronic valence band. At the same time, Peierls excitations driven by the lattice dynamics. A 5.7 THz phonon modes split the degeneracy, in a particular, which in turn induces a rapid metallization. This mode is observed in THz pump measurements, far below the critical temperature in the M₁ phase. Our combined approach sheds light in the nature of the transition, which is in our view mediated by a combination of the lattice dynamics and electronic excitations. Finally, we report a possibility in the theory for a novel mechanism to induce an electronic metal-insulator hysteresis via the electron-phonon coupling to the 6.5 THz phonon mode.   

Alternative approaches for calculations of exchange and correlation contributions to thermodynamic properties

The cumulant expansion of the one-electron Green’s function has been found to be an improved method for calculations of excited states and spectra for a wide variety of systems [1]. Additionally, an extension of the cumulant Green’s function approach to finite temperatures has yielded total energies and exchange correlation potentials in good agreement with quantum Monte-Carlo results [2]. Here we present an investigation of alternative thermodynamic pathways for properties such as the free energy, entropy, and heat capacity of the homogeneous electron gas. In addition we discuss approximate methods based on quasiparticle properties alone. These approximate methods improve the efficiency of the approach, and could be applied to real systems for which calculations of GW quasiparticle effects are computationally reasonable.
[1] J.S. Zhou et al., J Chem Phys. 143, 184109 (2015)
[2] J.J. Kas, J.J. Rehr, Phys. Rev. Lett. 119, 176403 (2017)   

Electron Hydrodynamics of Graphene from a First-Principles GW Approach: Electronic Compressibility, Backflows and Transport Coefficients

Doped graphene at low temperatures has experimental signatures of hydrodynamic behavior originating from the electron-electron interaction. Here, we use the GW approximation to study the electronic and thermal properties of graphene from first-principles within a Fermi liquid framework. We show how the electronic compressibility is modified by many-body contributions at finite temperature. Next, we solve the kinetic equation using an exact expression of the scattering matrix. We show how the commonly-used relaxation time approximation causes a severe underestimation of transport coefficients, and how a correct treatment of momentum dissipation is critical to the description of transport properties. We will present results for transport coefficients, including electrical conductivity, the electronic contribution to thermal conductivity and the viscosity coefficients, discussing corrections due to the interaction of carriers with the environment and the behavior of the electron liquid as a non-Newtonian fluid.   

Cumulant Green’s function approach for phonon satellites in resonant inelastic X-ray scattering

Resonant inelastic X-ray scattering (RIXS) probes various excitations in materials, including plasmons, magnons and phonons. Calculating RIXS spectra is challenging since it is a second-order process involving the coupling of core-excited states to bosonic collective modes, and requires summation over virtual intermediate states. Using a cumulant expansion [1], we develop a tractable excitonic Green’s function formulation of the RIXS cross section. We demonstrate our methodology by reproducing the phonon contribution to the RIXS spectrum of acetone [2].
The relative intensities of multiple phonon satellites are used to quantify the electron-phonon coupling strength. First, we show that RIXS actually probes exciton-phonon coupling, which can differ significantly from electron-phonon coupling. Second, we extend our numerical demonstration on acetone to the more challenging cases of quasi-1D Li₂CuO₂ and 3D SrTiO₃. This requires generalizing concepts of density functional perturbation theory to generate exciton-phonon coupling constants throughout the Brillouin zone. Comparison to experiment is made, resolving apparent anomalies in the spectra of Li₂CuO₂.

[1] Langreth, Phys Rev B 1, 471 (1970)
[2] Geondzhian and Gilmore, submitted   

Reexamining a local, real-space approach to screening

Various many-body perturbation theory techniques for calculating electron behavior rely on W, i.e., the screened Coulomb interaction. The exact screening requires complete knowledge of the dielectric response of the electronic system. As a simplification, calculations often begin with the RPA or random phase approximation. However, even at the RPA level the calculations are costly and scale poorly with system size. A local approach has been shown to be efficient while maintaining accuracy [1]. We present improvements to this scheme, including reconstruction of the all-electron character of the pseudopotential-based wave functions, improved scaling with system size, and a parallelized implementation. We discuss applications to Bethe-Salpeter calculations of core and valence spectroscopies.

[1] E. L. Shirley, Ultramicroscopy 106, 986 (2006)