Relativistic Self-Consistent $GW$: Exact Two-Component Formalism with One-Electron Approximation for Solids

Abstract

We present a formulation of relativistic self-consistent $GW$ for solids based on the exact two-component formalism with one-electron approximation (X2C1e) and non-relativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation without adjustable parameters. Our all-electron implementation is fully $ab$ $initio$ and does not require a pseudopotential constructed from atomic calculations. We examine the effect of the X2C1e approximation by comparison to the established four-component formalism and reach excellent agreement. The simplicity of X2C1e enables the construction of higher order theories, such as embedding theories, on top of perturbative calculations.

18 pages, 5 figures, 7 tables

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Cited by in corpus (16)

• Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Comparing self-consistent GW and vertex corrected G0W0 (G0W0Γ) accuracy for molecular ionization potentials
• Two-component $GW$ calculations: Cubic scaling implementation and comparison of vertex corrected and partially self-consistent $GW$ variants
• Challenges with relativistic GW calculations in solids and molecules
• Efficient anisotropic Migdal-Eliashberg calculations with the Intermediate Representation basis and Wannier interpolation
• Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions
• Band structures and ${\mathbb{Z}}_2$ invariants of two-dimensional transition metal dichalcogenide monolayers from fully-relativistic Dirac-Kohn-Sham theory using Gaussian-type orbitals
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• Exact Exchange with Range-separated Algorithm for Thermodynamic Limit of Periodic Hartree-Fock Theory
• TRIQS/Nevanlinna: Implementation of the Nevanlinna Analytic Continuation method for noise-free data
• Natural orbitals and two-particle correlators as tools for analysis of effective exchange couplings in solids
• Spin-dependent interactions in orbital-density-dependent functionals: non-collinear Koopmans spectral functionals
• Efficient Treatment of Relativistic Effects with Periodic Density Functional Methods: Energies, Gradients, and Stress Tensors
• Heating and cooling in self-consistent many-body simulations
• Efficient $GW$ band structure calculations using Gaussian basis functions and application to atomically thin transition-metal dichalcogenides