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

TL;DR

This paper introduces a relativistic self-consistent $GW$ method for solids using the exact two-component formalism with one-electron approximation, enabling accurate and parameter-free study of relativistic effects and electron correlation.

Contribution

It develops an all-electron, ab initio relativistic $GW$ approach based on the X2C1e formalism, simplifying calculations and allowing higher order theories to be built.

Findings

Excellent agreement with four-component formalism.

Enables study of scalar relativistic effects and spin-orbit coupling.

Facilitates development of advanced embedding theories.

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.