Discovering topological phases in gray-Tin

TL;DR

This paper uses advanced first-principles calculations to accurately predict and analyze various topological phases in gray-Tin, revealing new phases and providing a robust diagnostic method for topological behavior.

Contribution

It introduces a fully self-consistent relativistic GW approach to study topological phases in $eta$-Sn, surpassing traditional methods and predicting new phases.

Findings

Recovered experimentally observed phases of $eta$-Sn.

Predicted new trivial and topological insulators.

Identified a Dirac semimetal phase in $eta$-Sn.

Abstract

Non-trivial topological phases often emerge in narrow-gap semiconductors with a delicate blend of spin-orbit coupling and electron correlation. The diamond-lattice allotrope of Sn ($\alpha$-Sn) exemplifies this behavior, hosting multiple topological phases that can be tuned by small distortions in the lattice. Despite rapid experimental progress, theoretical descriptions of $\alpha$-Sn lack predictive power and rely mainly on tight-binding models and density functional theory with uncontrolled approximations. We employ first-principles fully self-consistent, relativistic GW (scGW) to overcome these limitations. The scGW recovers the experimentally observed zero-gap semiconductor and the strain-induced topological insulator and Dirac semimetal phases, while also predicting new trivial and topological insulators and a Dirac semimetal phase, further demonstrating the versatility of $\alpha$-Sn for band engineering. Additionally, we propose a robust diagnostic of topological behavior based on a combined analysis of band and orbital-occupation dispersions, tailored for correlated methods where standard mean-field-based topological invariants fall short. Our findings pave the way for studying a broad class of topological materials using accurate first-principles methods beyond density functional theory.