Identifying Band Inversions in Topological Materials Using Diffusion Monte Carlo

Topological insulators are characterized by insulating bulk states and robust metallic surface states. Band inversion is a hallmark of topological insulators: at time-reversal invariant points in the Brillouin zone, spin-orbit coupling (SOC) induces a swapping of orbital character at the bulk band edges. Reliably detecting band inversion in solid-state systems with many-body methods would aid in identifying possible candidates for spintronics and quantum computing. In this work, we develop a novel method to detect band inversion within continuum quantum Monte Carlo (QMC) methods that can accurately treat the electron correlation and spin-orbit coupling crucial to the physics of topological insulators. Our approach projects orbital occupations throughout the first Brillouin zone onto an atomic basis via a Löwdin population analysis on the one-body reduced density matrix produced with Diffusion Monte Carlo (DMC). We first demonstrate this technique on bismuth telluride, which displays band inversion between its Bi-p and Te-p states at the Γ-point. We show an increase in charge on the bismuth p orbital and a decrease in charge on the tellurium p orbital when comparing band structures with and without SOC. Additionally, we use our method to compare the degree of band inversion present in monolayer Bi₂Te₃, which has no interlayer van der Waals interactions, to that seen in the bulk. We lastly describe applications of this methods to more correlated topological materials. The method presented here will enable future, many-body studies of band inversion that can shed light on the delicate interplay between correlation and topology in correlated topological materials.