Detecting Band Inversions in Topological Insulators with Diffusion Monte Carlo

Topological insulators are characterized by insulating bulk states and robust metallic surface states that are protected against perturbations by time-reversal symmetry. Band inversion is a hallmark of topological insulators; at time-reversal invariant points in the Brillouin zone, spin-orbit coupling 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 applications and improve our understanding of the physics behind topologically nontrivial systems. In this work, we develop a novel method to detect band inversion within continuum quantum Monte Carlo (QMC) that can accurately treat the electron correlation and spin-orbit coupling crucial to the physics of heavier elements. Our method projects occupations throughout the first Brillouin zone onto an atomic basis via Löwdin population analysis on the one-body reduced density matrix produced with QMC to resolve orbital occupancies across momentum space. This method has been integrated into QMCPACK, an open source ab initio QMC package, so that these ground state methods can be used to complement experimental studies and validate prior DFT work on predicting the band structures of correlated topological insulators. We demonstrate this new technique on the topological insulator bismuth telluride, which displays band inversion between the Bi-p and Te-p states at the gamma point.