Abstract
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 applications and improve our understanding of the physics behind topologically nontrivial systems. Density functional theory (DFT) methods are a well-established means of investigating these interesting materials due to their favorable balance of computational cost and accuracy but often struggle to accurately model the electron–electron correlations present in the many materials containing heavier elements. 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 that are crucial to the physics of topological insulators. Our approach applies a momentum-space-resolved atomic population analysis throughout the first Brillouin zone utilizing the Löwdin method and the one-body reduced density matrix produced with diffusion Monte Carlo (DMC). We integrate this method 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 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 bilayer and bulk. 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.
| Original language | English |
|---|---|
| Pages (from-to) | 7485-7494 |
| Number of pages | 10 |
| Journal | Journal of Chemical Theory and Computation |
| Volume | 21 |
| Issue number | 15 |
| DOIs | |
| State | Published - Aug 12 2025 |
Funding
The authors thank Daniel Staros and Paul Kent for fruitful conversations. A.L. (implementation, data analysis, writing), C.A.M. (code development, writing), J.A. (mentorship, writing), B.M.R. (mentorship, writing), and J.T.K. (concept, mentorship, analysis, writing) were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, as part of the Computational Materials Sciences Program and Center for Predictive Simulation of Functional Materials. An award of computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract No. DE-AC05-00OR22725. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231. Sandia National Laboratories is a multimission laboratory managed and operated by the National Technology Engineering Solutions of Sandia, LLC (NTESS), a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration (DOE/NNSA) under Contract No. DE-NA0003525. This written work is authored by an employee of the NTESS. The employee, not the NTESS, owns the right, title, and interest in and to the written work and is responsible for its contents. Any subjective views or opinions that might be expressed in the written work do not necessarily represent the views of the U.S. Government. The publisher acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this written work or allow others to do so, for the U.S. Government purposes. The DOE will provide public access to results of federally sponsored research in accordance with the DOE Public Access Plan. This paper has been authored by UT-Battelle, LLC under Contract No. DE-AC05–00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).