Lopez Annette, Melton Cody A, Ahn Jeonghwan, Rubenstein Brenda M, Krogel Jaron T
Department of Physics, Brown University, Providence, Rhode Island 02912, United States.
High Energy Density Physics Theory, Sandia National Laboratories, Albuquerque, New Mexico 87123, United States.
J Chem Theory Comput. 2025 Jul 21. doi: 10.1021/acs.jctc.5c00838.
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 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 BiTe, 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.
拓扑绝缘体的特征是具有绝缘的体态和稳健的金属表面态。能带反转是拓扑绝缘体的一个标志。在布里渊区的时间反演不变点处，自旋轨道耦合（SOC）会在体能带边缘引起轨道特征的交换。用多体方法可靠地检测固态系统中的能带反转，将有助于识别自旋电子学和量子计算应用的可能候选材料，并增进我们对拓扑非平凡系统背后物理原理的理解。密度泛函理论（DFT）方法由于在计算成本和准确性之间具有良好的平衡，是研究这些有趣材料的一种成熟手段，但在准确模拟许多含重元素材料中存在的电子 - 电子相关性方面常常面临困难。在这项工作中，我们开发了一种新方法，用于在连续量子蒙特卡罗（QMC）方法中检测能带反转，该方法能够准确处理对拓扑绝缘体物理特性至关重要的电子相关性和自旋轨道耦合。我们的方法在整个第一布里渊区内应用基于洛丁方法和扩散蒙特卡罗（DMC）产生的单粒子约化密度矩阵的动量空间分辨原子布居分析。我们将此方法集成到开源QMC软件包QMCPACK中，以便这些基态方法可用于补充实验研究，并验证先前DFT在预测相关拓扑绝缘体能带结构方面的工作。我们在拓扑绝缘体碲化铋上演示了这种新技术，碲化铋在Γ点处其Bi - p和Te - p态之间显示出能带反转。当比较有无SOC的能带结构时，我们发现铋 - p轨道上的电荷增加，碲 - p轨道上的电荷减少。此外，我们用我们的方法比较了单层BiTe（不存在层间范德华相互作用）中存在的能带反转程度与双层和体材料中的能带反转程度。这里提出的方法将使未来对能带反转的多体研究能够揭示相关拓扑材料中相关性和拓扑之间的微妙相互作用。
