Spin-orbit spillage as a measure of band inversion in insulators

Abstract

We propose a straightforward and effective approach for quantifying the band inversion induced by spin-orbit coupling in band insulators. In this approach we define a quantity as a function of wavevector in the Brillouin zone measuring the spillage between the occupied states of a system with and without SOC. Plots of the spillage throughout the BZ provide a ready indication of the number and location of band inversions driven by SOC. To illustrate the method, we apply this approach to the 2D Kane-Mele model, a 2D Bi bilayer with applied Zeeman field, and to first-principles calculations of some 3D materials including both trivial and \Z2\ topological insulators. We argue that the distribution of spillage in the BZ is closely related to the topological indices in these systems. Our approach provides a fresh perspective for understanding topological character in band theory, and should be helpful in searching for new materials with non-trivial band topology.

arXiv comment7 pages, 6 figures

References in corpus (24)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
• Maximally localized Wannier functions: Theory and applications
• Spin Hall effect
• Maximally-localized Wannier functions for entangled energy bands
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Computing topological invariants without inversion symmetry
• Spectral and Fermi surface properties from Wannier interpolation
• A sudden collapse in the transport lifetime across the topological phase transition in $(B{i}_{1-x}I{n}_x{)}_{2}S{e}_3$
• Topological-Metal to Band-Insulator Transition in (Bi1-xInx)2Se3 Thin Films
• Smooth gauge for topological insulators
• Topological phase transitions in (Bi${}_{1-x}$In${}_x{)}_2$Se${}_3$ and (Bi${}_{1-x}$Sb${}_x{)}_2$Se${}_3$
• Topological phases of Bi(111) bilayer in an external exchange field
• Three-dimensional topological insulators: A review on host materials
• Engineering quantum anomalous Hall phases with orbital and spin degrees of freedom

Cited by in corpus (13)

• The Joint Automated Repository for Various Integrated Simulations (JARVIS) for data-driven materials design
• Abundance of ${\mathbb{Z}}_2$ topological order in exfoliable two-dimensional insulators
• Discovering Inorganic Electrides from an Automated Computational Screening
• Two Dimensional Antiferromagnetic Chern Insulator NiRuCl6
• Flux states and topological phases from spontaneous time-reversal symmetry breaking in CrSi(Ge)Te${}_3$-based systems
• High-throughput search for magnetic topological materials using spin-orbit spillage, machine-learning and experiments
• Recent progress in the JARVIS infrastructure for next-generation data-driven materials design
• High-throughput Discovery of Topologically Non-trivial Materials using Spin-orbit Spillage
• First Principles Modeling of Topological Insulators: Structural Optimization and Exchange Correlation Functionals
• Quadrupole moments, edge polarizations, and corner charges in the Wannier representation
• Single-point spin Chern number in a supercell framework
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Entanglement entropy and entanglement spectrum of Bi${}_{1-x}$Sb${}_x$ (111) bilayers