An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection

Abstract

We introduce a new expression for the Z2 topological invariant of band insulators using non- Abelian Berry's connection. Our expression can identify the topological nature of a general band insulator without any of the gauge fixing problems that plague the concrete implementation of previous invariants. The new expression can be derived from the "partner switching" of the Wannier function center during time reversal pumping and is thus equivalent to the Z2 topological invariant proposed by Kane and Mele.

14 pages, 8 figures

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• Geometry-Driven Moiré Engineering in Twisted Bilayers of High-Pseudospin Fermions
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• A Coherent Physics Picture of Topological Insulators at Single-Particle Level
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Electronic structures and stability investigation of the new class of large band gap topological insulators MTl${}_4$Te${}_3$ (M = Cd, Hg)
• Pressure-induced Superconductivity in Noncentrosymmetric Weyl Semimetals LaAlX (X = Si and Ge)
• TopologicalNumbers.jl: A Julia package for topological number computation
• Two-dimensional MX family of Dirac materials with tunable electronic and topological properties
• Increasing the number of topological nodal lines in semimetals via uniaxial pressure
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Shaping Maximally Localized Wannier Functions via Discrete Adiabatic Transport
• Topological electronic structure of YbMg${}_2$Bi${}_2$ and CaMg${}_2$Bi${}_2$
• The possible coexistence of superconductivity and topological electronic states in 1T-RhSeTe
• The enabling electronic motif for topological insulation in ABO3 perovskites and its structural stability
• Substrate-induced magnetism and topological phase transition in silicene
• Topological Pseudospin Hall Effect and Multi-frequency Corner Modes in Kagome-based Lattices
• Hinge modes of three-dimensional Euler insulators
• Systematic study for two-dimensional $Z_2$ topological phase transitions at high-symmetry points in all layer groups
• Exact Mappings in Condensed Matter Physics
• Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
• Topological property of graphene with triangular array of nanoholes
• Periodic Behavior of Topology in Graphene with Nanohole Array
• Tunable SSH model in ferromagnetic systems
• Zero Indirect Band Gap and Flat Bands in a Niobium Oxyiodide Cluster Material
• Three-dimensional spinless Euler insulators with rotational symmetry
• Comparison of finite-temperature topological indicators based on Uhlmann connection
• A first-principles investigation of Topological Phase Transition in face-centred cubic LiMgBi
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Graphyne as a second-order and real Chern topological insulator in two dimensions
• Kagome edge states under lattice termination, spin-orbit coupling, and magnetic order