Local formula for the $Z_2$ invariant of topological insulators

Abstract

We proposed a formula for the $Z_2$ invariant for topological insulators, which remains valid without translational invariance. Our formula is a local expression, in the sense that the contributions mainly come from quantities near a point. Using almost commute matrices, we proposed a method to approximate this invariant with local information. The validity of the formula and the approximation method is proved.

Final version published on PRB

References in corpus (9)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Sinc approximation of algebraically decaying functions
• On the $Z_2$ classification of Quantum Spin Hall Models
• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder

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• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Structural spillage: an efficient method to identify non-crystalline topological materials
• The KO-valued spectral flow for skew-adjoint Fredholm operators
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
• Topological phases of amorphous matter
• Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker