Topological meaning of Z${}_2$ numbers in time reversal invariant systems

Abstract

We show that the Z${}_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is the basic topological invariant characterizing time reversal systems, we show that the relative phase between the Kramers doublet reduces the topological quantum number Z to Z${}_2$.

arXiv comment4 pages, typos corrected

References in corpus (18)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Topological invariants of time-reversal-invariant band structures
• Quantum Spin Hall Effect
• Universal Intrinsic Spin-Hall Effect
• Dissipationless Quantum Spin Current at Room Temperature
• Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Quantum spin Hall effect in three dimensional materials: Lattice computation of Z${}_2$ topological invariants and its application to Bi and Sb
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Explicit Gauge Fixing for Degenerate Multiplets: A Generic Setup for Topological Orders
• Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect

Cited by in corpus (18)

• Topological Insulators
• Non-Hermitian Boundary Modes
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Measurement of Chern numbers through center-of-mass responses
• ${\mathbb{Z}}_2$ Topological Invariant for Magnon Spin Hall Systems
• Z2 invariant protected bound states in topological insulators
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Floquet Hopf Insulators
• Three-dimensional topological magnon systems
• Notes on topological insulators
• Symmetry protected Z2-quantization and quaternionic Berry connection with Kramers degeneracy
• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• Quantization of non-Abelian Berry phase for time reversal invariant systems
• Real-space representation of the second Chern number
• A non-perturbative expression for the transmission through a leaky chiral edge mode
• Quantum Spin Hall Effect in a Three-orbital Tight-binding Hamiltonian