Three-Band Model for Quantum Hall and Spin Hall Effects

Abstract

Topological properties of a certain class of spinless three-band Hamiltonians are shown to be summed up by the Skyrmion number in momentum space, analogous to the case of two-band Hamiltonian. Topological tight-binding Hamiltonian on a Kagome lattice is analyzed with this view. When such a Hamiltonian is "folded", the two bands with opposite Chern numbers merge into a degenerate band exhibiting non-Abelian gauge connection. Conserved pseudo-spin current operator can be constructed in this case and used to compute the pseudo-spin Hall conductance. Our model Hamiltonians belong to the symmetry class D and AI according to the ten-fold classification scheme.

5 pages, 1 figure

References in corpus (9)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
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• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
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• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Spiral spin textures of bosonic Mott insulator with SU(3) spin-orbit coupling
• Weyl-triplons in SrCu2(BO3)2
• $SU(3)$ Topological Insulators in the Honeycomb Lattice
• Realization of a transition between type-I and type-II Dirac semimetals in monolayers
• Effect of hybridization symmetry on topological phases of odd-parity multiband superconductors
• Soliton Defects in One-dimensional Topological Three-band Hamiltonian
• Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions