Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices

Abstract

We formulate the lattice version of the three-dimensional SU(2) Landau level problem with time reversal invariance. By taking a Landau-type gauge, the system is reduced into the one-dimensional SU(2) Harper equation characterized by a periodic spin-dependent gauge potential. The surface spectra indicate the spatial separation of helical states with opposite eigenvalues of the lattice helicty operator. The band topology is investigated from both the analysis of the boundary helical Fermi surfaces and the calculation of the Z2-index based on the bulk wavefunctions. The transition between a 3D weak topological insulator to a strong one is studied as varying the anisotropy of hopping parameters.

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Cited by in corpus (8)

• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory