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

TL;DR

This paper formulates a 3D SU(2) lattice Landau level problem with time reversal symmetry, analyzing topological phases and surface states, revealing transitions between weak and strong topological insulators.

Contribution

It introduces a lattice model for the 3D SU(2) Landau problem with time reversal symmetry and studies its topological phase transitions.

Findings

Identification of helical surface states with opposite lattice helicity

Calculation of Z2 topological indices confirming topological phases

Observation of phase transition from weak to strong topological insulator

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.