Hidden symmetry-protected Z2 topological insulator in a cubic lattice

Abstract

Usually ${Z}_{2}$ topological insulators are protected by time-reversal symmetry. Here we present a new type of ${Z}_{2}$ topological insulators in a cubic lattice which is protected by a novel hidden symmetry, while time-reversal symmetry is broken. The hidden symmetry has a composite antiunitary operator consisting of fractional translation, complex conjugation, sublattice exchange, and local gauge transformation. Based on the hidden symmetry, we define the hidden symmetry polarization and ${Z}_{2}$ topological invariant to characterize the topological insulators. The surface states have band structures with an odd number of Dirac cones, where pseudospin-momentum locking occurs. When the hidden symmetry-breaking perturbations are added on the boundaries, a gap opens in the surface band structure, which confirms that the topological insulator and the surface states are protected by the hidden symmetry. We also discuss the realization and detection of this new kind of ${Z}_{2}$ topological insulator in optical lattices with ultracold atom techniques.