Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice

TL;DR

This paper introduces a new class of $Z_2$ topological insulators in cubic lattices protected by a novel hidden symmetry, independent of time reversal symmetry, with unique surface states and potential realization in ultracold atom systems.

Contribution

It proposes a new type of $Z_2$ topological insulator protected by a hidden symmetry involving complex operations, expanding the understanding of topological phases beyond time reversal symmetry.

Findings

Surface states exhibit odd number of Dirac cones with pseudospin-momentum locking.

Breaking the hidden symmetry opens a gap in surface states, confirming their topological protection.

Theoretical framework for hidden-symmetry polarization and $Z_2$ invariant is established.

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 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 aslo discuss the realization and detection of this new kind of $Z_2$ topological insulator in optical lattices with ultracold atom techniques.