Fermionic atoms in a spin-dependent optical lattice potential: topological insulators with broken time-reversal symmetry

TL;DR

This paper introduces a new method using spin-dependent optical lattices with fermionic atoms to explore topological phases and transitions, revealing rich band topology and edge states without time-reversal symmetry.

Contribution

It proposes a novel SDOL-based approach to study topological matter, demonstrating topological phase transitions and edge states in a system lacking time-reversal symmetry.

Findings

Identification of topological phase transitions driven by magnetic field.

Observation of topological edge states with non-trivial density and spin currents.

Rich energy band topology without parity-time-reversal symmetry.

Abstract

We propose a novel approach to study the topological properties of matter. In this approach, fermionic atoms are placed in an external magnetic field and in a two-dimensional spin-dependent optical lattice (SDOL) created by intersecting laser beams with a superposition of polarizations. To demonstrate the utility of the SDOL-based technique we compute the topological invariants (Chern numbers) for the SDOL bands as a function of an external magnetic field, and show the existence of a rich topology of the energy bands for this system which does not have parity-time-reversal symmetry. We explicitly consider $^{6}$Li $F=1/2$ atoms. Using a projection matrix method we observe topological phase transitions between an ordinary insulator, an abelian topological insulator, and a non-abelian topological insulator as the external magnetic field strength is varied. Upon introducing edges for the SDOL we find topological edge states (that are correlated with the band Chern numbers) that simultaneously exhibit non-trivial density and spin currents with both a rotational flow contribution and flow along the edge of the SDOL.