Fermionic atoms in a spin-dependent optical lattice potential as a topological insulator

Zoom link: https://us06web.zoom.us/j/84410325975?pwd=d3Rwa3FaeHk3dG1CMk1TVHNJeFZlQT09

Abstract

We propose a new method to study topological properties of matter by putting fermionic atoms in an external magnetic field and a 2D spin-dependent optical lattice (SDOL). To reveal the utility of SDOL-based technique we calculate topological invariants for the SDOL bands as a function of an external magnetic field, demonstrating the existence of a rich topology of the energy bands. We observe topological phase transitions between an ordinary insulator, an Abeliean 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 correlate with the band Chern numbers and which exhibit simultaneously nontrivial density and spin currents having both a rotational flow contribution and flow along the edge of the SDOL.