Topological Phases for Fermionic Cold Atoms on the Lieb Lattice

TL;DR

This paper explores topological phases in fermionic cold atoms on the Lieb lattice, demonstrating quantum Hall and spin Hall effects induced by gauge fields, and proposes experimental schemes for realization with cold atoms.

Contribution

It introduces a model for topological phases in cold atoms on the Lieb lattice, including methods to realize gauge fields and spin-orbit coupling experimentally.

Findings

Observation of quantum Hall effect due to Abelian gauge fields.

Demonstration of quantum spin Hall effect with non-Abelian gauge fields.

Proposal of experimental schemes for cold atom realization.

Abstract

We investigate the properties of the Lieb lattice, i.e a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the energy spectrum. Then we explore the effects of an intrinsic spin-orbit term - a non-Abelian gauge field - and demonstrate the occurrence of the quantum spin Hall effect in this model. Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at low energy and derive the Landau levels in the presence of external Abelian and non-Abelian gauge fields. Finally, we describe concrete schemes for realizing these gauge fields with cold fermionic atoms trapped in an optical Lieb lattice. In particular, we provide a very efficient method to reproduce the intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes. Consequently, our model could be implemented in order to produce a variety of topological states with cold-atoms.