Effect of disorders on topological phases in one-dimensional optical superlattices

Abstract

In a recent paper, Lang et al. proposed that edge states and topological phases can be observed in one-dimensional optical superlattices. They showed that the topological phases can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions. However, disorders are not considered in their model. To study the effect of disorders on the topological phases, we introduce random potentials to the model for optical superlattcies. Our calculations show that edge states are robust against the disorders. We find the edge states are very sensitive to the number of the sites in the optical superlattice and we propose a simple rule to describe the relationship between the edge states and the number of sites. The density plateaus are also robust against weak disorders provided that the average density is calculated over a long interval. The widths of the plateaus are proportional to the widths of the bulk energy gaps when there are disorders. The disorders can diminish the bulk energy gaps. So the widths of the plateaus decrease with the increase of disorders and the density plateaus disappear when disorders are too strong. The results in our paper can be used to guide the experimental detection of topological phases in one-dimensional systems.

Impurity-induced Shiba bound state in the BCS–BEC crossover regime of two-dimensional Fermi superfluid*

“…Experimental realizations of Fermi degeneracy and Fermi superfluid in ultra-cold atom systems have provided more opportunities for us to deepen our understanding of many important problems in condensed matter physics, [1,2] e.g., the topological superfluid phase. [3,4] In particular, interactions between different spin states can be tuned by the technique of Feshbach resonance. [5,6] Therefore, the system can change from weakly the interacting Bardeen-Cooper-Schrieffer (BCS) regime with loosely overlapping Cooper pairs to the strongly interacting Bose-Einstein condensation (BEC) regime with tightly bound molecules (BCS-BEC crossover).…”