Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder

TL;DR

This paper investigates a spin-1/2 fermionic ladder with spin-orbit coupling and magnetic field, identifying topological phases via fractional edge modes and winding numbers, and proposes experimental detection methods with cold atoms, also analyzing interaction effects.

Contribution

It characterizes the topological phase of a fermionic ladder with spin-orbit coupling, proposing experimental schemes for detection and exploring interaction effects on topological stability.

Findings

Identification of fractionalized edge modes

Proposal of protocols for topological signature detection

Interactions can extend the topological phase

Abstract

We consider a spin-1/2 fermionic ladder with spin-orbit coupling and a perpendicular magnetic field, which shares important similarities with topological superconducting wires. We fully characterize the symmetry-protected topological phase of this ladder through the identification of fractionalized edge modes and non-trivial spin winding numbers. We propose an experimental scheme to engineer such a ladder system with cold atoms in optical lattices, and we present two protocols that can be used to extract the topological signatures from density and momentum-distribution measurements. We then consider the presence of interactions and discuss the effects of a contact on-site repulsion on the topological phase. We find that such interactions could enhance the extension of the topological phase in certain parameters regimes.