Seeing Majorana fermions in time-of-flight images of spinless fermions coupled by s-wave pairing

TL;DR

This paper proposes a method using time-of-flight measurements to identify topological invariants in superconducting systems, enabling detection of Majorana fermions in cold atom experiments with robustness against experimental imperfections.

Contribution

It introduces a practical measurement scheme for detecting Chern numbers in superconductors, linking theoretical topological phases to observable experimental signatures.

Findings

The measurement scheme accurately identifies Chern numbers in simulated models.

The approach is robust against experimental inaccuracies and finite temperature effects.

Application to a spinless fermion model reveals phases supporting Majorana modes.

Abstract

The Chern number, nu, as a topological invariant that identifies the winding of the ground state in the particle-hole space, is a definitive theoretical signature that determines whether a given superconducting system can support Majorana zero modes. Here we show that such a winding can be faithfully identified for any superconducting system (p-wave or s-wave with spin-orbit coupling) through a set of time-of-flight measurements, making it a diagnostic tool also in actual cold atom experiments. As an application, we specialize the measurement scheme for a chiral topological model of spinless fermions. The proposed model only requires the experimentally accessible s-wave pairing and staggered tunnelling that mimics spin-orbit coupling. By adiabatically connecting this model to Kitaev's honeycomb lattice model, we show that it gives rise to nu = \pm 1 phases, where vortices bind Majorana fermions, and nu=\pm 2 phases that emerge as the unique collective state of such vortices. Hence, the preparation of these phases and the detection of their Chern numbers provide an unambiguous signature for the presence of Majorana modes. Finally, we demonstrate that our detection procedure is resilient against most inaccuracies in experimental control parameters as well as finite temperature.