Generating end modes in a superconducting wire by periodic driving of the hopping

TL;DR

This paper demonstrates that periodic modulation of hopping in a p-wave superconducting wire can induce localized end modes, including unusual anomalous modes with complex Floquet eigenvalues, revealing a novel bulk-boundary correspondence.

Contribution

It introduces a method to generate and analyze end modes in a superconducting wire through periodic driving of the hopping amplitude, highlighting the existence of anomalous Floquet end modes.

Findings

Periodic driving creates end-localized modes in superconducting wires.

Anomalous end modes with complex Floquet eigenvalues are identified.

Bulk-boundary correspondence relates Floquet eigenvalues to end mode peaks.

Abstract

We show that harmonic driving of either the magnitude or the phase of the nearest-neighbor hopping amplitude in a p-wave superconducting wire can generate modes localized near the ends of the wire. The Floquet eigenvalues of these modes can either be equal to $\pm 1$ (which is known to occur in other models) or can lie near other values in complex conjugate pairs which is unusual; we call the latter anomalous end modes. All the end modes have equal probabilities of particles and holes. If the amplitude of driving is small, we observe an interesting bulk-boundary correspondence: the Floquet eigenvalues and the peaks of the Fourier transform of the end modes lie close to the Floquet eigenvalues and momenta at which the Floquet eigenvalues of the bulk system have extrema.