Relation between scattering matrix topological invariants and conductance in Floquet Majorana systems

TL;DR

This paper investigates the relationship between topological invariants derived from scattering matrices and conductance measurements in Floquet Majorana systems, revealing a close quantitative link and protocol-dependent discrepancies.

Contribution

It demonstrates that the sum of conductance at multiples of the driving frequency closely matches stroboscopic conductance, and analyzes protocol-dependent differences in a driven Kitaev chain.

Findings

Sum of DC conductance at voltages multiples of the driving frequency approximates stroboscopic conductance.

Quantitative differences depend on the driving protocol and the zero mode weight at the chain end.

Discrepancies are larger when the zero mode weight varies strongly with the offset time.

Abstract

We analyze the conductance of a one-dimensional topological superconductor periodically driven to host Floquet Majorana zero-modes for different configurations of coupling to external leads. We compare the conductance of constantly coupled leads, as in standard transport experiments, with the stroboscopic conductance of pulsed coupling to leads used to identify a scattering matrix topological index for periodically driven systems. We find that the sum of DC conductance at voltages multiples of the driving frequency is quantitatively close to the stroboscopic conductance at all voltage biases. This is consistent with previous work which indicated that the summed conductance at zero/pi resonance is quantized. We quantify the difference between the two in terms of the width of their respective resonances and analyze that difference for two different stroboscopic driving protocols of the Kitaev chain. While the quantitative differences are protocol-dependent, we find that generically the discrepancy is larger when the zero mode weight at the end of the chain depends strongly on the offset time between the driving cycle and the pulsed coupling period.