Effect of incommensurate disorder on the resonant tunneling through Majorana bound states on the topological superconductor chains

TL;DR

This study investigates how incommensurate disorder affects electron transport in topological superconducting chains, revealing robust Majorana states with quantized conductance and a disorder-driven phase transition.

Contribution

It demonstrates the resilience of Majorana bound states against incommensurate disorder and identifies the critical disorder strength for topological phase transition.

Findings

Quantized conductance of e^2/h persists over wide parameter range.

Disorder suppresses current and narrows the linear response regime.

Critical disorder causes a transition to localized phase with zero conductance.

Abstract

We study the transport through the Kitaev's chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of $e^2/h$, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate disorder suppresses the current at finite voltage bias, and then narrows the linear response regime of the $I-V$ curve which exhibits two plateaus corresponding to the superconducting gap and the band edge respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value $2+2\Delta$ with $\Delta$ the p-wave pairing amplitude, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage will also cause an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose $I-V$ curve exhibits an exponential shape.