Majorana bound states in a disordered quantum dot chain

TL;DR

This paper investigates the stability of Majorana bound states in a disordered quantum dot chain, revealing their robustness against certain types of disorder and identifying conditions that lead to topological phase transitions.

Contribution

It introduces a method to identify topological phases in disordered quantum dot chains and analyzes the effects of different disorder types on Majorana states.

Findings

Majorana states are sensitive to strong spin-independent disorder.

Majorana states are robust against uniform spin-flip disorder.

Sign-flip in spin-flip hopping induces topological phase transitions.

Abstract

We study Majorana bound states in a disordered chain of semiconductor quantum dots proximity-coupled to an s-wave superconductor. By calculating its topological quantum number, based on the scattering-matrix method and a tight-binding model, we can identify the topological property of such an inhomogeneous one-dimensional system. We study the robustness of Majorana bound states against disorder in both the spin-independent terms (including the chemical potential and the regular spin-conserving hopping) and the spin-dependent term, i.e., the spin-flip hopping due to the Rashba spin-orbit coupling. We find that the Majorana bound states are not completely immune to the spin-independent disorder, especially when the latter is strong. Meanwhile, the Majorana bound states are relatively robust against spin-dependent disorder, as long as the spin-flip hopping is of uniform sign (i.e., the varying spin-flip hopping term does not change its sign along the chain). Nevertheless, when the disorder induces sign-flip in spin-flip hopping, the topological-nontopological phase transition takes place in the low-chemical-potential region.