Robustness of Topological Order in Semiconductor-Superconductor Nanowires in the Coulomb Blockade Regime

TL;DR

This paper demonstrates that topological order in semiconductor-superconductor nanowires can be detected through Coulomb blockade transport measurements, showing robustness against disorder and geometry variations, and highlights the extended coherence length in the nontrivial phase.

Contribution

It provides a novel method to identify topological phases via excitation spectra and flux periodicity, emphasizing robustness and potential for device applications.

Findings

Topological order causes an $h/e$ flux periodicity in the excitation spectrum.

The topological transition is marked by a gap closing and reopening.

The nontrivial phase exhibits a much longer coherence length.

Abstract

Semiconductor-superconductor hybrid systems are promising candidates for the realization Majorana fermions and topological order, i.e. topologically protected degeneracies, in solid state devices. We show that the topological order is mirrored in the excitation spectra and can be observed in nonlinear Coulomb blockade transport through a ring-shaped nanowire. Especially, the excitation spectrum is almost independent of magnetic flux in the topologically trivial phase but acquires a characteristic $h/e$ magnetic flux periodicity in the nontrivial phase. The transition between the trivial and nontrivial phase is reflected in the closing and reopening of an excitation gap. We show that the signatures of topological order are robust against details of the geometry, electrostatic disorder, and the existence of additional subbands and only rely on the topology of the nanowire and the existence of a superconducting gap. Finally, we show that the coherence length in the nontrivial phase is much longer than in the trivial phase. This opens the possibility to coat the nanowire with superconducting nanograins and thereby significantly reduce the current due to cotunneling of Cooper pairs and to enhance the Coulomb charging energy without destroying the superconducting gap.