Dimensional crossover in spin-orbit-coupled semiconductor nanowires with induced superconducting pairing

TL;DR

This paper demonstrates that zero-energy states in short and long spin-orbit-coupled superconducting nanowires are connected, with tunable crossings protected by symmetry, revealing key aspects of Majorana physics observable in experiments.

Contribution

It shows the adiabatic connection between Majorana modes in long wires and zero-energy states in short wires, clarifying their relation and experimental signatures.

Findings

Zero-energy crossings can be tuned by magnetic field.

These states are protected by particle-hole symmetry.

The low-energy physics in short and long wires are related.

Abstract

We show that the topological Majorana modes in nanowires much longer than the superconducting coherence length are adiabatically connected with discrete zero-energy states generically occurring in short nanowires. We demonstrate that these zero-energy crossings can be tuned by an external magnetic field and are protected by the particle-hole symmetry. We study the evolution of the low-energy spectrum and the splitting oscillations as a function of magnetic field, wire length, and chemical potential, manifestly establishing that the low-energy physics of short wires is related to that occurring in long wires. This physics, which represents a hallmark of spinless p-wave superconductivity, can be observed in tunneling conductance measurements.