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

Understand

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.