Robustness of Majorana bound states in the short junction limit

Abstract

We study the effects of strong coupling between a superconductor and a semiconductor nanowire on the creation of the Majorana bound states, when the quasiparticle dwell time in the normal part of the nanowire is much shorter than the inverse superconducting gap. This "short junction" limit is relevant for the recent experiments using the epitaxially grown aluminum characterized by a transparent interface with the semiconductor and a small superconducting gap. We find that the small superconducting gap does not have a strong detrimental effect on the Majorana properties. Specifically, both the critical magnetic field required for creating a topological phase and the size of the Majorana bound states are independent of the superconducting gap. The critical magnetic field scales with the wire cross section, while the relative importance of the orbital and Zeeman effects of the magnetic field is controlled by the material parameters only: $g$-factor, effective electron mass, and the semiconductor-superconductor interface transparency.

13 pages, 12 Figures

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• Andreev rectifier: a nonlocal conductance signature of topological phase transitions
• Full proximity treatment of topological superconductors in Josephson-junction architectures
• Progress in superconductor-semiconductor topological Josephson junctions
• Renormalization of the Majorana bound state decay length in a perpendicular magnetic field
• Microwave Sensing of Andreev Bound States in a Gate-Defined Superconducting Quantum Point Contact
• Non-local transport signatures of topological superconductivity in a phase-biased planar Josephson junction
• Enhancement of the topological regime in elongated Josephson junctions
• Interplay between evanescent scattering modes and finite dispersion in superconducting junctions