Low-energy in-gap states of vortices in superconductor-semiconductor heterostructures

Abstract

The recent interest in the low-energy states in vortices of semiconductor-superconductor heterostructures are mainly fueled by the prospects of using Majorana zero modes for quantum computation. The knowledge of low-lying states in the vortex core is essential as they pose a limitation on the topological computation with these states. Recently, the low-energy spectra of clean heterostructures, for superconducting-pairing profiles that vary slowly on the scale of the Fermi wavelength of the semiconductor, have been analytically calculated. In this work, we formulate an alternative method based on perturbation theory to obtain concise analytical formulas to predict the low-energy states including explicit magnetic-field and gap profiles. We provide results for both a topological insulator (with a linear spectrum) as well as for a conventional electron gas (with a quadratic spectrum). We discuss the spectra for a wide range of parameters, including both the size of the vortex and the chemical potential of the semiconductor, and thereby provide a tool to guide future experimental efforts. We compare these findings to numerical results.

10 pages, 9 figures

References in corpus (6)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Flux-induced topological superconductivity in full-shell nanowires
• Phase controlled superconducting proximity effect probed by tunneling spectroscopy
• Analytic Model for the Energy Spectrum of a Graphene Quantum Dot in a Perpendicular Magnetic Field
• Majorana state on the surface of a disordered 3D topological insulator
• Bound fermion states in pinned vortices in the surface states of a superconducting topological insulator: The Majorana bound state

Cited by in corpus (5)

• Statistical Majorana Bound State Spectroscopy
• Geometry-independent tight-binding method for massless Dirac fermions in two dimensions
• Influence of disorder on antidot vortex Majorana states in 3D topological insulators
• Interaction between spin and Abrikosov vortices in doped topological insulators
• Unveiling In-Gap States and Majorana Zero Modes in Superconductor-Topological Insulator Bilayer model