Majorana Modes of Giant Vortices

TL;DR

This paper analytically studies Majorana zero modes in giant vortices within topological superconductors, revealing their structure, robustness, and experimental signatures, which differ from previous estimates and depend mainly on vortex radius.

Contribution

It provides an analytic solution for Majorana zero modes in large winding number vortices, showing their structure and robustness, and predicts observable signatures for experiments.

Findings

Zero modes are not pinned to the vortex boundary.

Majorana modes are composed of warped Landau level states.

Local density of states shows signatures for experimental detection.

Abstract

We study Majorana zero modes bound to giant vortices in topological superconductors or topological insulator/normal superconductor heterostructures. By expanding in inverse powers of a large winding number $n$, we find an analytic solution for asymptotically all $n$ zero modes required by the index theorem. Contrary to the existing estimates, the solution is not pinned to the vortex boundary and is composed of the warped lowest Landau level states. While the dynamics which shapes the zero modes is a subtle interference of the magnetic effects and Andreev reflection, the solution is very robust and is determined by a single parameter, the vortex radius. The resulting local density of states has a number of features which give remarkable signatures for an experimental observation of the Majorana fermions in two dimensions.