Emergence of multiple zero modes bound to vortices in extended topological Josephson junctions

TL;DR

This paper investigates the conditions under which multiple zero-energy modes emerge in topological Josephson junctions on 3D topological insulators, revealing new Dirac cones and symmetry-protected zero modes that impact observable quantum phenomena.

Contribution

It demonstrates the breakdown of the Fu-Kane effective theory at zero effective velocity and identifies the emergence of additional zero modes bound to vortices under certain conditions.

Findings

Multiple zero modes can appear at vortices in extended topological Josephson junctions.

Additional zero modes are symmetry-protected and can be lifted by symmetry-breaking.

Presence of extra low-energy states affects Josephson current and microwave spectra.

Abstract

We study planar Josephson junctions formed on the surface of a three-dimensional topological insulator (Fu-Kane proposal) and examine the experimentally relevant parameter regimes in which the effective velocity of the emergent one-dimensional Majorana modes approaches zero. We show that the frequently employed Fu-Kane effective theory breaks down in this case. As parameters like the chemical potential or the width of the junction are tuned, instances of vanishing effective velocity mark the emergence of additional 'Dirac cones' at zero energy and finite momentum. If the junction is subjected to an external magnetic field, Josephson vortices may then bind a number of zero modes in addition to the topological Majorana mode. The additional zero modes are 'symmetry-protected' and can be lifted by a broken mirror symmetry (which is to be expected in realistic scenarios) as well as by an in-plane magnetization (or Zeeman field). We note that the ensuing presence of additional low-energy Andreev states can significantly contribute to measured quantities like the Josephson current or microwave absorption spectra.