# Majorana Kramers pair in a nematic vortex

## TL;DR

This paper demonstrates that a nematic vortex in an odd-parity topological superconductor can host Majorana Kramers pairs without breaking time-reversal symmetry, with potential realization in doped Bi2Se3.

## Contribution

It introduces the concept of a TR-invariant nematic vortex hosting Majorana Kramers pairs and provides analytic solutions for zero modes in such vortices.

## Key findings

- Nematic vortices can host Majorana Kramers pairs without magnetic fields.
- Analytic solutions for zero modes in continuous nematic vortices are provided.
- Discrete nematic vortices formed by domain meeting also support Majorana modes.

## Abstract

A time-reversal (TR) invariant topological superconductor is characterized by a Kramers pair of Majorana zero-energy modes on boundaries and in a core of a TR invariant vortex. A vortex defect that preserves TR symmetry has remained primarily of theoretical interest, since typically a magnetic field, which explicitly breaks TR, needs to be applied to create vortices in superconductors. In this work, we show that an odd-parity topological superconductor with a nematic pairing order parameter can host a nematic vortex that preserves TR symmetry and binds a Majorana Kramers pair. Such a nematic superconductor could be realized in metal-doped Bi$_2$Se$_3$, as suggested by recent experiments. We provide an analytic solution for the zero modes in a continuous nematic vortex. In lattice, crystalline anisotropy can pin the two-component order parameter along high-symmetry directions. We show that a discrete nematic vortex, which forms when three nematic domains meet, also supports a TR pair of Majorana modes. Finally, we discuss possible experiments to probe the zero modes.