Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly

TL;DR

This paper demonstrates that surface rotation anomalies in topological crystalline insulators with superconductivity lead to double Majorana zero modes in vortices, with a rich topological classification influenced by symmetry and chemical potential.

Contribution

It reveals how surface rotation anomalies and symmetries in TCIs induce double Majorana modes and expand vortex topological classifications beyond previous models.

Findings

Majorana zero modes bound to vortices depend on chemical potential.

Rotation symmetry enriches vortex classification from Z2 to Z2×Z2.

Magnetic-mirror symmetry further enhances topological classification to Z×Z.

Abstract

The interplay of time-reversal and $n$-fold rotation symmetries ($n=2,4,6$) is known to bring a new class of topological crystalline insulators (TCIs) having $n$ surface Dirac cones due to surface rotation anomaly. We show that the proximity-induced $s$-wave superconductivity on the surface of these TCIs yields a topological superconducting phase in which two Majorana zero modes are bound to a vortex, and that $n$-fold rotation symmetry ($n=2,4,6$) enriches the topological classification of a superconducting vortex from $\mathbb{Z}_2$ to $\mathbb{Z}_2\times\mathbb{Z}_2$. Using a model of a three-dimensional high-spin topological insulator with $s$-wave superconductivity and two-fold rotation symmetry, we show that, with increasing chemical potential, the number of Majorana zero modes at one end of a vortex changes as $2\to1\to0$ through two topological vortex phase transitions. In addition, we show that additional magnetic-mirror symmetry further enhances the topological classification to $\mathbb{Z} \times \mathbb{Z}$