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

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 $2\to 1\to 0$ through two topological vortex phase transitions. In addition, we show that additional magnetic-mirror symmetry further enhances the topological classification to $\mathbb{Z}\times \mathbb{Z}$

10 pages, 4 figures

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• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Fragile topology in nodal-line semimetal superconductors
• Fusion Rules of Majorana-Kramer-Pairs in Time-Reversal-Invariant Topological Superconductors
• Angular momentum of vortex-core Majorana zero modes
• Coexistence of gapless and gapped vortex modes with Majorana corner states in a 2D second-order topological superconductor
• Majorana Zero Modes and Topological Nature in Bi2Ta3S6-family Superconductors
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators