Demonstrating Lattice-Symmetry-Protection in Topological Crystalline Superconductors

Abstract

We propose to study the lattice-symmetry protection of Majorana zero bound modes in topological crystalline superconductors (SCs). With an induced $s$-wave superconductivity in the $(001)$-surface of the topological crystalline insulator Pb${}_{1-x}$Sn${}_x$Te, which has a C${}_4$ rotational symmetry, we show a new class of 2D topological SC with four Majorana modes obtained in each vortex core, while only two of them are protected by the cyclic symmetry. Furthermore, applying an in-plane external field can break the four-fold symmetry and lifts the Majorana modes to finite energy states in general. Surprisingly, we show that even the C${}_4$ symmetry is broken, two Majorana modes are restored exactly one time whenever the in-plane field varies $\pi /2$, i.e. $1/4$-cycle in the direction. This novel phenomenon has a profound connection to the four-fold cyclic symmetry of the original crystalline SC and uniquely demonstrates the lattice-symmetry protection of the Majorana modes. We further generalize these results to the system with generic C${}_{2N}$ symmetry, and show that the symmetry class of the topological crystalline SC can be demonstrated by the $2N$ times of restoration of two Majorana modes when the external symmetry-breaking field varies one cycle in direction.

4+pages, 2 figures. Figures and discussions have been updated

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Cited by in corpus (18)

• Classification of topological quantum matter with symmetries
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Majorana Fermions and Topology in Superconductors
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
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• Weak-link Josephson Junctions Made from Topological Crystalline Insulators
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Non-Abelian Majorana modes protected by an emergent second Chern number
• Competing Vortex Topologies in Iron-based Superconductors
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Lattice symmetries and the topological protected transport of colloidal particles
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• Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes
• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Angular momentum of vortex-core Majorana zero modes
• Fusion Rules of Majorana-Kramer-Pairs in Time-Reversal-Invariant Topological Superconductors