Existence of Majorana-Fermion Bound States on Disclinations and the Classification of Topological Crystalline Superconductors in Two Dimensions

Jeffrey C. Y. Teo; Taylor L. Hughes

doi:10.1103/PhysRevLett.111.047006

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Existence of Majorana-Fermion Bound States on Disclinations and the Classification of Topological Crystalline Superconductors in Two Dimensions

Jeffrey C. Y. Teo, Taylor L. Hughes

DOI 10.1103/PhysRevLett.111.047006 · Physical Review Letters

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Abstract

We prove a topological criterion for the existence of a zero-energy Majorana bound state on a disclination, a rotation symmetry breaking point defect, in fourfold symmetric topological crystalline superconductors (TCS) in two dimensions. We first establish a complete topological classification of TCS using the Chern invariant and three integral rotation invariants. By analytically and numerically studying disclinations, we algebraically deduce a Z2 index that identifies the parity of the number of Majorana zero modes at a disclination. Surprisingly, we also find weakly protected Majorana fermions bound at the corners of superconductors with trivial Chern and weak invariants.