Topological classification of intrinsic 3D superconductors using anomalous surface construction

Abstract

Intrinsic topological superconductors have protected gapless Majorana modes, bound and/or propagating, at the natural boundaries of the sample, without requiring field, defect, or heterostructure. We establish the complete classification/construction of intrinsic topological superconductors jointly protected by point-group and time-reversal symmetries in three dimensions. This is obtained from enumerating distinct ways for stacking $n$th-order irreducible building blocks, minimal anomalous surface states of $n$th-order topological superconductors. Particularly, our method provides a unified description of possible surface anomalies away from high-symmetry points/lines in terms of the homotopy group of the surface mass field.

43 pages, 9 figures, 6 tables

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Topological Crystalline Insulators
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Topology of crystalline insulators and superconductors
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Axion topological field theory of topological superconductors
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator

Cited by in corpus (10)

• Topological Superconductivity from Unconventional Band Degeneracy with Conventional Pairing
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Higher-order topological superconductors characterized by Fermi level crossings
• Diversified Ruderman-Kittel-Kasuya-Yosida Interactions in a Nonsymmorphic Crystal
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators