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.

arXiv comment43 pages, 9 figures, 6 tables

References in corpus (102)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Helical liquids and Majorana bound states in quantum wires
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• 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
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Dirac semimetal in three dimensions
• Topological nodal semimetals
• Topological superconductors: a review
• Colloquium: Topological Band Theory
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Topological Crystalline Insulators in the SnTe Material Class
• Majorana fermions in a tunable semiconductor device
• The (High Quality) Topological Materials In The World
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Topological nodal line semimetals with and without spin-orbital coupling
• Catalogue of Topological Electronic Materials
• Higher-Order Topology in Bismuth
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Topological Superconductivity in CuxBi2Se3
• Topological classification of crystalline insulators through band structure combinatorics
• Majorana mode in vortex core of Bi2Te3/NbSe2 topological insulator-superconductor heterostructure
• Chiral Topological Superconductor From the Quantum Hall State
• Topology of crystalline insulators and superconductors
• Topological superconducting phase in helical Shiba chains
• Evaluation of Spin-Triplet Superconductivity in Sr2RuO4
• Charge Transport in Weyl Semimetals
• Hourglass Fermions
• Microscopic evidence for a chiral superconducting order parameter in the heavy fermion superconductor UTe2
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Chiral Superconductors
• Topological Quantum Computation Based on Chiral Majorana Fermions
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Fermi Surface Topological Invariants for Time Reversal Invariant Superconductors
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Time Reversal Invariant Topological Superconductivity and Majorana Kramers Pairs
• Topological odd-parity superconductors
• Topological superconductivity on the surface of Fe-based superconductors
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Robust and clean Majorana zero mode in the vortex core of high-temperature superconductor (Li0.84Fe0.16)OHFeSe
• Topological Mirror Superconductivity
• Weak-Pairing Higher Order Topological Superconductors
• Observation of half-integer level shift of vortex bound states in an iron-based superconductor
• Majorana Kramers pairs in higher-order topological insulators
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Flux-induced Majorana modes in full-shell nanowires
• Topological superconductivity in full shell proximitized nanowires
• Flux-induced topological superconductivity in full-shell nanowires
• Topological phases protected by point group symmetry
• Signature of Dispersing 1D Majorana Channels in an Iron-based Superconductor
• Building crystalline topological phases from lower-dimensional states
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Gauging spatial symmetries and the classification of topological crystalline phases
• Rotation Anomaly and Topological Crystalline Insulators
• Majorana bound states without vortices in topological superconductors with electrostatic defects
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Majorana bound states in magnetic skyrmions
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Majorana Fermion Surface Code for Universal Quantum Computation
• Theory of interacting topological crystalline insulators
• Axion topological field theory of topological superconductors
• Quaternion, harmonic oscillator, and high-dimensional topological states
• Topological states from topological crystals
• Tunable vortex Majorana zero modes in LiFeAs superconductor
• Braiding Majorana corner modes in a second-order topological superconductor
• Topological quantum states of matter in iron-based superconductors: From concepts to material realization
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Measurement-only quantum computation with Majorana corner modes
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Quantum anomalous vortex and Majorana zero mode in iron-based superconductor Fe(Te,Se)
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Real-space recipes for general topological crystalline states
• Higher order topological superconductors as generators of quantum codes
• Minimalist approach to the classification of symmetry protected topological phases
• Bound states of a ferromagnetic wire in a superconductor
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Artificial Graphene: Unconventional Superconductivity in a Honeycomb Superlattice
• The classification of surface states of topological insulators and superconductors with magnetic point group symmetry
• High-$T_c$ Superconductor Fe(Se,Te) Monolayer: an Intrinsic, Scalable and Electrically-tunable Majorana Platform
• Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly

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• 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