A new class of $(2+1)$-d topological superconductor with ${\mathbb{Z}}_8$ topological classification

Abstract

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a ${\mathbb{Z}}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by ${\mathbb{Z}}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.

5 pages main text and 3 pages appendix. 1 figure

References in corpus (5)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Topological field theory and thermal responses of interacting topological superconductors

Cited by in corpus (113)

• Classification of topological quantum matter with symmetries
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Topological Superconductivity in Twisted Multilayer Graphene
• Interacting fermionic topological insulators/superconductors in three dimensions
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Classification of interacting electronic topological insulators in three dimensions
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Subsystem symmetry protected topological order
• Topological phases protected by point group symmetry
• Interaction effect on topological classification of superconductors in two dimensions
• State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Topological Transition on the Conformal Manifold
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Theory of interacting topological crystalline insulators
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Fractal Symmetric Phases of Matter
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Symmetry-protected topological invariants of symmetry-protected topological phases of interacting bosons and fermions
• Global Anomalies on the Hilbert Space
• Discrete Theta Angles, Symmetries and Anomalies
• Exotic Quantum Phase Transitions of $(2+1)d$ Dirac fermions
• Symmetric Mass Generation
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Symmetric Fermion Mass Generation as Deconfined Quantum Criticality
• Construction and classification of symmetry protected topological phases in interacting fermion systems
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Composite Dirac liquids: parent states for symmetric surface topological order
• Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Chiral-symmetry protected exceptional torus in correlated nodal-line semi-metals
• Comments on Symmetric Mass Generation in 2d and 4d
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Symmetry protected topological phases under decoherence
• Bona fide interaction-driven topological phase transition in correlated SPT states
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Non-Hermitian Mott Skin Effect
• Exceptional band touching for strongly correlated systems in equilibrium
• Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions
• Anomalous Symmetries End at the Boundary
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model
• Duality Defects in $E_8$
• Decorated ${\mathbb{Z}}_2$ Symmetry Defects and Their Time-Reversal Anomalies
• CPT theorem and classification of topological insulators and superconductors
• Edge quantum criticality and emergent supersymmetry in topological phases
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators
• Gapped Chiral Fermions
• Weak symmetry breaking in two dimensional topological insulators
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Fermion masses through four-fermion condensates
• The fate and heir of Majorana zero modes in a quantum wire array
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Quantum Monte Carlo study of strange correlator in interacting topological insulators
• Fermion masses without symmetry breaking in two spacetime dimensions
• Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry
• Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors
• Correlation effects on topological crystalline insulators
• Fermion decoration construction of symmetry protected trivial orders for fermion systems with any symmetries $G_f$ and in any dimensions
• Dimensional hierarchy of fermionic interacting topological phases
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Fate of exceptional points under interactions: Reduction of topological classifications
• Chiral Lattice Fermions From Staggered Fields
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• Reduction of topological $\mathbb{Z}$ classification in cold atomic systems
• Fermi Surface Symmetric Mass Generation
• Disentangling interacting symmetry protected phases of fermions in two dimensions
• Partition Functions and Stability Criteria of Topological Insulators
• Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Bosonic Short Range Entangled states Beyond Group Cohomology classification
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• Topological Defects in Floquet Circuits
• Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom
• Definition and Classification of Fermi Surface Anomalies
• Interacting topological mirror excitonic insulator in one dimension
• Criteria for protected edge modes with ${\mathbb{Z}}_2$ symmetry
• Gauging anomalous unitary operators
• Interacting Topological Insulators with Synthetic Dimensions
• Topological phases of parafermionic chains with symmetries
• Topological Charge/spin density Wave in InAs/GaSb Quantum Wells under an In-plane Magnetic Field
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Notes on 8 Majorana Fermions
• Fermionic Symmetry Protected Topological Phase Induced by Interactions
• Interacting topological phases in thin films of topological mirror Kondo insulators
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries
• A search for correlation-induced adiabatic paths between distinct topological insulators
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Stacking Group Structure of Fermionic Symmetry-Protected Topological Phases
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Topological Dipole Insulator
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases