Classification of reflection symmetry protected topological semimetals and nodal superconductors

Abstract

While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superconductor), (ii) whether the mirror symmetry commutes or anticommutes with the nonspatial symmetries and (iii) how the Fermi surfaces (nodal lines or points) transform under the mirror reflection and nonspatial symmetries. The classification is derived by examining all possible symmetry-allowed mass terms that can be added to the Bloch or Bogoliubov-de Gennes Hamiltonian in a given symmetry class and by explicitly deriving topological invariants. We discuss several examples of reflection symmetry protected topological semimetals and nodal superconductors, including topological crystalline semimetals with mirror ${\mathbb{Z}}_2$ numbers and topological crystalline nodal superconductors with mirror winding numbers.

27 pages, 6 figures, 5 tables. Introduction video: http://www.youtube.com/watch?v=9_0TBJ7pYpw

References in corpus (18)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Quantum Spin Hall Effect: Theory and Experiment
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• The space group classification of topological band insulators
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Nodal Spin Density Wave and band topology of the FeAs based materials
• Topological Weyl Semi-metal from a Lattice Model
• Topological Blount's theorem of odd-parity superconductors
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Topologically protected flat zero-energy surface bands in non-centrosymmetric superconductors
• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors

Cited by in corpus (71)

• Topological nodal line semimetals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Non-Hermitian topological phenomena: A review
• Potential ring of Dirac nodes in a new polymorph of Ca${}_3$P${}_2$
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Topological Nodal Line Semimetals in CaP3 family of materials
• Topological surface states in nodal superconductors
• Quantum Transport in Topological Semimetals under Magnetic Fields
• Topological transition from nodal to nodeless Zeeman splitting in altermagnets
• Graph Theory Data for Topological Quantum Chemistry
• Observation of enhanced free-electron radiation from photonic flatband resonances
• Topological Semimetal Nanostructures: From Properties to Topotronics
• Inflated nodes and surface states in superconducting half-Heusler compounds
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Realizing exceptional points of any order in the presence of symmetry
• Photovoltaic anomalous Hall effect in line-node semimetals
• Surface floating 2D bands in layered nonsymmorphic semimetals: ZrSiS and related compounds
• Topologically stable gapless phases in nonsymmorphic superconductors
• Low Carrier Density Metal Realized in Candidate Line-Node Dirac Semimetals CaAgP and CaAgAs
• Crystalline Kitaev spin liquids
• Chern-Simons Theory and Wilson Loops in the Brillouin Zone
• Extended topological group structure due to average reflection symmetry
• Unconventional superconductivity in altermagnets with spin-orbit coupling
• Topological Nodal-Line Fermions in the Non-Centrosymmetric Superconductor Compound PbTaSe2
• Evidence of topological nodal lines and surface states in the centrosymmetric superconductor SnTaS2
• Nodal-line semimetals from Weyl superlattices
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Quantum anomalous Hall insulator in ionic Rashba lattice of correlated electrons
• S-wave Superconductivity in the Dirac Line-nodal Material CaSb2
• Nodal topological superconductivity in nodal-line semimetals
• Weyl nodal ring states and Landau quantization with very large magnetoresistance in square-net magnet EuGa${}_4$
• Topological Mott insulator in the odd-integer filled Anderson lattice model with Hatsugai-Kohmoto interactions
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Abundant surface-semimetal phases in three-dimensional obstructed atomic insulators
• Theoretical study of topological properties of ferromagnetic pyrite CoS${}_2$
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Type-I and type-II topological nodal superconductors with $s$-wave interaction
• Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between pairings restricted and extended in the $\text{k}$-space
• Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles
• Topology of chalcogen chains
• Spin-orbit enabled unconventional Stoner magnetism
• Dispersive Drumhead States in Nodal-Line Semimetal Junctions
• Multi higher-order Dirac and nodal line semimetals
• Tight-Binding Model and Electronic Property of Dirac Nodal Line in Single-Component Molecular Conductor [Pt(dmdt)${}_2$]
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors
• Noncollinear Magnetic Modulation of Weyl Nodes in Ferrimagnetic Mn${}_3$Ga
• From chiral d-wave to nodal line superconductivity in the harmonic honeycomb lattices
• Non-Bloch Dirac Points and Phase Diagram in the Stacked Non-Hermitian SSH Model
• Topological Degeneracy Induced by Twisting
• Layer Construction of Three-Dimensional Z2 Monopole Charge Nodal Line Semimetals and prediction of the abundant candidate materials
• Parallel and anti-parallel helical surface states for topological semimetals
• Two-dimensional flat band on the (011) surface of UTe${}_2$: Implication for STM measurements with a superconducting tip
• Takagi Topological Insulator on the Honeycomb Lattice
• Existence of nodal-arc and its evolution into Weyl-nodes in the presence of spin-orbit coupling in TaAs & TaP
• Electronic Structure of a Nodal Line Semimetal Candidate TbSbTe
• Emergent topology in thin films of nodal line semimetals
• Nodal-line semimetals and their variance
• Interfaces of nodal-line semimetals: drum states, transport and refraction
• Detecting the topological winding of superconducting nodes via Local Density of States
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Tunable zero-energy Dirac and Luttinger nodes in a two-dimensional topological superconductor
• Topological Light Nodal Lines in FCC Lattice
• Electronic band structure of a nodal line semimetal candidate ErSbTe
• Topological Fermi-arc-like surface states in Kramers nodal line metals
• Fragment-orbital-dependent spin fluctuations in the single-component molecular conductor [Ni(dmdt)${}_2$]
• Theory of Hofstadter Superconductors
• Nodal Line Topological Superfluid and Multiply Protected Majorana Fermi Arc in a Three-Dimensional Time-Reversal-Invariant Superfluid Model
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
• Conductivity scaling and absence of localization in disordered nodal line semimetals