Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene

Abstract

We construct the general extension of the four-dimensional Jackiw-Rossi-Dirac Hamiltonian that preserves the antilinear reflection symmetry between the positive and negative energy eigenstates. Among other systems, the resulting Hamiltonian describes the s-wave superconducting vortex at the surface of the topological insulator, at a finite chemical potential, and in the presence of both Zeeman and orbital couplings to the external magnetic field. Here we find that the bound zero-mode exists only when the Zeeman term is below a critical value. Other physical realizations pertaining to graphene are considered, and some novel zero-energy wave functions are analytically computed.

6 revtex pages; typos corrected, published version

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Interactions and phase transitions on graphene's honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Theory of interacting electrons on the honeycomb lattice
• Chiral Gauge Theory for Graphene
• Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice
• Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate
• Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene
• Restoration of the magnetic hc/e-periodicity in unconventional superconductors
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• Persistence of zero modes in a gauged Dirac model for bilayer graphene
• Dirac-Bogoliubov-deGennes quasiparticles in a vortex lattice

Cited by in corpus (17)

• Topological classification of defects in non-Hermitian systems
• Antiunitary symmetry protected higher order topological phases
• Absence of interaction corrections in graphene conductivity
• Universality of conductivity in interacting graphene
• Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models
• Quantum phase transition and fractional excitations in a topological insulator thin film with Zeeman and excitonic masses
• Asymmetric spatial structure of zero modes for birefringent Dirac fermions
• Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension
• Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions
• Pairing symmetry and vortex zero-mode for superconducting Dirac fermions
• Quantum critical point in the superconducting transition on the surface of topological insulator
• $Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions
• Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene
• D3-D7 Holographic dual of a perturbed 3D CFT
• Bogoliubov quasiparticles coupled to the antiferromagnetic spin mode in a vortex core
• Half vortex and fractional electrical charge in two dimensions
• Zero modes and index theorems for non-Hermitian Dirac fermions