Isospin of topological defects in Dirac systems

Abstract

We study the Dirac quasiparticles in $d$-dimensional lattice systems of electrons in the presence of domain walls ($d=1$), vortices ($d=2$), or hedgehogs ($d=3$) of superconducting and/or insulating, order parameters, which appear as mass terms in the Dirac equation. Such topological defects have been known to carry non-trivial quantum numbers such as charge and spin. Here we discuss their additional internal degree of freedom: irrespectively of the dimensionality of space and the nature of orders that support the defect, an extra mass-order-parameter is found to emerge in their core. Six linearly independent local orders, which close two mutually commuting three-dimensional Clifford algebras are proven to be in general possible. We show how the particle-hole symmetry restricts the defects to always carry the quantum numbers of a single effective isospin-1/2, quite independently of the values of their electric charge or true spin. Examples of this new degree of freedom in graphene and on surfaces of topological insulators are discussed.

7 PRB pages, one table, one figure; thoroughly revised and extended version, more discussion of physical examples in graphene and topological insulator surface, two Appendices with mathematical details, many new references; several typos corrected, published version

References in corpus (12)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• "Deconfined" quantum critical points
• Electron fractionalization in two-dimensional graphenelike structures
• Density waves and Cooper pairing on the honeycomb lattice
• Exciton condensation and charge fractionalization in a topological insulator film
• Theory of integer quantum Hall effect in graphene
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions
• Effective field theory with a $\theta$-vacua structure for 2d spin systems

Cited by in corpus (41)

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• Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
• Strain-induced time-reversal odd superconductivity in graphene
• SO(5) symmetry in the quantum Hall effect in graphene
• Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
• Fate of superconductivity in three-dimensional disordered Luttinger semimetals
• Skyrmions with quadratic band touching fermions: A way to achieve charge 4e superconductivity
• Excitonic instability of three-dimensional gapless semiconductors: Large-N theory
• Floquet scattering of quadratic band-touching semimetals through a time-periodic potential well
• Compatible orders and fermion-induced emergent symmetry in Dirac systems
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator
• Classification of massive and gapless phases in bilayer graphene
• Zero modes and charged Skyrmions in graphene bilayer
• Asymmetric spatial structure of zero modes for birefringent Dirac fermions
• Itinerant quantum multi-criticality of two dimensional Dirac fermions
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Tunneling in Fermi Systems with Quadratic Band Crossing Points
• Search for plasmons in isotropic Luttinger semimetals
• Emergent symmetries and coexisting orders in Dirac fermion systems
• Bogoliubov-Fermi surface with inversion symmetry and electron-electron interactions: relativistic analogies and lattice theory
• $Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• $SO(8)$ unification and the large-N theory of superconductor-insulator transition of two-dimensional Dirac fermions
• Majorana mass, time reversal symmetry, and the dimension of space
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Topological defects of Néel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice
• Conserved charges of order-parameter textures in Dirac systems
• Anatomy of plasmons in generic Luttinger semimetals
• Hidden role of antiunitary operators in Fierz transformation
• SO(4) multicriticality of two-dimensional Dirac fermions
• Spontaneous breaking of the $\text{SO}(2N)$ symmetry in the Gross-Neveu model
• Trapping massless Dirac particles in a rotating saddle
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Half vortex and fractional electrical charge in two dimensions
• Delta-function-potential junctions with quasiparticles occupying tilted bands with quadratic-in-momentum dispersion
• Spectral flow for Aharonov--Bohm rings generated by zero-mass lines
• Transmission through rectangular potentials in semimetals featuring quadratic dispersion
• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling