Lattice realization of the generalized chiral symmetry in two dimensions

Abstract

While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a continuous "algebraic deformation" of Hamiltonians, which generates lattice models with the generalized chiral symmetry from those with the conventional chiral symmetry. This enables us to explicitly express zero modes of the deformed Hamiltonian in terms of that of the original Hamiltonian. Another virtue is that the deformation can be extended to non-uniform systems, such as fermion-vortex systems and disordered systems. Application to fermion vortices in a deformed system shows how the zero modes for the conventional Dirac fermions with vortices can be extended to the tilted case.

11 pages, 10 figures

References in corpus (8)

• Electron fractionalization in two-dimensional graphenelike structures
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Novel electric field effects on Landau levels in Graphene
• Theory of Anomalous Quantum Hall Effects in Graphene
• Possible Verification of Tilted Anisotropic Dirac Cone in α-(BEDT-TTF)_2 I_3 Using Interlayer Magnetoresistance
• Irrational vs. rational charge and statistics in two-dimensional quantum systems
• Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields
• Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator

Cited by in corpus (4)

• Magnetic description of the Fermi arc in type-I and type-II Weyl semimetals
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions
• Anomalous magnetic transport and extra quantum oscillation in semi-metallic photon-like fermion gas