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.

arXiv comment11 pages, 10 figures

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Cited by in corpus (6)

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