Lattice realization of the generalized chiral symmetry in two dimensions

TL;DR

This paper establishes a rigorous lattice formulation of generalized chiral symmetry for Dirac fermions, enabling analysis of zero modes in tilted and non-uniform systems, with implications for graphene and organic metals.

Contribution

It introduces a method to define and deform lattice Hamiltonians with generalized chiral symmetry from conventional models, extending to non-uniform systems.

Findings

Lattice models with generalized chiral symmetry are explicitly constructed.

Zero modes of deformed Hamiltonians are expressed in terms of original models.

Application demonstrates extension of zero modes to tilted Dirac fermions with vortices.

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.