Generalization of Chiral Symmetry for Tilted Dirac Cones

Abstract

The notion of chiral symmetry for the conventional Dirac cone is generalized to include the tilted Dirac cones, where the generalized chiral operator turns out to be non-hermitian. It is shown that the generalized chiral symmetry generically protects the zero modes (n=0 Landau level) of the Dirac cone even when tilted. The present generalized symmetry is equivalent to the condition that the Dirac Hamiltonian is elliptic as a differential operator, which provides an explicit relevance to the index theorem.

4 pages, 1 figure, to appear in the proceedings of the APCTP Conference on Localisation 2011

References in corpus (8)

• The electronic properties of graphene
• Anderson Transitions
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• 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
• Pedestrian index theorem a la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene
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• Crossover from Positive to Negative Interlayer Magnetoresistance in Multilayer Massless Dirac Fermion System with Non-Vertical Interlayer Tunneling

Cited by in corpus (7)

• Magnetic breakdown and Klein tunneling in a type-II Weyl semimetal
• Topologically protected Landau level in the vortex lattice of a Weyl superconductor
• Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator
• Bulk-edge correspondence with generalized chiral symmetry
• Lattice realization of the generalized chiral symmetry in two dimensions
• Electro-Optics of Current-carrying Graphene
• Landau levels and optical conductivity in the mixed state of a generic Weyl superconductor