Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac Cones

Abstract

While it has been well-known that the chirality is an important symmetry for Dirac-fermion systems that gives rise to the zero-mode Landau level in graphene, here we explore whether this notion can be extended to tilted Dirac cones as encountered in organic metals. We have found that there exists a "generalized chiral symmetry" that encompasses the tilted Dirac cones, where a generalized chiral operator $\gamma$, satisfying ${\gamma }^{†}H+H\gamma =0$ for the Hamiltonian $H$, protects the zero mode. We can use this to show that the $n=0$ Landau level is delta-function-like (with no broadening) by extending the Aharonov-Casher argument. We have numerically confirmed that a lattice model that possesses the generalized chirality has an anomalously sharp Landau level for spatially correlated randomness.

4 pages, 2 figures

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• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
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• Zero-energy states in corrugated bilayer graphene
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• Anomalous criticality in the quantum Hall transition at $n=0$ Landau level of graphene with chiral-symmetric disorders
• Conductance plateau transitions in quantum Hall wires with spatially correlated random magnetic fields

Cited by in corpus (22)

• Volkov-Pankratov states in topological heterojunctions
• Metallic Interface Emerging at Magnetic Domain Wall of Antiferromagnetic Insulator---Fate of Extinct Weyl Electrons
• Type-II Dirac surface states in topological crystalline insulators
• Magnetic description of the Fermi arc in type-I and type-II Weyl semimetals
• Longitudinal conductivity of massless fermions with tilted Dirac cone in magnetic field
• Synthetic non-Abelian gauge fields and gravitomagnetic effects in tilted Dirac cone systems
• Tilted Dirac cones and asymmetric conical diffraction in photonic Lieb-kagome lattices
• Electrically charged Andreev modes in two-dimensional tilted Dirac cone systems
• 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
• Generalization of Chiral Symmetry for Tilted Dirac Cones
• Lattice realization of the generalized chiral symmetry in two dimensions
• Topologically protected Landau levels in bilayer graphene in finite electric fields
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Dirac fermions in graphene and analogues: magnetic field and topological properties
• Emergent chiral symmetry in non-bipartite kagome and pyrochlore lattices with spin-orbit coupling
• Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions
• Tilted Dirac Fermions
• Three-Dimensional Topological Semimetal/Insulator States in α-Type Organic Conductors with Interlayer Spin-Orbit Interaction
• Algebraic structure of Dirac fermion state in α-(BDET-TTF)_2I_3
• Landau levels and optical conductivity in the mixed state of a generic Weyl superconductor