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

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

2011-01-22

arxiv.org/abs/1101.4273v1

Phys. Rev. B83, 153414 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 2 figures

Scientific paper

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 $\gamma^{\dagger} H + H\gamma =0$ 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.

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