Generalized chiral symmetry and stability of zero modes for tilted Dirac cones

While it is well known that 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 find that there exists a "generalized chiral symmetry" that encompasses tilted Dirac cones, where a generalized chiral operator gamma, satisfying gamma(dagger) H + H gamma = 0 for Hamiltonian H, protects the zero mode. We use this to show that the n = 0 Landau level is delta-function-like (with no broadening) by extending the Aharonov-Casher argument. We confirm numerically that a lattice model that possesses generalized chirality has an anomalously sharp Landau level for spatially correlated randomness.