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

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