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

TL;DR

This paper introduces a generalized chiral symmetry for tilted Dirac cones in organic metals, demonstrating its role in protecting zero modes and ensuring sharp Landau levels even with disorder.

Contribution

It extends the concept of chiral symmetry to tilted Dirac cones, showing that a generalized chiral operator preserves zero modes and leads to delta-function-like Landau levels.

Findings

Generalized chiral symmetry exists for tilted Dirac cones.

Zero modes are protected by this symmetry, remaining sharp.

Numerical simulations confirm sharp Landau levels with correlated disorder.

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