Flat band, tunable chiral anomaly, and pitchfork bifurcation in a honeycomb lattice

Chiral anomaly engineering has been established as one of the mechanisms for achieving energy efficient dissipationless transport. Here we show how to design tunable chiral anomalies in a honeycomb lattice free of any magnetic fields. By applying an external electric field to a flat band material with a broken inversion symmetry, we generate electronic modes exhibiting chiral anomalies capable of disorder resilient transport in the bulk of the material. As the electric field increases, the system exhibits an unusual cubic-like dispersion. By providing a performance comparable to other honeycomb lattice-based ballistic conductors such as armchair nanotube, zigzag nanoribbon and hypothetical cumulenic carbyne, this scheme opens a new research avenue for the design of energy efficient information processing and higher-order dispersion materials.