Tunable chiral anomalies and coherent transport on a honeycomb lattice

The search for energy efficient materials is urged not only by the needs of modern electronics but also by emerging applications in neuromorphic computing and artificial intelligence. Currently, there exist two mechanisms for achieving dissipationless transport: superconductivity and the quantum Hall effect. Here we reveal that dissipationless transport is theoretically achievable on a honeycomb lattice by rational design of chiral anomalies. Breaking the usual assumption of commensurability leads to electronic modes exhibiting chiral anomalies capable of dissipationless coherent transport in the material bulk, rather than on the edge. The dissipationless transport undergoes a pitchfork bifurcation marking the onset of a novel cubic dispersion phase. These results open a new research avenue for the design of energy efficient information processing and higher-order dispersion materials.