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The search for energy efficient materials is urged not only by the needs ofmodern electronics but also by emerging applications in neuromorphic computingand artificial intelligence. Currently, there exist two mechanisms forachieving dissipationless transport: superconductivity and the quantum Halleffect. Here we reveal that dissipationless transport is theoreticallyachievable on a honeycomb lattice by rational design of chiral anomalies.Breaking the usual assumption of commensurability leads to electronic modesexhibiting chiral anomalies capable of dissipationless coherent transport inthe material bulk, rather than on the edge. The dissipationless transportundergoes a pitchfork bifurcation marking the onset of a novel cubic dispersionphase. These results open a new research avenue for the design of energyefficient information processing and higher-order dispersion materials.

Tunable chiral anomalies and coherent transport on a honeycomb lattice