  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
tunable without any magnetic fields. Breaking the usual assumption of
commensurability and applying an external electric field lead to electronic
modes exhibiting chiral anomalies capable of dissipationless transport in the
material bulk, rather than on the edge. As the electric field increases, the
system reaches a cubic-like dispersion material phase. While providing
performance comparable to other known honeycomb lattice-based ballistic
conductors such as an armchair nanotube, zigzag nanoribbon and hypothetical
cumulenic carbyne, this scheme provides routes to a strongly correlated
localization due to flat band dispersion and to exotic cubic dispersion
material featuring a pitchfork bifurcation and a critical slowing down
phenomena. These results open a new research avenue for the design of energy
efficient information processing and higher-order dispersion materials.
