  In thermodynamic equilibrium, current in metallic systems is carried by
electronic states near the Fermi energy whereas the filled bands underneath
contribute little to conduction. Here we describe a very different regime in
which carrier distribution in graphene and its superlattices is shifted so far
from equilibrium that the filled bands start playing an essential role, leading
to a critical-current behavior. The criticalities develop upon the velocity of
electron flow reaching the Fermi velocity. Key signatures of the
out-of-equilibrium state are current-voltage characteristics resembling those
of superconductors, sharp peaks in differential resistance, sign reversal of
the Hall effect, and a marked anomaly caused by the Schwinger-like production
of hot electron-hole plasma. The observed behavior is expected to be common for
all graphene-based superlattices.
