Magnetoresistance measurements on graphene have revealed a wealth of novel physics [1–5].
These phenomena are typically studied at low
currents so that the carriers remain in thermal equilibrium. At high currents electrons are
driven far from equilibrium so that their kinetic
energy exceeds the thermal energy of the lattice. “Hot electron” conditions are of fundamental interest and have been exploited for technology, for example high performance GaAs Gunn
oscillators  and quantum cascade lasers .
They are anticipated to be particularly prominent in graphene due to the small carrier effective mass and weak electron-phonon coupling.
Here we report three non-equilibrium phenomena in monolayer graphene at high currents: (i)
a “Doppler-like” shift and splitting of the frequencies of the transverse acoustic (TA) phonons
emitted when the electrons undergo inter-Landau
level (LL) transitions; (ii) intra-LL Mach effect
with the emission of transverse acoustic phonons
when the electrons drift at supersonic speed, and
(iii) the onset of elastic inter-LL transitions at a
critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-ofequilibrium phenomena in other two-dimensional