  A fundamental instability in the nonequilibrium conduction band under a
electric field bias is proposed via the spontaneous emission of coherent
phonons. Analytic theory, supported by numerical calculations, establishes that
the quantum avalanche, an abrupt nonequilibrium occupation of excited bands,
results from the competition between the collapse of the band minimum via the
phonon emission and the dephasing of the electron with the environment. The
continuous avalanche transition is a quantum phase transition with the
nonequilibrium phase diagram determined by the avalanche parameter $\beta$,
with peculiar reentrant avalanche domes close to the phase boundary. We further
confirm the nature of the quantum avalanche with the temperature dependence.
