  In order to observe many-body localisation in electronic systems, decoupling
from the lattice phonons is required, which is possible only in
out-of-equilibrium systems. We show that such an electron-phonon decoupling may
happen in suspended films and it manifests itself via a bistability in the
electron temperature. By studying the electron-phonon cooling rate in
disordered, suspended films with two-dimensional phonons, we derive the
conditions needed for such a bistability, which can be observed experimentally
through hysteretic jumps of several orders of magnitude in the nonlinear
current-voltage characteristics. We demonstrate that such a regime is
achievable in systems with an Arrhenius form of the equilibrium conductivity,
while practically unreachable in materials with Mott or Efros-Shklovskii
hopping.
