  We investigate the dynamical control of the heat flux exchanged in near-field
regime between a membrane made with a phase-change material and a substrate
when the temperature of the membrane is tuned around its critical value. We
show that in interaction with an external source of thermal radiation, this
system is multistable and behaves as a thermal transistor, being able to
dynamically modulate and even amplify super-Planckian heat fluxes. This
behavior could be used to dynamically control heat fluxes exchanged at the
nanoscale in systems out of thermal equilibrium and to process thermal
information employing suspended membranes.

Mesoscale and Nanoscale Physics