Magnetic field-induced giant enhancement of electron-phonon energy transfer in strongly disordered conductors

Relaxation of soft modes (e.g. charge density in gated semiconductor heterostructures, spin density in the presence of magnetic field) slowed down by disorder may lead to giant enhancement of energy transfer (cooling power) between overheated electrons and phonons at low bath temperature. We show that in strongly disordered systems with time-reversal symmetry broken by external or intrinsic exchange magnetic field the cooling power can be greatly enhanced. The enhancement factor as large as $10^{2}$ at magnetic field $B \sim 10$ Tesla in 2D {\rm InSb} films is predicted. A similar enhancement is found for the ultrasound attenuation.