Ultrafast electronic relaxation in superheated bismuth

Interaction of moving electrons with vibrating ions in the lattice forms the basis for many physical properties from electrical resistivity and electronic heat capacity to superconductivity. In ultrafast laser interaction with matter the electrons are heated much faster than the electron-ion energy equilibration, leading to a two-temperature state with electron temperature far above that of the lattice. The rate of temperature equilibration is governed by the strength of electron-phonon energy coupling, which is conventionally described by a coupling constant, neglecting the dependence on the electron and lattice temperature. The application of this constant to the observations of fast relaxation rate led to a controversial notion of 'ultra-fast non-thermal melting' under extreme electronic excitation. Here we provide theoretical grounds for a strong dependence of the electron-phonon relaxation time on the lattice temperature. We show, by taking proper account of temperature dependence, that the heating and restructuring of the lattice occurs much faster than were predicted on the assumption of a constant, temperature independent energy coupling. We applied the temperature-dependent momentum and energy transfer time to experiments on fs-laser excited bismuth to demonstrate that all the observed ultra-fast transformations of the transient state of bismuth are purely thermal in nature. The developed theory, when applied to ultrafast experiments on bismuth, provides interpretation of the whole variety of transient phase relaxation without the non-thermal melting conjecture.