Electron relaxation in metals: Theory and exact analytical solutions

Abstract

The nonequilibrium dynamics of electrons is of a great experimental and theoretical value, providing important microscopic parameters of the Coulomb and electron-phonon interactions in metals and other cold plasmas. Because of the mathematical complexity of collision integrals, theories of electron relaxation often rely on the assumption that electrons are in a "quasiequilibrium" ͑QE͒ with a time-dependent temperature, or on the numerical integration of the time-dependent Boltzmann equation. We transform the integral Boltzmann equation to a partial differential Schrödinger-type equation with imaginary time in a one-dimensional "coordinate" space reciprocal to energy which allows for exact analytical solutions in both cases of electron-electron and electron-phonon relaxations. The exact relaxation rates are compared with the QE relaxation rates at high and low temperatures.

Mechanisms of nonthermal destruction of the superconducting state and melting of the charge-density-wave state by femtosecond laser pulses

“…After absorption of a photon, the PE electrons and holes lose energy very rapidly through "avalanche" scattering with phonons on a timescale of τ E < 100 fs for YBCO and < 60 fs for LSCO 19 , creating a large non-equilibrium phonon population in the process. The phonons whose energy exceeds the gap ω ph > 2∆ can subsequently excite QPs from the condensate, but these recombine again and so a bot- tleneck occurs, in which high-frequency phonons are in temporarily in quasi-equilibrium with QPs as described by Kusar et al for LaSrCuO 1 .…”

Theory of photoexcited carrier relaxation across the energy gap of phase-ordered materials

“…Therefore, we obtain a nondiverging τ at T c if p = 0, which readily follows from Eq. (22). When p = 0, on the other hand, I TA ≡ 0 for arbitrary T [because I TA ∝ w 2 2 ; see Eq.…”

“…Figure 3(a) shows the T dependence of τ that we have formulated in Eq. (22). The parameter p (≡ w 2 /w 1 ) is the coupling strength through which the HEPs decay into TA modes, and it is tuned from 0 to 0.5 in increments of 0.1.…”

Microscopic insight into the pump–probe relaxation dynamics of superconductors: Model study of MgB2 relaxation within nonlinear response theory

“…The interpretation of experimental results relies on various types of phenomenological equations of motion for the relaxation of "hot electrons" and/or high-energy phonons in coupling to bosonic degrees of freedom [3][4][5][6][7]. The assumption of quasi-equilibrium, which is often behind these methods, is discussed in [8], where the authors present an analytic solution of excited state relaxation dynamics within the Boltzmann kinetic equation, the method of which deals with electrons and phonons out of equilibrium.…”

“…The interpretation of experimental results relies on various types of phenomenological equations of motion for the relaxation of "hot electrons" and/or high-energy phonons in coupling to bosonic degrees of freedom [3][4][5][6][7]. The assumption of quasi-equilibrium, which is often behind these methods, is discussed in [8], where the authors present an analytic solution of excited state relaxation dynamics within the Boltzmann kinetic equation, the method of which deals with electrons and phonons out of equilibrium.In general, however, phenomenological treatments not only ignore nonlinear aspects of processes running in PP experiments, but ignore also the microscopic character of nonequilibrium states -coherences and/or populations, which can evolve in the studied system over a sequence of different time periods via the interaction of matter with the incident fields. In these circumstances, mainly in the case of superconductors, it is difficult to disclose the relationship between the derived relaxation parameters, i.e.…”