Phonon-Electron Equilibriation: A Keldysh Field Theoretic Approach

Abstract

In this work we develop a non-equilibrium approach to study the time evolution of a coupled electron-phonon many-body system, with electronic initial states driven far-away from the ground states (the Hot Electron problem) to probe its behaviour with regards to thermalisation. The equilibration of “hot electrons”, excited to a high energy state either by external electromagnetic waves or by collision with high energy particles, is relevant to a large class of problems, viz. in pump-probe spectroscopy, stability of solid state transistors, response of photodetectors, operation of thermoelectric devices etc. Most previous studies of the “hot electron” problem treat the phonons as a thermal bath whose density matrix (or distribution functions) remain invariant with time. In this project we wish to delve in with the self-consistent time evolution of the coupled system using Schwinger-Keldysh field theory.

We construct an evolution scheme where we assume quassi-static of the electronic sector whereas the phononic sector has been treated preserving is complete non-equilibrium nature. Here we first develop the iteration for phonons and test its dynamics coupling with an Ohmic Bath. Equipped with this we wish to couple this to the system electrons and study their joint dynamics in a self-consitent way.