Review of the theoretical description of time-resolved angle-resolved photoemission spectroscopy in electron-phonon mediated superconductors

TL;DR

This paper reviews theoretical approaches to time-resolved ARPES in electron-phonon superconductors, focusing on nonequilibrium Migdal-Eliashberg theory, relaxation dynamics, and effects of ultrashort laser pulses on superconductivity.

Contribution

It introduces methods to solve nonequilibrium Migdal-Eliashberg equations and discusses how ultrashort laser pulses influence relaxation and superconductivity in these materials.

Findings

Exact sum rule results for relaxation processes

Numerical rules of thumb for energy transfer from electrons to phonons

Excitation of Higgs oscillations enhances superconductivity

Abstract

We review recent work on the theory for pump/probe photoemission spectroscopy of electron-phonon mediated superconductors in both the normal and the superconducting states. We describe the formal developments that allow one to solve the Migdal-Eliashberg theory in nonequilibrium for an ultrashort laser pumping field, and explore the solutions which illustrate the relaxation as energy is transferred from electrons to phonons. We focus on exact results emanating from sum rules and approximate numerical results which describe rules of thumb for relaxation processes. In addition, in the superconducting state, we describe how Higg's oscillations can be excited due to the nonlinear coupling with the electric field and how pumping the system can enhance superconductivity.