Review of the Theoretical Description of Time‐Resolved Angle‐Resolved Photoemission Spectroscopy in Electron‐Phonon Mediated Superconductors

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 Anderson-Higgs oscillations can be excited due to the nonlinear coupling with the electric field and describe mechanisms where pumping the system enhances superconductivity.

Analysis of time-resolved single-particle spectrum on the one-dimensional extended Hubbard model

“…However, the theoretical investigation and numerical simulations of trARPES are quite demanding due to the dual difficulty of quantum correlation and nonequilibrium effects. There are mainly two ways to obtain time-resolved single-particle spectra that can be compared with trARPES data: one is to use nonequilibrium Green's functions to address the nonequilibrium issue, at the same time combined with other methods to cope with correlation effects, e.g., by equations of mo-tion or the dynamical mean-field theory [19][20][21][22]; an alternative and perhaps more straightforward way relies on unbiased numerical methods, for instance, the timedependent exact diagonalization (ED). However due to the heavy constraint on system size in ED, the (timedependent) correlation functions can only be defined discretely in the momentum space if periodic boundary conditions (BC) are imposed [23].…”

Nonequilibrium mean-field theory of resistive phase transitions

“…Far-from-equilibrium transport theory has found countless applications in nano-junctions, based on the Landauer-Büttikker formalism [10]. Recently, stimulated by progress in ultrafast measurement techniques [11], the relaxation dynamics of electrons at the femto-second scale has been extensively studied in solids and optical lattices [12]. The general idea behind our work is rather to understand how the electronic state continuously evolves away from equilibrium when a steady finite electric field is adiabatically turned on.…”

Collapse of superconductivity in cuprates via ultrafast quenching of phase coherence

“…At and above the critical fluence F C ≈ 15 µJ/cm 2 [ [21][22][23], the increase of Γ p is such that superconductivity is suppressed. Quantitatively, we observe that the non-thermal melting of the condensate [21][22][23][24][25][26] is achieved when Γ p ≈ Ω Θ .TR-ARPES provides direct snapshots of the one-electron removal spectral function A(k, ω) [27] and its temporal evolution [28,29] due to the perturbation by an ultrashort pump pulse. The spectral function A(k, ω) depends on both the electron self-energy Σ(ω)=Σ (ω)+iΣ (ω) and the bare energy dispersion k :(1)For a superconductor, Σ(ω) at the Fermi momentum k = k F can be approximated well bywhere ∆ is the superconducting gap amplitude, Γ s the single-particle scattering rate and Γ p the pair-breaking scattering rate, as proposed in Ref.…”