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arXiv:1010.5868 · Journal of the Physical Society of Japan

Relaxation Dynamics of Photoinduced Changes in the Superfluid Weight of High-TcSuperconductors

Takanobu Jujo

Published Dec 27, 2010• 0 citations
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Abstract

In the transient state of d-wave superconductors, we investigate the temporal variation of photoinduced changes in the superfluid weight. We derive the formula that relates the nonlinear response function to the nonequilibrium distribution function. The latter qunatity is obtained by solving the kinetic equation with the electron-electron and the electron-phonon interaction included. By numerical calculations, a nonexponential decay is found at low temperatures in contrast to the usual exponential decay at high temperatures. The nonexponential decay originates from the nonmonotonous temporal variation of the nonequilibrium distribution function at low energies. The main physical process that causes this behavior is not the recombination of quasiparticles as previous phenomenological studies suggested, but the absorption of phonons.

DOI
10.1143/jpsj.80.014701

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In the transient state of d-wave superconductors, we investigate the temporal variation of photoinduced changes in the superfluid weight. We derive the formula that relates the nonlinear response function to the nonequilibrium distribution function. The latter qunatity is obtained by solving the kinetic equation with the electron-electron and the electron-phonon interaction included. By numerical calculations, a nonexponential decay is found at low temperatures in contrast to the usual exponential decay at high temperatures. The nonexponential decay originates from the nonmonotonous temporal variation of the nonequilibrium distribution function at low energies. The main physical process that causes this behavior is not the recombination of quasiparticles as previous phenomenological studies suggested, but the absorption of phonons.
The relaxation of a ddd-wave superconductor that has been driven out of equilibrium by an optical pulse is investigated. We consider a simple model for the low-energy nonequilibrium state, one in which the unpaired quasiparticles form Fermi spheres near the gap nodes, and calculate the decay rate of the quasiparticle population due to phonon-assisted recombination. In the high density limit for the photoinjected quasiparticles, the decay rate dn∕dtdn∕dtdn∕dt is found to vary as n5∕2{n}^{5∕2}n5∕2, which differs from the n2{n}^{2}n2 form commonly adopted in phenomenological models of the relaxation dynamics. In the low density limit, the decay is exponential. From numerical estimates, we determine that phonon-assisted recombination could play an important role over the picosecond time scales of current interest. We compare our results to pump-probe optical experiments on high TC{T}_{C}TC​ cuprates and find reasonable agreement for the decay rate in underdoped YBCO for low laser intensity.
The latest generation of high quality, narrow gap, superconducting tunnel junctions (STJs) exhibits a steady-state and time-dependent behavior which cannot be described satisfactorily by previous treatments of nonequilibrium quasiparticle (qp) dynamics. These effects are particularly evident in experiments using STJs as detectors of photons, over the range from near infrared to x ray. In this paper, we present a detailed theoretical analysis of the spectral and temporal evolution of the nonequilibrium qp and phonon distributions in such STJs excited by single photons, over a wide range of excitation energy, bias voltage, and temperature. By solving the coupled set of kinetic equations describing the interacting excitations, we show that the nonequilibrium qp distribution created by the initial photoabsorption does not decay directly back to the initial undisturbed state in thermal equilibrium. Instead, it undergoes a rapid adiabatic relaxation to a long-lived, excited state, the spectral distribution of which is nonthermal, maintained by a balance between qp creation, recombination, and trapping. The model is able to describe successfully photoabsorption data taken on several different aluminum STJs, using a single set of parameters. Of particular note is the conclusion that the local traps responsible for qp loss are situated specifically in the region of Nb contacts.
Motivated by the experiment by M. Budden {\em et al.} [Nature Physics {\bf 17}, 611 (2021)], who observed signatures of long-lived photo-induced superconductivity, we develop an accurate analytical/computational approach to non-equilibrium superconductivity following a quench. We consider the BCS-Holstein model, which includes both integrable local electron-electron interactions and integrability-breaking electron-phonon coupling. We develop Keldysh-Eliashberg theory on the Kadanoff-Baym contour, which enables us to describe non-equilibrium dynamics of the superconductor. We consider a quench in interactions, which results in a dynamic transition from the initial superconducting state to a normal thermal state in the end of the evolution. It is shown that the dynamics contain two stages: The early-time integrable behavior, involving coherent oscillations of the superconducting order parameter, crosses over to the late-time ergodic dynamics exhibiting a thermal decay into an equilibrium state. In the former regime, our computational approach both reproduces exact analytical results on the integrable dynamics of the order parameter and generalizes those to the case of an initial thermal state. The method also succeeds for the first time in describing both integrable-to-thermalizing crossover and the late-time thermal decay, which is shown to be consistent with the time-dependent Ginzburg-Landau theory (with the exponential decay time dependent on the density of quasiparticle excitations). We observe the electron distribution function approaching the Fermi-Dirac thermal distribution at final stages. The details of two-time non-equilibrium dynamics depend on the density of quasiparticles in the initial state and the integrability-breaking parameters, which under certain conditions may result in a long-lived transient superconductivity consistent with experiment.
We show that in low-dimensional disordered conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In the quasi-one-dimensional case, both behave at small time as e(-(t/tau(in))3/2) where the inelastic time, tau(in), identical for both processes, is a power T-2/3 of the temperature. The nonexponential quasiparticle decay results from a modified derivation of the Fermi golden rule. This result implies the existence of an unusual distribution of relaxation times.
We use density-matrix theory to calculate the ultrafast dynamics of unconventional superconductors from a microscopic viewpoint. We calculate the time evolution of the optical conductivity as well as pump-probe spectra for a ddd-wave order parameter. Three regimes can be distinguished in the spectra. The Drude response at low photon energies is the only one of those which has been experimentally measured so far. At higher energies, we predict two more regimes: the pair-breaking peak, which is reduced as Cooper pairs are broken up by the exciting pulse, and a suppression above the pair-breaking peak due to nonequilibrium quasiparticles. Furthermore, we consider the influence of the electron-phonon coupling and derive rate equations that have been widely used so far.
Time-resolved measurements of quasiparticle (QP) relaxation dynamics on the femtosecond timescale are reported as a function of temperature and doping in YBa 2 Cu 3 O 7 − δ for (0.48 < δ < 0.1). In the underdoped state (δ > 0.15), there is no evidence for any changes in the low-energy gap structure at T c from either photoinduced QP absorption or QP relaxation time data. In combination with the sum rule, this implies the existence of pre-formed pairs up to a much higher temperature T *. Near δ = 0.1 a rapid cross-over is observed, to a state where the QP recombination time diverges and the photoinduced QP density falls to zero at T c , indicating the existence of a temperature-dependent superconducting gap which closes at T c .