Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

Murakami, Yuta; Werner, Philipp; Tsuji, Naoto; Aoki, Hideo

doi:10.1103/physrevb.91.045128

Cited by 72 publications

(80 citation statements)

References 71 publications

(120 reference statements)

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“…We also note that, when the renormalized phonon frequency is comparable to the SC gap, the strong el-ph coupling leads to a highly asymmetric renormalized phonon spectrum in the SC state with a sharp peak below the SC gap [see Figs and Appendix A]. In the normal state, on the other hand, the phonon spectrum exhibits an almost symmetric single peak with a low-energy tail, and the renormalized phonon frequency is softened by the el-ph coupling [34,39]. These features in the phonon spectra have indeed been experimentally observed in some strongly coupled SCs [44][45][46][47][48], and theoretically explained as an effect of the phonon self-energy [49] (phonon anomaly).…”

Section: A Dynamical Pair Susceptibility and Collective Amplitude Modesmentioning

confidence: 99%

“…However, because of a dynamical sign problem [33] it is difficult to access the time scales needed to study the relatively slow dynamics of phonons and order parameters. In order to avoid this difficulty, we employ the self-consistent (renormalized) Migdal approximation [34][35][36][37][38][39][40][41][42], which is justified when the phonon frequency ω 0 is small compared to the electronic bandwidth [34][35][36]38,40]. In the self-consistent Migdal approximation, the electron self-energy (ˆ ) and phonon self-energy ( ) in the effective impurity model are given bŷ…”

Section: Model and Methodsmentioning

confidence: 99%

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Multiple amplitude modes in strongly coupled phonon-mediated superconductors

et al. 2016

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We study collective amplitude modes of the superconducting order parameter in strongly coupled electronphonon systems described by the Holstein model using the nonequilibrium dynamical mean-field theory with the self-consistent Migdal approximation as an impurity solver. The frequency of the Higgs amplitude mode is found to coincide with the superconducting gap even in the strongly coupled (beyond BCS) regime. Besides the Higgs mode, we find another collective mode involving the dynamics of both the phonons and the superconducting order parameter. The frequency of this mode, higher than twice the renormalized phonon frequency in the superconducting phase, is shown to reflect a strong electron-mediated phonon-phonon interaction. Both of collective modes are predicted to contribute to time-resolved photoemission spectra after a strong laser pump as vertex corrections to produce resonance peaks, which allows one to distinguish them from quasiparticle excitations.

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Section: A Dynamical Pair Susceptibility and Collective Amplitude Modesmentioning

confidence: 99%

Section: Model and Methodsmentioning

confidence: 99%

Multiple amplitude modes in strongly coupled phonon-mediated superconductors

et al. 2016

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“…The electron-phonon coupling itself can induce the damping of phonons. 76 A finite γ is not necessarily phenomenological, but can be actually modeled by phonons coupled to a heat bath comprising many harmonic oscillators (Caldeira-Leggett-type model 77 ). In the application of the dotted DMFT, which we shall introduce in the next section, it turns out that it is important to take a nonzero γ (avoiding infinitely long-lived phonons) to stabilize the convergence of the dotted DMFT calculation.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear light–Higgs coupling in superconductors beyond BCS: Effects of the retarded phonon-mediated interaction

2016

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We study the contribution of the Higgs amplitude mode on the nonlinear optical response of superconductors beyond the BCS approximation by taking into account the retardation effect in the phonon-mediated attractive interaction. To evaluate the vertex correction in nonlinear optical susceptibilities that contains the effect of collective modes, we propose an efficient scheme which we call the "dotted DMFT" based on the nonequilibrium dynamical mean-field theory (nonequilibrium DMFT) to go around the difficulty of solving the Bethe-Salpeter equation and analytical continuation. The vertex correction is represented by the derivative of the self-energy with respect to the external driving field, which is self-consistently determined by the differentiated ("dotted") DMFT equations. We apply the method to the Holstein model, a prototypical electron-phonon-coupled system, to calculate the susceptibility for the third-harmonic generation including the vertex correction. The results show that, in sharp contrast to the BCS theory, the Higgs mode can contribute to the third-harmonic generation for general polarization of the laser field with an order of magnitude comparable to the contribution from the pair breaking or charge density fluctuations. The physical origin is traced back to the nonlinear resonant light-Higgs coupling, which has been absent in the BCS approximation.

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“…IV C and IV D we use this formalism to study the transient dynamics. The DMFT formalism for the real-time dynamics, both in electron and electron-phonon-coupled systems, has been discussed in previous works [22][23][24]38] and will not be presented in detail here.…”

Section: A Nonequilibrium Green's Functionsmentioning

confidence: 99%

“…Specifically, we study the time-periodic nonequilibrium steady state (NESS) and the nonequilibrium transient dynamics of the Holstein model, a prototypical model of electron-phonon systems, using the nonequilibrium dynamical mean-field theory (DMFT) combined with the Migdal approximation [22][23][24][25]. To investigate the time-periodic NESS of the electron-phonon (el-ph) system with externally driven phonons, we extend the Floquet DMFT formalism, which has been previously only applied to purely electronic systems [26][27][28][29][30][31], to the Holstein case.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

Murakami¹,

Tsuji²,

Eckstein³

et al. 2017

Phys. Rev. B

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We perform a systematic analysis of the influence of phonon driving on the superconducting Holstein model coupled to heat baths by studying both the transient dynamics and the nonequilibrium steady state (NESS) in the weak and strong electron-phonon coupling regimes. Our study is based on the nonequilibrium dynamical mean-field theory, and for the NESS we present a Floquet formulation adapted to electron-phonon systems. The analysis of the phonon propagator suggests that the effective attractive interaction can be strongly enhanced in a parametric resonant regime because of the Floquet side bands of phonons. While this may be expected to enhance the superconductivity (SC), our fully self-consistent calculations, which include the effects of heating and nonthermal distributions, show that the parametric phonon driving generically results in a suppression or complete melting of the SC order. In the strong coupling regime, the NESS always shows a suppression of the SC gap, the SC order parameter, and the superfluid density as a result of the driving, and this tendency is most prominent at the parametric resonance. Using the real-time nonequilibrium DMFT formalism, we also study the dynamics towards the NESS, which shows that the heating effect dominates the transient dynamics, and SC is weakened by the external driving, in particular at the parametric resonance. In the weak coupling regime, we find that the SC fluctuations above the transition temperature are generally weakened under the driving. The strongest suppression occurs again around the parametric resonances because of the efficient energy absorption.

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Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

Cited by 72 publications

References 71 publications

Multiple amplitude modes in strongly coupled phonon-mediated superconductors

Multiple amplitude modes in strongly coupled phonon-mediated superconductors

Nonlinear light–Higgs coupling in superconductors beyond BCS: Effects of the retarded phonon-mediated interaction

Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

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