Resonant generation of coherent phonons in a superconductor by ultrafast optical pump pulses

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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“…Note that the resonance between coherent phonons and the order parameter oscillation in the regime of ω 0 ∼ 2∆ has been discussed in Ref. 32. …”

Section: Resultsmentioning

confidence: 99%

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

2016

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“…Before this experiment [15], the amplitude Higgs mode had been observed only in a special case, 2H -NbSe 2 , where SC coexists with a charge density wave [4][5][6]18,19]. Theoretical studies of the SC order parameter dynamics have so far primarily focused on the static mean-field dynamics [1][2][3][5][6][7][8][9][10][11][12][13]17,19,[22][23][24]. One important conclusion of these works is that the frequency of the Higgs amplitude mode (ω H ) should coincide with the SC gap (2 SC ) in the BCS regime [27], which is a threshold for quasiparticle excitations.…”

Section: Introductionmentioning

confidence: 99%

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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“…In the past few years, fueled by recent advances in femtosecond terahertz (THz) laser technology 3 , many experimental 4-17 and theoretical [18][19][20][21][22][23][24][25][26][27][28][29][30][31] studies have focused on the ultrafast time response of the BCS state subjected to nonadiabatic perturbations. For example, Matsunaga et al 4,5 have employed THz pump-THz probe spectroscopy to investigate the nonadiabatic dynamics of superconducting thin films after the injection of Bogoliubov quasiparticles with energies just above the gap edge.…”

Section: Introductionmentioning

confidence: 99%

Signatures of nonadiabatic BCS state dynamics in pump-probe conductivity

et al. 2014

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We theoretically study the pump-probe response of nonequilibrium BCS superconductors coupled to optical phonons. For ultrashort pump pulses a nonadiabatic regime emerges, which is characterized by oscillations of the superconducting order parameter as well as by the generation of coherent phonons. Using the density-matrix formalism, we compute the pump-probe response in the nonadiabatic regime of the coupled Bogoliubov quasiparticle-phonon system and determine the signatures of the order parameter and the phonon oscillations in the pump-probe conductivity. We find that the nonadiabatic dynamics of the BCS superconductor reflects itself in oscillations of the pump-probe response as functions of delay time δt between pump and probe pulses. We argue that from the analysis of this oscillatory behavior both frequency and decay time of the algebraically decaying order-parameter oscillations can be inferred. Similarly, the coherent phonons are evidenced in the pump-probe conductivity by oscillations with the frequency of the phonons. Remarkably, we find that the oscillatory response in the pump-probe conductivity is resonantly enhanced when the frequency of the order-parameter oscillations is tuned to the phonon energy.

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Resonant generation of coherent phonons in a superconductor by ultrafast optical pump pulses

Cited by 71 publications

References 43 publications

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

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

Multiple amplitude modes in strongly coupled phonon-mediated superconductors

Signatures of nonadiabatic BCS state dynamics in pump-probe conductivity

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