Time-resolved optical conductivity and Higgs oscillations in two-band dirty superconductors

Haenel, Rafael; Froese, Paul; Manske, Dirk; Schwarz, Lukas

doi:10.1103/physrevb.104.134504

Cited by 25 publications

(22 citation statements)

References 48 publications

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“…For what concerns the amplitude fluctuations, the general behavior is rather different from the single-band case, where the spectral function of the so-called Higgs mode has a well-defined resonance at twice the gap value. As it has been already noticed in previous works [22,23,25,26], for multiband superconductors amplitude fluctuations in each band carry information on the optical gaps of both the bands. This rich phenomenology, which already challenges the interpretation of experiments with conventional spectroscopies, makes the understanding of high-field THz spectroscopies rather complex [21,23,25,26].…”

Section: Introductionmentioning

confidence: 59%

“…In addition to the above modifications of the quasiparticle excitations, multiband superconductors host also a spectrum of collective fluctuations much richer than in the single-band case [15][16][17][18][19][20][21][22][23][24][25][26]. Indeed, by considering for the sake of discussion the two-bands case, each order parameter admits both amplitude and phase fluctuations below T c .…”

Section: Introductionmentioning

confidence: 99%

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Contribution of Collective Excitations to Third Harmonic Generation in Multiband Superconductors: the case of MgB$_2$

Fiore,

Udina,

Marciani

et al. 2022

Preprint

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Multiband superconductors can host collective excitations with marked differences with respect to their single-band counterpart. We first study the spectrum of collective amplitude fluctuations in a clean two-bands superconductor, showing that the spectral weight of the Higgs mode rapidly deviates from the naive extension of the single band case as the interband coupling is turned on. These results are then used to critically analyze the non-linear optical response in MgB2, providing an explanation for the apparently contradictory results of recent experiments, pointing towards a selective relevance either of the Leggett mode or of the amplitude fluctuations at twice the lower gap. By using exact numerical simulations and realistic estimate of disorder we compute the relative contribution of the quasiparticle, amplitude and phase fluctuations to the non-linear optical response. We show that at low pumping frequency only the resonance at twice the smaller gap emerges, as due to the BCS response, while the Leggett mode dominates only in a narrow range of higher pumping frequencies matching its low-temperature value. Our findings provide a fresh perspective on the potential of non-linear THz spectroscopy to detect collective modes in other multiband systems, as e.g. iron-based superconductors.

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Section: Introductionmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Contribution of Collective Excitations to Third Harmonic Generation in Multiband Superconductors: the case of MgB$_2$

Fiore,

Udina,

Marciani

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…Here we discuss how the presence of the symmetry restricts the coupling between electromagnetic fields and the collective excitations, which is governed by the vector Q µ,α defined in Eq. (30). For instance, as we detail in Appendix B, Q µ,α (iΩ) must be real due to the inherent particle-hole symmetry.…”

Section: Symmetry Considerationmentioning

confidence: 99%

“…Studies on optical responses of superconducting collective modes have mostly focused on the nonlinear regime so far [19,[22][23][24][25][26][27][28][29][30]. Indeed, for single-band superconductors, a single photon process for the Higgs mode is prohibited by the inherent particle-hole symmetry [22,31,32].…”

Section: Introductionmentioning

confidence: 99%

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Optical response of the Leggett mode in multiband superconductors in the linear response regime

Kamatani,

Kitamura,

Tsuji

et al. 2021

Preprint

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We study optical responses of Leggett modes in multiband superconductors in the linear response regime. The Leggett mode is a collective mode unique to multiband superconductors that arises from relative phase fluctuations of superconducting orders for different bands. We use the Ginzburg-Landau (GL) description to study the collective modes in multiband systems. We find that multiband superconductors generally allow a linear coupling between the Leggett mode and external electric fields due to the presence of a cross term between different components of superconducting orders in the GL theory. The presence of a linear coupling for the Leggett mode is in sharp contrast with the absence of that for Higgs (amplitude) modes in single-band superconductors that only support nonlinear optical responses such as third harmonic generation (THG). We further confirm such a linear coupling in multiband superconductors by a more microscopic description based on a diagrammatic approach. We study the collective modes within the random phase approximation (RPA) and compute their contribution to the linear optical conductivity. These findings suggest a new route to observe the Leggett mode by optical absorption.

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Recent Development of Ultrafast Optical Characterizations for Quantum Materials

2022

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or far-infrared energy region are therefore of particular importance, for the THz frequencies (1 THz≈4.1 meV) are close to the energy scales of a number of important single-particle and collective excitations of quantum material systems, for example, pairing energy gaps of superconductors, lattice vibration modes (phonons), collective spin waves (magnons), Josephson plasmon in high temperature superconductors, and binding energy of bound electron-hole pairs (excitons), [1] and they are linked to a large number of fundamental physical problems currently under intensive investigations in condensed matter physics. The information yielded from equilibrium optical measurements are usually prerequisites for understanding the nonequilibrium optical properties probed by ultrafast time-resolved spectroscopy techniques.In the last three decades, we have witnessed a rapid development in ultrafast laser and nonlinear optical techniques. The intense ultrashort optical pulses at wavelengths spanning the electromagnetic spectrum from terahertz through visible to X-ray have been generated from table-top laser sources and free-electron laser facilities. A variety of time-resolved spectroscopy techniques on the basis of pump-probe scheme have been developed. Depending on the fluence of pump pulses, photoexcitations can induce different effects and phenomena. For sufficiently weak perturbations, the photoexcitation of charge carriers does not change the free-energy landscape and the system relaxes back to the equilibrium state in a short time scale. The relaxation process is determined by the same interactions (e.g for example, electron-electron, electron-phonon) that govern the equilibrium properties. In principle, one can extract the coupling strength of electron to other degrees of freedom from the relaxation dynamics. In addition, the ultrashort laser pulse whose duration is shorter than the periodicity of targeted lattice/spin modes can trigger coherent oscillations at the corresponding frequencies of collective modes, for example, phonon, magnon, etc. with decay times that are related to the dephasing times. This enables one to detect collective-mode excitations that may not be easily accessed to or probed by other techniques.By contrast, with strong pump pulses, the photoexcitation can excite a sufficient number of electrons or drive the motion of collective mode to a large amplitude. The corresponding perturbation to the lattice/spin degrees of freedom can be large enough to modify the free-energy landscape. As a result, The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an im...

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Time-resolved optical conductivity and Higgs oscillations in two-band dirty superconductors

Cited by 25 publications

References 48 publications

Contribution of Collective Excitations to Third Harmonic Generation in Multiband Superconductors: the case of MgB$_2$

Contribution of Collective Excitations to Third Harmonic Generation in Multiband Superconductors: the case of MgB$_2$

Optical response of the Leggett mode in multiband superconductors in the linear response regime

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

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