Nonlinear Response of Diffusive Superconductors to $ac$-electromagnetic Fields

Abstract

Motivated by the recent experimental progress in studying conventional and unconventional superconductors in a pump-probe setup, we perform a comprehensive theoretical analysis of the nonlinear response of a diffusive BCS conventional superconductor to the action of an alternating electromagnetic field using a generalized Usadel equation. We analyze the response up to the second order of the perturbation in the amplitude of the vector potential $\vec{A}$, the superconducting order parameter $\Delta$ and in the third order for the current $\vec{j}$. On the basis of this approach, we derive general expressions for the retarded (advanced) Green's functions, as well as the Keldysh function for an arbitrary number of harmonics of the incident field. Most importantly, we analyze the set of physical observables in a non-equilibrium superconductor, such as frequency and the temperature dependencies of the zero harmonic $\delta (\Delta {)}_0$ (Eliashberg effect), the second harmonic $\delta (\Delta {)}_{2\Omega }$, as well as the third harmonic for the electric current $j(3\Omega )$ under the action of a monochromatic irradiation. For the same set of parameters, we also analyze the behavior of the reflectivity and the down-conversion intensity of a thin superconducting film, discussed recently in the context of parametric amplification of superconductivity. We derive these quantities microscopically and show the connection of the down-conversion intensity to the third harmonic generation currents induced by the amplitude mode and the direct action of the electric field on the charge carriers.

arXiv comment16 pages, 8 figures, typos are corrected, further details of the derivations are added

References in corpus (54)

• An optically stimulated superconducting-like phase in K3C60 far above equilibrium Tc
• Quasiclassical Green's function approach to mesoscopic superconductivity
• Higgs Amplitude Mode in BCS Superconductors Nb${}_{1-x}$Ti${}_x$N induced by Terahertz Pulse Excitation
• Optically enhanced coherent transport in YBa2Cu3O6.5 by ultrafast redistribution of interlayer coupling
• Optically induced coherent transport far above Tc in underdoped YBa2Cu3O6+x
• Solitons and Rabi Oscillations in a Time-Dependent BCS Pairing Problem
• Higgs Mode in Superconductors
• Evidence for metastable photo-induced superconductivity in K${}_3$C${}_{60}$
• Theory of Anderson pseudospin resonance with Higgs mode in superconductors
• Dynamical vanishing of the order parameter in a fermionic condensate
• Non-linear optical effects and third-harmonic generation in superconductors: Cooper-pairs vs Higgs mode contribution
• Optically induced superconductivity in striped La2-xBaxCuO4 by polarization-selective excitation in the near infrared
• Quantum quench phase diagrams of an s-wave BCS-BEC condensate
• Pressure tuning of light-induced superconductivity in K3C60
• Photo-molecular high temperature superconductivity
• Amplitude Higgs mode and admittance in superconductors with a moving condensate
• Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impurities
• Nonequilibrium dynamics of weakly and strongly paired superconductors
• Nature and Raman signatures of the Higgs amplitude mode in the coexisting superconducting and charge-density-wave state
• Nonlinear optical response of collective modes in multiband superconductors assisted by nonmagnetic impurities
• Pump frequency resonances for light-induced incipient superconductivity in YBa${}_2$Cu${}_3$O${}_{6.5}$
• Signatures of nonadiabatic BCS state dynamics in pump-probe conductivity
• Third harmonic generation from collective modes in disordered superconductors
• Theory of light-induced resonances with collective Higgs and Leggett modes in multiband superconductors
• Light Quantum Control of Persisting Higgs Modes in Iron-Based Superconductors
• Dynamics of the BCS-BEC crossover in a degenerate Fermi gas
• Electronic Origin of High-Tc Maximization and Persistence in Trilayer Cuprate Superconductors
• Higgs-mediated optical amplification in a non-equilibrium superconductor
• Rapid ramps across the BEC-BCS crossover: a novel route to measuring the superfluid gap
• Higgs-mode resonance in third harmonic generation in NbN superconductors: multiband electron-phonon coupling, impurity scattering, and polarization-angle dependence
• Non-equilibrium phenomena in superconductors probed by femtosecond time-domain spectroscopy
• Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases
• Spectroscopic signatures of time-reversal symmetry breaking superconductivity
• Quasiclassical Theory on Third-Harmonic Generation in Conventional Superconductors with Paramagnetic Impurities
• Near-infrared light-induced superconducting-like state in underdoped YBa${}_2$Cu${}_3$O${}_y$ studied by $c$-axis terahertz third-harmonic generation
• Theory of nonequilibrium dynamics of multiband superconductors
• Spectroscopic signatures of nonequilibrium pairing in atomic Fermi gases
• Superconductivity in the presence of microwaves: Full phase diagram
• A phase diagram for light-induced superconductivity in $\kappa$-(ET)${}_2$-X
• Magnetic-Field Tuning of Light-Induced Superconductivity in Striped La${}_{2-x}$Ba${}_x$CuO${}_4$
• Wigner distribution function formalism for superconductors and collisionless dynamics of the superconducting order parameter
• Thermodynamic properties of the Dynes superconductors
• Optical Saturation Produces Spurious Evidence for Photoinduced Superconductivity in K${}_3$C${}_{60}$
• Impact of damping on superconducting gap oscillations induced by intense Terahertz pulses
• Supercurrent induced resonant optical response
• Impurity scattering in superconductors revisited
• Following the Higgs mode across the BCS-BEC crossover in two dimensions
• Non-equilibrium dynamics across the BEC-BCS crossover
• The discovery, disappearance and re-emergence of radiation-stimulated superconductivity
• Higgs modes in proximized superconducting systems
• Microwave response of a superconductor beyond the Eliashberg theory
• Collisionless dynamics of superconducting gap excited by spin-splitting field
• Electrical conductivity and nuclear magnetic resonance relaxation rate of Eliashberg superconductors in the weak-coupling limit
• Theory of absorption spectrum in the nonequilibrium steady state of superconductors under microwave irradiation

Cited by in corpus (8)

• Quantum geometry induced microwave enhancement of flat band superconductivity
• Spatially resolved collective modes in d-wave superconductors
• Two-dimensional coherent spectroscopy of disordered superconductors in the narrow-band and broad-band limits
• Nonequilibrium nonlinear response theory of amplitude-dependent dissipative conductivity in disordered superconductors
• Optical Pumping of Bardeen-Cooper-Schrieffer Superconductors
• Optical conductivity of a dirty current-carrying superconductor
• Hybrid collective excitations in topological superconductor/ferromagnetic insulator heterostructures
• Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles