Third harmonic generation from collective modes in disordered superconductors

Abstract

Recent experiments with strong THz fields in both conventional and unconventional superconductors have clearly evidenced a marked third-harmonic generation below the superconducting temperature $T_c$. Its interpretation challenged substantial theoretical work aimed at establishing the relative efficiency of quasiparticle excitations and collective modes in triggering such a resonant response. Here we compute the non-linear current by implementing a time-dependent Bogoljubov de-Gennes approach, with the twofold aim to account non-perturbatively for the effect of local disorder, and to include the contribution of all collective modes, i.e. superconducting amplitude (Higgs) and phase fluctuations, and charge fluctuations. We show that, in agreement with previous work, already at small disorder the quasiparticle response is dominated by paramagnetic effects. We further demonstrate that paramagnetic processes mediate also the response of all collective modes, with a substantial contribution of charge/phase fluctuations. These processes, which have been overlooked so far, turn out to dominate the third-order current at strong disorder. In addition, we show that disorder strongly influences the polarization dependence of the non-linear response, with a marked difference between the clean and the disordered case. Our results are particularly relevant for recent experiments in cuprates, whose band structure is in a first approximation reproduced by our lattice model.

References in corpus (36)

• Inelastic Light Scattering From Correlated Electrons
• Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach
• Higgs Amplitude Mode in BCS Superconductors Nb${}_{1-x}$Ti${}_x$N induced by Terahertz Pulse Excitation
• Amplitude / Higgs Modes in Condensed Matter Physics
• Nature of the superconductor-insulator transition in disordered superconductors
• Inhomogeneous Pairing in Highly Disordered s-wave Superconductors
• Higgs Mode in Superconductors
• Theory of Anderson pseudospin resonance with Higgs mode in superconductors
• The Higgs Mode in Disordered Superconductors Close to a Quantum Phase Transition
• Non-linear optical effects and third-harmonic generation in superconductors: Cooper-pairs vs Higgs mode contribution
• Strongly disordered TiN and NbTiN s-wave superconductors probed by microwave electrodynamics
• Higgs mode in the d-wave superconductor Bi2Sr2CaCu2O8+x driven by an intense terahertz pulse
• Phase-resolved Higgs response in superconducting cuprates
• Polarization-resolved terahertz third-harmonic generation in a superconductor NbN: dominance of Higgs mode beyond the BCS approximation
• Discovery of Terahertz Second Harmonic Generation from Lightwave Acceleration of Symmetry--Breaking Nonlinear Supercurrents
• Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impurities
• Classification and characterization of nonequilibrium Higgs modes in unconventional superconductors
• Non-relativistic dynamics of the amplitude (Higgs) mode in superconductors
• Nonlinear optical response of collective modes in multiband superconductors assisted by nonmagnetic impurities
• Fluctuations, dissipation, and nonuniversal superfluid jumps in two-dimensional superconductors
• Signature of the Leggett mode in the A1g Raman response: from MgB2 to iron-based superconductors
• Superfluid density and phase relaxation in superconductors with strong disorder
• Theory of coherent oscillations detection in THz pump-probe spectroscopy: from phonons to electronic collective modes
• Optical excitation of phase modes in strongly disordered superconductors
• Anomalous gap edge dissipation in disordered superconductors on the brink of localization
• Polarization dependence of the third-harmonic generation in multiband superconductors
• Higgs-mode resonance in third harmonic generation in NbN superconductors: multiband electron-phonon coupling, impurity scattering, and polarization-angle dependence
• Optical signatures of the superconducting Goldstone mode in granular aluminum: experiments and theory
• Superconducting fluctuations probed by the Higgs mode in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ thin films
• Gauge-invariant microscopic kinetic theory of superconductivity: application to electromagnetic response of Nambu-Goldstone and Higgs modes
• On the application of Mattis-Bardeen theory in strongly disordered superconductors
• Conservation laws, vertex corrections, and screening in Raman spectroscopy
• Superconducting Energy Scales and Anomalous Dissipative Conductivity in Thin Films of Molybdenum Nitride
• Lightwave Terahertz Quantum Manipulation of Non-equilibrium Superconductor Phases and their Collective Modes
• Amplitude, density and current correlations of strongly disordered superconductors
• Two-particle spectral function for disordered s-wave superconductors: local maps and collective modes

Cited by in corpus (45)

• High harmonic spectroscopy of quantum phase transitions in a high-T${}_c$ superconductor
• Revealing novel aspects of light-matter coupling in terahertz two-dimensional coherent spectroscopy: the case of the amplitude mode in superconductors
• Non-linear Terahertz Driving of Plasma Waves in Layered Cuprates
• Spectroscopic signatures of time-reversal symmetry breaking superconductivity
• Band-selective third-harmonic generation in superconducting MgB${}_2$: Possible evidence for Higgs amplitude mode in the dirty limit
• Fano interference of the Higgs mode in cuprate high-Tc superconductors
• High-order nonlinear terahertz probing of the two-band superconductor MgB${}_2$: Third- and fifth-order harmonic generation
• THz non-linear optical response in cuprates: predominance of the BCS response over the Higgs mode
• Nonlinear Response of Diffusive Superconductors to $ac$-electromagnetic Fields
• Contribution of Collective Excitations to Third Harmonic Generation in Multiband Superconductors: the case of MgB${}_2$
• Observation of terahertz second harmonic generation from Dirac surface states in the topological insulator Bi${}_2$Se${}_3$
• Phase signatures in third-harmonic response of Higgs and coexisting modes in superconductors
• Multi-Dimensional Coherent Spectroscopy of Light-Driven States and their Collective Modes in Multi-Band Superconductors
• Quench-drive spectroscopy and high-harmonic generation in BCS superconductors
• Calculation of an enhanced A1g symmetry mode induced by Higgs oscillations in the Raman spectrum of high-temperature cuprate superconductors
• The Higgs-Amplitude mode in the optical conductivity in the presence of a supercurrent: Gauge-invariant formulation with disorder
• Investigating Josephson plasmons in layered cuprates via nonlinear terahertz spectroscopy
• Third-harmonic generation in excitonic insulators
• Discovery of an Unconventional Quantum Echo by Interference of Higgs Coherence
• Collisionless dynamics in disordered superconductors
• Unlocking Quantum Control and Multi-Order Correlations via Terahertz Two-Dimensional Coherent Spectroscopy
• Nonlinear optical responses in superconductors under magnetic fields: quantum geometry and topological superconductivity
• Long-lived Higgs modes in strongly correlated condensates
• Direct observation of the Higgs particle in a superconductor by non-equilibrium Raman scattering
• Optical response of Higgs mode in superconductors at clean limit: formulation through Eilenberger equation and Ginzburg-Landau Lagrangian
• Thermal effects on collective modes in disordered $s$-wave superconductors
• Optically active Higgs and Leggett modes in multiband pair-density-wave superconductors with Lifshitz invariant
• Higgs and Nambu-Goldstone modes in condensed matter physics
• Higgs-mode-induced instability and kinetic inductance in strongly dc-biased dirty-limit superconductors
• Terahertz amplifiers based on gain reflectivity in cuprate superconductors
• Spatially resolved collective modes in d-wave superconductors
• Time-resolved optical conductivity and Higgs oscillations in two-band dirty superconductors
• Higgs physics in superconductors
• Reducing the frequency of the Higgs mode in a helical superconductor coupled to an LC-circuit
• 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
• Signatures of Bardasis-Schrieffer mode excitation in Third-Harmonic generated currents
• Terahertz pulse-driven collective mode in the nematic superconducting state of Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$
• Dynamical signatures and control of time-reversal breaking in twisted nodal superconductors
• Two-dimensional THz spectroscopy in electronic systems: a many-body diagrammatic approach
• Momentum-resolved two-dimensional spectroscopy as a probe of nonlinear quantum field dynamics
• Measuring intrinsic relaxation rates in superconductors using nonlinear response
• Subgap two-particle spectral weight in disordered $s$-wave superconductors: Insights from mode coupling approach
• Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles
• Raman response of collective modes in multicomponent superconductors