TY - GEN A1 - Seibold, Götz A1 - Udina, Mattia A1 - Castellani, Claudio A1 - Benfatto, Lara T1 - Third harmonic generation from collective modes in disordered superconductors T2 - Physical Review B N2 - Recent experiments with strong THz fields in both conventional and unconventional superconductors have clearly evidenced a marked third-harmonic generation below the superconducting temperature Tc. 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 nonlinear current by implementing a time-dependent Bogoljubov–de Gennes approach, with the twofold aim to account nonperturbatively 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 nonlinear 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. KW - High-order harmonic generation KW - Impurities in superconductors KW - Optical & microwave phenomena KW - Quasiparticles & collective excitations KW - Superconductivity KW - Disordered systems KW - Higgs bosons KW - Bogoliubov-de Gennes equations Y1 - 2021 UR - https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.014512 U6 - https://doi.org/10.1103/PhysRevB.103.014512 VL - 103 IS - 1 ER - TY - GEN A1 - Seibold, Götz A1 - Castellani, Claudio A1 - Lorenzana, José T1 - Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics T2 - Physical Review B N2 - We investigate the physics of an adiabatic transition from a BCS superconductor to a Fermi liquid for an exponentially slow decreasing pairing interaction. We show that, depending on the order of the thermodynamic limit and large times, a situation can arise in which the Fermi liquid keeps a memory of the parent BCS state. Furthermore, a time inversion of the interaction, supplemented by a manipulation analogous to a spin-/photon-echo experiment, allows us to recover the parent BCS state. Moreover, we study the evolution of the order parameter phase ϕ in transforming the BCS superconductor to a conventional metal. Since the global phase is the conjugate variable of the density, we explicitly show how to use the dynamics of ϕ together with gauge invariance to build up the noninteracting chemical potential away from particle-hole symmetry. We further analyze the role of ϕ in restoring the gauge-invariant current response when the noninteracting Fermi liquid is approached starting from a BCS superconductor in the presence of an external vector field. KW - Superconductivity KW - Nonequilibrium systems KW - Adiabatic approximation KW - BCS theory KW - Gauge symmetries KW - Variational approach Y1 - 2022 UR - https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.184513 U6 - https://doi.org/10.1103/PhysRevB.105.184513 SN - 2469-9969 VL - 105 IS - 18 SP - 184513-1 EP - 184513-14 ER - TY - GEN A1 - Seibold, Götz A1 - Benfatto, Lara A1 - Castellani, Claudio T1 - Application of the Mattis-Bardeen theory in strongly disordered superconductors T2 - Physical Review B N2 - The low-energy optical conductivity of conventional superconductors is usually well described by Mattis-Bardeen (MB) theory, which predicts the onset of absorption above an energy corresponding to twice the superconducing (SC) gap parameter Δ. Recent experiments on strongly disordered superconductors have challenged the application of the MB formulas due to the occurrence of additional spectral weight at low energies below 2Δ. Here we identify three crucial items that have to be included in the analysis of optical-conductivity data for these systems: (a) the correct identification of the optical threshold in the Mattis-Bardeen theory and its relation with the gap value extracted from the measured density of states, (b) the gauge-invariant evaluation of the current-current response function needed to account for the optical absorption by SC collective modes, and (c) the inclusion into the MB formula of the energy dependence of the density of states present already above Tc. By computing the optical conductivity in the disordered attractive Hubbard model, we analyze the relevance of all these items, and we provide a compelling scheme for the analysis and interpretation of the optical data in real materials. KW - Superconductivity KW - Superconductivity fluctuations KW - Impurities in superconductors Y1 - 2017 UR - https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.144507 U6 - https://doi.org/10.1103/PhysRevB.96.144507 VL - 96 IS - 14 SP - 144507 ER - TY - GEN A1 - Tea, C. A1 - Castellani, Claudio A1 - Seibold, Götz A1 - Benfatto, Lara T1 - Nonrelativistic Dynamics of the Amplitude (Higgs) Mode in Superconductors T2 - Physical Review Letters Y1 - 2015 UR - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.157002 U6 - https://doi.org/http://dx.doi.org/10.1103/PhysRevLett.115.157002 SN - 1079-7114 VL - 115 SP - 157002 ER - TY - GEN A1 - Lemarié, Gabriel A1 - Kamlapure, Anand A1 - Benfatto, Lara A1 - Lorenzana, José A1 - Seibold, Götz A1 - Ganguli, S. C. A1 - Raychaudhuri, Pratap A1 - Castellani, Claudio T1 - Universal scaling of the order-parameter distribution in strongly disordered superconductors T2 - Physical Review B N2 - We investigate theoretically and experimentally the statistical properties of the inhomogeneous order-parameter distribution (OPD) at the verge of the superconductor-insulator transition (SIT). We find within two prototype fermionic and bosonic models for disordered superconductors that one can identify a universal rescaling of the OPD. By performing scanning-tunneling microscopy experiments in three samples of NbN with increasing disorder we show that such a rescaling also describes the experimental data with excellent accuracy. These results can provide a breakthrough in our understanding of the SIT. Y1 - 2013 UR - http://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.184509 U6 - https://doi.org/10.1103/PhysRevB.87.184509 SN - 2469-9977 VL - 87 IS - 18 SP - 184509 ER - TY - GEN A1 - Seibold, Götz A1 - Becca, Federico A1 - Bucci, F. A1 - Castellani, Claudio A1 - Di Castro, Carlo A1 - Grilli, Marco T1 - Spectral properties of incommensurate charge-density wave systems Y1 - 2000 ER - TY - GEN A1 - Seibold, Götz A1 - Castellani, Claudio A1 - Di Castro, Carlo T1 - Fermi surface and electronic structure of incommensurate charge-density-wave systems Y1 - 2000 ER - TY - GEN A1 - Seibold, Götz A1 - Benfatto, Lara A1 - Castellani, Claudio A1 - Lorenzana, José T1 - Current Correlations in Strongly Disordered Superconductors T2 - Journal of Superconductivity and Novel Magnetism Y1 - 2016 UR - http://link.springer.com/article/10.1007%2Fs10948-015-3300-6 U6 - https://doi.org/10.1007/s10948-015-3300-6 VL - 29 IS - 3 SP - 577 EP - 580 ER - TY - GEN A1 - Benfatto, Lara A1 - Castellani, Claudio A1 - Seibold, Götz T1 - Linear and nonlinear current response in disordered d-wave superconductors T2 - Physical Review B N2 - We present a detailed theoretical investigation of the linear and nonlinear optical response in a model system for a disordered d-wave superconductor. By evaluating the quasiparticle contribution (BCS response) we show that for both quantities the gap symmetry considerably changes the paradigm of the optical response as compared to the conventional s-wave case. For what concerns the linear response our findings agree with previous work showing that in strongly disordered d-wave superconductors a large fraction of uncondensed spectral weight survives below Tc, making the optical absorption around the gap-frequency scale almost unchanged with respect to the normal state. Our numerical results are in excellent quantitative agreement with experiments in overdoped cuprates. In the nonlinear regime we focus on the third-harmonic generation (THG), finding that, as already established for the s-wave case, in general a large THG is triggered by disorder-activated paramagnetic processes. However, in the d-wave case the BCS response is monotonously increasing in frequency, losing any signature of THG enhancement when the THz pump frequency ω matches the gap maximum Δ, a hallmark of previous experiments in conventional s-wave superconductors. Our findings, along with the mild polarization dependence of the response, provide an explanation for recent THG measurements in cuprates, setting the framework for the theoretical understanding of nonlinear effects in unconventional cuprates. KW - Superconducting order parameter KW - Superfluid density KW - High-temperature superconductors KW - Superconductivity KW - Drude model KW - Numerical techniques KW - Reflectivity KW - Terahertz spectroscopy Y1 - 2023 UR - https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.134508 U6 - https://doi.org/10.1103/PhysRevB.108.134508 SN - 2469-9969 SN - 2469-9950 VL - 108 SP - 134508-1 EP - 134508-15 ER - TY - GEN A1 - Seibold, Götz A1 - Castellani, Claudio A1 - Di Castro, Carlo A1 - Grilli, Marco T1 - Fermi surface and photoemission lineshape of incommensurate CDW systems Y1 - 2000 ER - TY - CHAP A1 - Seibold, Götz A1 - Castellani, Claudio A1 - Di Castro, Carlo A1 - Grilli, Marco ED - Bianconi, Antonio ED - Saini, Naurang L. T1 - Domain wall structures in the two-dimensional Hubbard modelwith long-range Coulomb interaction T2 - Stripes and Related Phenomena Y1 - 2000 SN - 0-306-46419-5 U6 - https://doi.org/10.1007/0-306-47100-0_18 SP - 151 EP - 157 PB - Kluwer Academic Plenum CY - New York ER - TY - GEN A1 - Seibold, Götz A1 - Castellani, Claudio A1 - Di Castro, Carlo A1 - Grilli, Marco T1 - Striped phases in the two-dimensional Hubbard model with long-rangeCoulomb interaction Y1 - 1998 ER - TY - GEN A1 - Seibold, Götz A1 - Castellani, Claudio A1 - Di Castro, Carlo A1 - Grilli, Marco ED - Barnes, Stewart E. T1 - Role of the long-range Coulomb interaction on the formation of striped phases in the two-dimensional Hubbard model T2 - High temperature superconductivity, Coral Gables, Florida, January 1999 Y1 - 1999 SN - 1-56396-880-0 U6 - https://doi.org/10.1063/1.59651 PB - AIP Publishing CY - Melville, New York ER - TY - GEN A1 - Cea, Tommaso A1 - Bucheli, Daniel A1 - Seibold, Götz A1 - Benfatto, Lara A1 - Lorenzana, José A1 - Castellani, Claudio T1 - Optical excitation of phase modes in strongly disordered superconductors T2 - Physical Review B N2 - According to the Goldstone theorem the breaking of a continuous U(1) symmetry comes along with the existence of low-energy collective modes. In the context of superconductivity these excitations are related to the phase of the superconducting (SC) order parameter and for clean systems are optically inactive; that is, single-mode excitations do not directly couple to light. Here we show that for strongly disordered superconductors phase modes acquire a dipole moment and appear as a subgap spectral feature in the optical conductivity. This finding is obtained with both a gauge-invariant random-phase approximation scheme based on a fermionic Bogoliubov–de Gennes state and a prototypical bosonic model for disordered superconductors. In the strongly disordered regime, where the system displays an effective granularity of the SC properties, the optically active dipoles are linked to the isolated SC islands, offering a new perspective for realizing microwave optical devices. Y1 - 2014 UR - http://journals.aps.org/prb/abstract/10.1103/PhysRevB.89.174506 U6 - https://doi.org/10.1103/PhysRevB.89.174506 SN - 2469-9969 VL - 89 SP - 174506 ER - TY - GEN A1 - Seibold, Götz A1 - Benfatto, Lara A1 - Castellani, Claudio A1 - Lorenzana, José T1 - Amplitude, density, and current correlations of strongly disordered superconductors T2 - Physical Review B N2 - We investigate the disorder dependence of the static density, amplitude, and current correlations within the attractive Hubbard model supplemented with onsite disorder. It is found that strong disorder favors a decoupling of density and amplitude correlations due to the formation of superconducting (SC) islands. This emergent granularity also induces an enhancement of the density correlations on the SC islands whereas amplitude fluctuations are most pronounced in the “insulating” regions. While density and amplitude correlations are short ranged at strong disorder, we show that current correlations have a long-range tail due to the formation of percolative current paths in agreement with the constant behavior expected from the analysis of one-dimensional models. Y1 - 2015 UR - http://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.064512 U6 - https://doi.org/10.1103/PhysRevB.92.064512 SN - 2469-9969 VL - 92 IS - 6 SP - 064512 ER - TY - GEN A1 - Seibold, Götz A1 - Benfatto, Lara A1 - Castellani, Claudio A1 - Lorenzana, José T1 - Superfluid Density and Phase Relaxation in Superconductors with Strong Disorder T2 - Physical Review Letters N2 - We consider the attractive Hubbard model with on-site disorder as a prototype of a disordered superconductor. We solve the Bogoliubov–de Gennes equations on two-dimensional finite clusters at zero temperature and evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder. Moreover, the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the phase fluctuations is strongly enhanced by disorder. Beyond mean field, this provides an enhancement of quantum fluctuations inducing a zero-temperature transition to a nonsuperconducting phase of disordered preformed pairs. Finally, the connection of our findings with the glassy physics for extreme dirty superconductors is discussed. Y1 - 2012 UR - http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.207004 U6 - https://doi.org/10.1103/PhysRevLett.108.207004 SN - 1092-0145 VL - 108 IS - 20 SP - 207004 ER - TY - GEN A1 - Udina, Mattia A1 - Fioro, Jacopo A1 - Cea, Tommaso A1 - Castellani, Claudio A1 - Seibold, Götz A1 - Benfatto, Lara T1 - THz non-linear optical response in cuprates: predominance of the BCS response over the Higgs mode T2 - Faraday Discussions N2 - Recent experiments with strong THz fields in unconventional cuprate superconductors have clearly evidenced an increase of the non-linear optical response below the superconducting critical temperature Tc. As in the case of conventional superconductors, a theoretical estimate of the various effects contributing to the non-linear response is needed in order to interpret the experimental findings. Here, we report a detailed quantitative analysis of the non-linear THz optical kernel in cuprates within a realistic model, accounting for the band structure and disorder level appropriate for these systems. We show that the BCS quasiparticle response is the dominant contribution for cuprates, and its polarization dependence accounts very well for the third-harmonic generation measurements. On the other hand, the polarization dependence of the THz Kerr effect is only partly captured by our calculations, suggesting the presence of additional effects when the system is probed using light pulses with different central frequencies. Y1 - 2022 UR - https://pubs.rsc.org/en/content/articlelanding/2022/FD/D2FD00016D U6 - https://doi.org/10.1039/D2FD00016D SN - 1364-5498 VL - 237 SP - 168 EP - 185 ER -