@misc{SeiboldUdinaCastellanietal., author = {Seibold, G{\"o}tz and Udina, Mattia and Castellani, Claudio and Benfatto, Lara}, title = {Third harmonic generation from collective modes in disordered superconductors}, series = {Physical Review B}, volume = {103}, journal = {Physical Review B}, number = {1}, doi = {10.1103/PhysRevB.103.014512}, pages = {19}, 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 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.}, language = {en} } @misc{SeiboldBenfattoCastellani, author = {Seibold, G{\"o}tz and Benfatto, Lara and Castellani, Claudio}, title = {Application of the Mattis-Bardeen theory in strongly disordered superconductors}, series = {Physical Review B}, volume = {96}, journal = {Physical Review B}, number = {14}, doi = {10.1103/PhysRevB.96.144507}, pages = {144507}, abstract = {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.}, language = {en} } @misc{TeaCastellaniSeiboldetal., author = {Tea, C. and Castellani, Claudio and Seibold, G{\"o}tz and Benfatto, Lara}, title = {Nonrelativistic Dynamics of the Amplitude (Higgs) Mode in Superconductors}, series = {Physical Review Letters}, volume = {115}, journal = {Physical Review Letters}, issn = {1079-7114}, doi = {http://dx.doi.org/10.1103/PhysRevLett.115.157002}, pages = {157002}, language = {en} } @misc{LemarieKamlapureBenfattoetal., author = {Lemari{\´e}, Gabriel and Kamlapure, Anand and Benfatto, Lara and Lorenzana, Jos{\´e} and Seibold, G{\"o}tz and Ganguli, S. C. and Raychaudhuri, Pratap and Castellani, Claudio}, title = {Universal scaling of the order-parameter distribution in strongly disordered superconductors}, series = {Physical Review B}, volume = {87}, journal = {Physical Review B}, number = {18}, issn = {2469-9977}, doi = {10.1103/PhysRevB.87.184509}, pages = {184509}, abstract = {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.}, language = {en} } @misc{MondalKumarChandetal., author = {Mondal, Mintu and Kumar, Sanjeev and Chand, Madhavi and Kamlapure, Anand and Saraswat, Garima and Seibold, G{\"o}tz and Benfatto, Lara and Raychaudhuri, Pratap}, title = {Role of the Vortex-Core Energy on the Berezinskii-Kosterlitz-Thouless Transition in Thin Films of NbN}, doi = {10.1103/PhysRevLett.107.217003}, language = {en} } @misc{SeiboldBenfattoCastellanietal., author = {Seibold, G{\"o}tz and Benfatto, Lara and Castellani, Claudio and Lorenzana, Jos{\´e}}, title = {Current Correlations in Strongly Disordered Superconductors}, series = {Journal of Superconductivity and Novel Magnetism}, volume = {29}, journal = {Journal of Superconductivity and Novel Magnetism}, number = {3}, doi = {10.1007/s10948-015-3300-6}, pages = {577 -- 580}, language = {en} } @misc{BenfattoCastellaniSeibold, author = {Benfatto, Lara and Castellani, Claudio and Seibold, G{\"o}tz}, title = {Linear and nonlinear current response in disordered d-wave superconductors}, series = {Physical Review B}, volume = {108}, journal = {Physical Review B}, issn = {2469-9969}, doi = {10.1103/PhysRevB.108.134508}, pages = {134508-1 -- 134508-15}, abstract = {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.}, language = {en} } @misc{CeaBucheliSeiboldetal., author = {Cea, Tommaso and Bucheli, Daniel and Seibold, G{\"o}tz and Benfatto, Lara and Lorenzana, Jos{\´e} and Castellani, Claudio}, title = {Optical excitation of phase modes in strongly disordered superconductors}, series = {Physical Review B}, volume = {89}, journal = {Physical Review B}, issn = {2469-9969}, doi = {10.1103/PhysRevB.89.174506}, pages = {174506}, abstract = {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.}, language = {en} } @misc{SeiboldBenfattoCastellanietal., author = {Seibold, G{\"o}tz and Benfatto, Lara and Castellani, Claudio and Lorenzana, Jos{\´e}}, title = {Amplitude, density, and current correlations of strongly disordered superconductors}, series = {Physical Review B}, volume = {92}, journal = {Physical Review B}, number = {6}, issn = {2469-9969}, doi = {10.1103/PhysRevB.92.064512}, pages = {064512}, abstract = {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.}, language = {en} } @misc{SeiboldBenfattoCastellanietal., author = {Seibold, G{\"o}tz and Benfatto, Lara and Castellani, Claudio and Lorenzana, Jos{\´e}}, title = {Superfluid Density and Phase Relaxation in Superconductors with Strong Disorder}, series = {Physical Review Letters}, volume = {108}, journal = {Physical Review Letters}, number = {20}, issn = {1092-0145}, doi = {10.1103/PhysRevLett.108.207004}, pages = {207004}, abstract = {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.}, language = {en} }