arXiv subjects

C. Castellani

Publications and source records attributed to C. Castellani.

At least 19 recordsLinked to original sources

arXiv2023

Linear and non-linear current response in disordered d-wave superconductors

We present a detailed theoretical investigation of the linear and non-linear optical response in a model system for a disordered d-wave superconductor, showing that for both quantities the gap symmetry considerably changes the paradigm of the optical response based on 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 non-linear 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, loosing any signature of THG enhancement when the THz pump frequency $\omega$ matches the gap maximum $\Delta$, a hallmark of previous experiments in conventional s-wave superconductors. Our findings, along with the mild polarization dependence of the response, provides an explanation for recent THG measurements in cuprates, setting the framework for the theoretical understanding of non-linear effects in unconventional cuprates.

cond-mat.supr-con↗

arXiv2022

Comment on: Calculation of an Enhanced $A_{1g}$ Symmetry Mode Induced by Higgs Oscillations in the Raman Spectrum of High-Temperature Cuprate Superconductors

In a recent manuscript Phys. Rev. Lett. 127, 197001 (2021) Puviani et al. claim that the Higgs mode gives an enhancement of the Raman response in the symmetric $A_{1g}$ Raman channel of cuprates. Here we report a series of technical mistakes in their derivation that completely invalidate this conclusion. In particular, the Raman response function contains two renormalized vertices, with a clearly overcounting of diagrams and uncontrolled results for the Higgs-mode contribution.

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arXiv2021

Generalized plasma waves in layered superconductors

In a layered and strongly anisotropic superconductor the hybrid modes provided by the propagation of electromagnetic waves in the matter identify two well separate energy scales connected to the large in-plane plasma frequency and to the soft out-of-plane Josephson plasmon. Despite the wide interest in their detection and manipulation by means of different experimental protocols, a unified description of plasma waves valid at arbitrary energy and momentum is still lacking. Here we provide a complete description of generalized plasma waves in a layered superconductors by taking advantage of their connection to the gauge-invariant superconducting phase. We show that the anisotropy of the superfluid response leads to two intertwined hybrid light-matter modes with mixed longitudinal and transverse character, while a purely longitudinal plasmon is only recovered for wavevectors larger than the crossover scale set in by the plasma-frequencies anisotropy. Interestingly, below such scale both modes appears with equal weight in the physical density response. Our results open a promising perspective for plasmonic applications made possible by the next-generation spectroscopic techniques able to combine sub-micron momentum resolution with THz energy resolution.

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arXiv2021

Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics

We investigate the physics of an adiabatic transition from a BCS superconductor to a Fermi liquid for an exponentially slow decreasing pairing interaction. In particular, we show that the metal keeps memory of the parent BCS state so it is possible to reverse the dynamics and go back to the original state similarly to a spin/photon echo experiment. Moreover, we study the evolution of the order parameter phase phi 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 phi together with gauge invariance to build up the non-interacting chemical potential away from particle-hole symmetry. We further analyze the role of phi in restoring the gauge invariant current response when the non-interacting Fermi liquid is approached starting from a BCS superconductor in the presence of an external vector field.

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arXiv2020

Third harmonic generation from collective modes in disordered superconductors

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.

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arXiv2018

Polarization dependence of the third-harmonic generation in multiband superconductors

In a superconductor the third-harmonic generation (THG) of a strong THz pulse is enhanced below Tc by the resonant excitation of lattice-modulated charge fluctuations (LCF), which modulate the response according to the polarization of the field. Here we compute the THG within a multiband model for the prototype NbN superconductor. We show that the non-resonant contribution coming from the instantaneous electronic response and the finite width of the pulse significantly suppress the polarization dependence of the signal, challenging its observation in real systems.

cond-mat.supr-con↗

arXiv2017

Broadening of the Berezinskii-Kosterlitz-Thouless transition by correlated disorder

The Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional superconductors is usually expected to be protected against disorder. However, its typical signatures in real system, like e.g. the superfluid-density jump, are often at odd with this expectation. Here we show that the disorder-induced granularity of the superconducting state modifies the nucleation mechanism for vortex-antivortex pairs. This leads to a considerable smearing of the universal superfluid-density jump as compared to the paradigmatic clean case, in agreement with experimental observations.

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arXiv2017

On the application of Mattis-Bardeen theory in strongly disordered superconductors

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 Delta. 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 2Delta. Here we identify three crucial items which 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 conductvity 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.

cond-mat.supr-con↗

arXiv2016

Non-linear optical effects and third-harmonic generation in superconductors: Cooper-pairs vs Higgs mode contribution

The recent observation of a transmitted Thz pulse oscillating at three times the frequency of the incident light paves the way to a new protocol to access resonant excitations in a superconductor. Here we show that this non-linear optical process is dominated by light-induced excitation of Cooper pairs, in analogy with a standard Raman experiment. The collective amplitude (Higgs) fluctuations of the superconducting order parameter give in general a smaller contribution, unless one designs the experiment by combining properly the light polarization with the lattice symmetry.

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arXiv2015

Non-relativistic dynamics of the amplitude (Higgs) mode in superconductors

Despite the formal analogy with the Higgs particle, the amplitude fluctuations of the order parameter in weakly-coupled superconductors do not identify a real mode with a Lorentz-invariant dynamics. Indeed, its resonance occurs at $2Δ_0$, which coincides with the threshold $2E_{gap}$ for quasiparticle excitations, that spoil any relativistic dynamics. Here we investigate the fate of the Higgs mode in the unconventional case where $2E_{gap}$ becomes larger than $2Δ_0$, as due to strong coupling or strong disorder. We show that also in this situation the amplitude fluctuations never identify a real mode at $2Δ_0$, since such "bosonic" limit is always reached via a strong mixing with the phase fluctuations, which dominate the low-energy part of the spectrum. Our results have direct implications for the interpretation of the sub-gap optical absorption in disordered superconductors.

cond-mat.supr-con↗

arXiv2015

Amplitude, density and current correlations of strongly disordered superconductors

We investigate the disorder dependence of the static density, amplitude and current correlations within the attractive Hubbard model supplemented with on-site disorder. It is found that strong disorder favors a decoupling of density and amplitude correlations due to the formation of superconducting 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.

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arXiv2014

Optical excitation of phase modes in strongly disordered superconductors

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. 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 as well as with 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.

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arXiv2014

Leggett modes in iron-based superconductors as a probe of Time Reversal Symmetry Breaking

Since their discovery, it has been suggested that pairing in pnictides can be mediated by spin fluctuations between hole and electron bands. In this view, multiband superconductivity would substantially differ from other systems like MgB2, where pairing is predominantly intraband. Indeed, interband-dominated pairing leads to the coexistence of bonding and antibonding superconducting channels. Here we show that this has profound consequences on the nature of the low-energy superconducting collective modes. In particular, the so-called Leggett mode for phase fluctuations is absent in the usual two-band description of pnictides. On the other hand, when also the repulsion between the hole bands is taken into account, a more general three-band description should be used, and a Leggett mode is then allowed. Such a model, that has been proposed for strongly hole-doped 122 compounds, can also admit a low-temperature s+is phase which breaks the time reversal symmetry. We show that the (quantum and thermal) transition from the ordinary superconductor to the s+is state is accompanied by the vanishing of the mass of Leggett-like phase fluctuations, regardless the specific values of the interaction parameters. This general result can be obtained by means of a generalized construction of the effective action for the collective degrees of freedom that allows us also to deal with the non-trivial case of dominant interband pairing.

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arXiv2013

Universal scaling of the order-parameter distribution in strongly disordered superconductors

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 describes also with an excellent accuracy the experimental data. These results can provide a breakthrough in our understanding of the SIT.

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arXiv2012

Unconventional Hall effect in pnictides from interband interactions

We calculate the Hall transport in a multiband systems with a dominant interband interaction between carriers having electron and hole character. We show that this situation gives rise to an unconventional scenario, beyond the Boltzmann theory, where the quasiparticle currents dressed by vertex corrections acquire the character of the majority carriers. This leads to a larger (positive or negative) Hall coefficient than what expected on the basis of the carrier balance, with a marked temperature dependence. Our results explain the puzzling measurements in pnictides and they provide a more general framework for transport properties in multiband materials.

cond-mat.str-el↗

arXiv2012

Metal-superconductor transition in two-dimensional electron systems with fractal-like mesoscopic disorder

Motivated by recent experimental data on thin film superconductors and oxide interfaces we propose a random-resistor network apt to describe the occurrence of a metal-superconductor transition in a two-dimensional electron system with disorder on the mesoscopic scale. We explore the interplay between the statistical distribution of local critical temperatures and the occurrence of a lower-dimensional (e.g., fractal-like) structure of a superconducting cluster embedded in the two-dimensional network. The thermal evolution of the resistivity is determined by an exact calculation and, for comparison, a mean-field approach called effective medium theory (EMT). Our calculations reveal the relevance of the distribution of critical temperatures for clusters with low connectivity. In addition, we show that the presence of spatial correlations requires a modification of standard EMT to give qualitative agreement with the exact results.

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arXiv2012

Beresinskii-Kosterlitz-Thouless transition within the sine-Gordon approach: the role of the vortex-core energy

One of the most relevant manifestations of the Beresinskii-Kosterlitz-Thouless transition occurs in quasi-two-dimensional superconducting systems. The experimental advances made in the last decade in the investigation of superconducting phenomena in low-dimensional correlated electronic systems raised new questions on the nature of the BKT transitions in real materials. A general issue concerns the possible limitations of theoretical predictions based on the XY model, that was studied as a paradigmatic example in the original formulation. Here we review the work we have done in revisiting the nature of the BKT transition within the general framework provided by the mapping into the sine-Gordon model. While this mapping was already known since long, we recently emphasized the advantages on such an approach to account for new variables in the BKT physics. One such variable is the energy needed to create the core of the vortex, that is fixed within the XY model, while it attains substantially different values in real materials. This has interesting observable consequences, especially in the case when additional relevant perturbations are present, as a coupling between stacked two-dimensional superconducting layers or a finite magnetic field.

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arXiv2012

Current-current Fermi-liquid corrections to the superconducting fluctuations on conductivity and diamagnetism

We analyze the behavior of the superconducting-fluctuations contribution to diamagnetism and conductivity in a model system having current-current interactions. We show that in proximity to a Mott-insulating phase one recovers an overall suppression of the fluctuating contribution to the conductivity with respect to diamagnetism, in close analogy with recent experiments on the underdoped phase of cuprate superconductors.

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