Signatures of Unconventional Superconductivity in Granular Aluminum

Bachar, N.; Pracht, Uwe S.; Farber, E.; Dressel, Martin; Deutscher, G.; Scheffler, Marc

doi:10.1007/s10909-014-1244-z

Cited by 18 publications

(19 citation statements)

References 22 publications

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“…in the quantity 2 in Eq. (16). However, this procedure in the present case is quite cumbersome since 2 also appears in the frequency-dependent DOS.…”

Section: Effect Of a Pseudogap In The Mattis-bardeen Formulamentioning

confidence: 87%

Application of the Mattis-Bardeen theory in strongly disordered superconductors

2017

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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 . 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 2. 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

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“…in the quantity 2 in Eq. (16). However, this procedure in the present case is quite cumbersome since 2 also appears in the frequency-dependent DOS.…”

Section: Effect Of a Pseudogap In The Mattis-bardeen Formulamentioning

confidence: 87%

Application of the Mattis-Bardeen theory in strongly disordered superconductors

2017

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“…This implies that in addition to the thermally excited quasiparticles another dissipative channel is present. While various complex mechanisms leading to finite in-gap absorption in disordered SC have been recently addressed in both theory [39][40][41] and experiment [42][43][44], here, we can model t and φ/ν reasonably well by simply adding a Drude contribution to the MB dynamics…”

Section: Anomalous Dissipative Conductivitymentioning

confidence: 95%

Superconducting energy scales and anomalous dissipative conductivity in thin films of molybdenum nitride

et al. 2016

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We report investigations of molybdenum nitride (MoN) thin films with different thickness and disorder and with superconducting transition temperature 9.89 K ≥ Tc ≥ 2.78 K. Using terahertz frequency-domain spectroscopy we explore the normal and superconducting charge carrier dynamics for frequencies covering the range from 3 to 38 cm −1 (0.1 to 1.1 THz). The superconducting energy scales, i.e. the critical temperature Tc, the pairing energy ∆, and the superfluid stiffness J, and the superfluid density ns can be well described within the Bardeen-Cooper-Schrieffer theory for conventional superconductors. At the same time, we find an anomalously large dissipative conductivity, which cannot be explained by thermally excited quasiparticles, but rather by a temperature-dependent normal-conducting fraction, persisting deep into the superconducting state. Our results on this disordered system constrain the regime, where discernible effects stemming from the disorder-induced superconductor-insulator transition possibly become relevant, to MoN films with a transition temperature lower than at least 2.78 K.

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“…InO x and NbN, and understood theoretically as the effect of the localization of bosonic pairs with large E gap [36][37][38]. However, in both cases it has not been proven yet the existence or not of a sharp Higgs mode at 2∆ 0 , which is also the prerequisite used recently [14] to interpret the observed sub-gap optical absorption in films of disordered superconductors [14,[39][40][41].In this Letter we demonstrate the lack of a LI Higgs resonance at 2∆ 0 for fermionic superconductors. At weak coupling, where the amplitude and phase sectors are decoupled because of the particle-hole symmetry of the BCS solution, this is a well-known[4, 5, 10] effect of the quasiparticles proliferation at 2∆ 0 , which overdamp the Higgs mode and spoil its relativistic dynamics.…”

mentioning

confidence: 99%

“…Let us finally comment on the relevance of these results for experiments in disordered films of superconductors, where a dissipative absorption σ(ω) at ω < 2E gap and T T c has been recently found [14,[39][40][41]. Since in this regime quasiparticle excitations are suppressed, the extra-absorption should arise from the SC collective modes, whose leading-order contribution to the current J can be written in general as [49,56]…”

mentioning

confidence: 99%

“…On the other hand, in the presence of disorder the one-phason process of Fig. 3a contributes also to the finite-frequency optical response [5,11,58], making it the most plausible candidate to explain the experimental findings [14,[39][40][41]. In particular, for the fermionic model (S1) it has been proven [5] that the phase fluctuations give the largest contribution to sub-gap absorption, via a process equivalent to the one depicted in Fig.…”

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confidence: 99%

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Nonrelativistic Dynamics of the Amplitude (Higgs) Mode in Superconductors

et al. 2015

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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 a "bosonic" limit is always reached via 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 subgap optical absorption in disordered superconductors.

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Signatures of Unconventional Superconductivity in Granular Aluminum

Cited by 18 publications

References 22 publications

Application of the Mattis-Bardeen theory in strongly disordered superconductors

Application of the Mattis-Bardeen theory in strongly disordered superconductors

Superconducting energy scales and anomalous dissipative conductivity in thin films of molybdenum nitride

Nonrelativistic Dynamics of the Amplitude (Higgs) Mode in Superconductors

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