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arXiv:1509.05138

Superfluid density of a pseudogapped superconductor near SIT

M. V. Feigel’man, L. B. Ioffe

Published Sep 17, 2015• 0 citations
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Abstract

We analyze critical behavior of superfluid density $ρ_s$ in strongly disordered superconductors near superconductor-insulator transition and compare it with the behavior of the spectral gap $Δ$ for collective excitations. We show that in contrast to conventional superconductors, the superconductors with preformed pairs display unusual scaling relation $ρ_s \propto Δ^2$ close to superconductor-insulator transition. This relation have been reported in very recent experiments.

DOI
10.48550/arxiv.1509.05138

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We analyze the critical behavior of the superfluid density ${\ensuremath{\rho}}_{s}$ in strongly disordered superconductors near the superconductor-insulator transition and compare it with the behavior of the spectral gap $\mathrm{\ensuremath{\Delta}}$ for collective excitations. We show that, in contrast to conventional superconductors, the superconductors with preformed pairs display an unusual scaling relation ${\ensuremath{\rho}}_{s}\ensuremath{\propto}{\mathrm{\ensuremath{\Delta}}}^{2}$ close to the superconductor-insulator transition. This relation has been reported in very recent experiments.
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We show, using a Bogoliubov-de Gennes (BdG) mean field theory, that the local pairing amplitude Δ(r) becomes highly inhomogeneous with increasing disorder in an s-wave superconductor. The probability distribution P(Δ) is peaked about the BCS value at low disorder, but with increasing disorder, progressively develops into a broad distribution with significant build up of weight near Δ≈0. At high disorder, the system is found to form superconducting "islands" separated by a non-superconducting sea. Surprisingly, a finite energy gap persists into the highly disordered state in spite of many sites having negligible pairing amplitude and is understood in detail within the BdG framework. Once the pairing amplitude becomes inhomogeneous, the role of quantum phase fluctuations becomes crucial in driving a superconductor-insulator transition at a critical disorder. The insulator is unusual as it has a finite gap for all disorder strengths in marked contrast to the Anderson insulator in non-interacting systems. We treat the phase fluctuations within a self consistent harmonic approximation and obtain the superfluid stiffness as a function of disorder, which agrees well with our earlier quantum Monte Carlo studies.