Influence of Harris disorder on quantum-critical superconductivity

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Original abstract

In the Hertz theory, a quantum critical metal is described by the coupling of a Fermi surface to fluctuations of a Landau-damped bosonic field $φ$, which may represent either an order parameter or a Higgs field for a transition without symmetry breaking. Scattering from $φ$ produces non-Fermi-liquid behavior in the normal state, while the same fluctuations mediate enhanced Cooper pairing. By the Harris criterion, symmetry-preserving disorder couples most strongly to the coefficient of the $φ^2$ term, locally tuning the system toward or away from criticality. This random mass (``Harris disorder'') leads to a finite density of localized low-energy $φ$ modes even when the fermionic states remain extended and continue to provide Landau damping. We study the onset of pairing mediated by these localized overdamped bosonic modes. Starting from a real-space linearized Usadel equation for the two-particle propagator, we show that the localized bosonic wave functions generate both a spatially random pairing vertex and an effective random potential for Cooper pairs. Numerical solution, a self-consistent Born approximation, and Lifshitz-tail analysis reveal two regimes of the pairing instability. At high temperatures, pairing nucleates compact superconducting puddles on the most localized bosonic modes. At lower temperatures, an extended pairing eigenstate appears, but its transition scale and spatial structure remain strongly affected by mesoscopic correlation effects and enhanced probability of returns to favorable regions of the localized bosonic glue. The resulting distribution of local pairing scales has a power-law tail, in contrast to the stretched-exponential tails of disordered BCS superconductors. This mechanism provides a route to broad gap inhomogeneity and superconducting puddles in quantum-critical metals, and offers an interpretation of STM measurements of the cuprates.

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• Official / arXiv page
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