Nonperturbative Microscopic Theory of Superconducting Fluctuations near a Quantum Critical Point

Victor Galitski

doi:10.1103/PhysRevLett.100.127001

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Nonperturbative Microscopic Theory of Superconducting Fluctuations near a Quantum Critical Point

Victor Galitski

DOI 10.1103/PhysRevLett.100.127001 · Physical Review Letters

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Abstract

We consider an anisotropic gap superconductor in the vicinity of the disorder-driven quantum critical point. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action, which is a critical theory with the dynamic critical exponent, z=2. This allows us to use the parquet method to calculate the nonperturbative effect of quantum superconducting fluctuations on thermodynamics. We derive a general expression for the fluctuation magnetic susceptibility, which exhibits a crossover from the logarithmic dependence, χ∝lnδn, valid beyond the Ginzburg region to χ∝ln1/5δn valid in the immediate vicinity of the transition (where δn is the deviation from the critical disorder concentration). These nonperturbative results may describe the quantum critical behavior of overdoped high-temperature cuprates, disordered p-wave superconductors, and conventional superconducting films with magnetic impurities.