Superconducting quantum criticality and the anomalous scaling: A nonlinear relativistic equation

Yong Tao

doi:10.1016/j.physc.2023.1354424

paper

Superconducting quantum criticality and the anomalous scaling: A nonlinear relativistic equation

arXiv:2312.07567 · doi:10.1016/j.physc.2023.1354424

Abstract

By using the Landau-Ginzburg-Wilson paradigm, we show that, near a quantum critical point (QCP), Cooper pairs at zero temperature would obey a nonlinear relativistic equation, where the imaginary time emerges as a novel dimension. This relativistic equation is applicable to certain superconductors at zero temperature for which the Faber-Pippard coherence length formula holds at and above the upper critical dimension. Here, we further show that the relativistic equation leads to a testable prediction in the vicinity of the QCP $T_{c} = 0$ , with $T_{c}$ being the transition temperature. That is, for 2D overdoped (clean) superconducting films, when the parameter $T_{c} / (c_{0} v_{F})$ is lower than a characteristic scale, the Lorentz symmetry of relativistic equation arouses an anomalous scaling $ξ_{0} \propto T_{c}^{- 1.34}$ , where $ξ_{0}$ denotes the zero-temperature coherence length, $v_{F}$ denotes the Fermi velocity, and $c_{0}$ denotes the Faber-Pippard coefficient. However, when the parameter $T_{c} / (c_{0} v_{F})$ is large enough, the Lorentz symmetry may be broken so that the Faber-Pippard scaling $ξ_{0} \propto T_{c}^{- 1}$ is restored.

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