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

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 Tc=0, with Tc being the transition temperature. That is, for 2D overdoped (clean) superconducting films, when the parameter Tc/(c0νF) is lower than a characteristic scale, the Lorentz symmetry of relativistic equation arouses an anomalous scaling ξ0∝Tc−1.34, where ξ0 denotes the zero-temperature coherence length, νF denotes the Fermi velocity, and c0 denotes the Faber-Pippard coefficient. However, when the parameter Tc/(c0νF) is large enough, the Lorentz symmetry may be broken so that the Faber-Pippard scaling ξ0∝Tc−1 is restored.