Gauge-Invariant Wigner Function Extended to High Temperature Superconductivity

Abstract

The realization of gauge-invariant Wigner function (GIWF) has revolutionized studies on quantized and classical electromagnetic fields and has been adapted to a magnetostatic phenomenon in superconducting systems. We apply the quantum fluid moment hierarchy equations in solving the conservative moment equation of the gauge-invariant Wigner operator. The results show that the lower critical field (𝐻𝑐1), the vortex radius (𝑟0) and the penetration depth (𝜆) show dependence on Cooper pair excitation energy (𝐸𝑘).