Failure of hydrodynamics within the vortex liquid phase

TL;DR

This paper demonstrates that traditional hydrodynamic models fail to accurately describe the vortex liquid phase in type-II superconductors, advocating for a more comprehensive approach that includes higher-order spatial gradients.

Contribution

It reveals the failure of hydrodynamics in vortex liquids due to negative viscosity coefficients and proposes a method using time-dependent Ginzburg-Landau theory to better understand electric field distributions.

Findings

Hydrodynamic approach is invalidated by negative viscosity coefficients.

Higher-order spatial gradients are necessary for accurate modeling.

Time-dependent Ginzburg-Landau theory can determine electric field near boundaries.

Abstract

The recent discovery that some of the coefficients of the viscosity tensor are negative is shown to invalidate the hydrodynamic approach to the vortex liquid phase of a type-II superconductor. A satisfactory theory requires retention of all the spatial gradients of the velocities or electric fields and not just the first derivatives, as assumed in a hydrodynamic theory. We illustrate such a procedure by using time-dependent Ginzburg-Landau theory to determine the electric field distribution near a single ``twin-plane boundary" due to a current passing through the boundary.