Stability of the vortex lattice in D-wave superconductors

TL;DR

This paper derives the vibration spectrum of the vortex lattice in d-wave superconductors using hydrodynamic equations, identifying stability conditions for specific lattice configurations relative to critical magnetic fields.

Contribution

It introduces a hydrodynamic approach to analyze vortex lattice stability and identifies the critical field for lattice transition in d-wave superconductors.

Findings

Rhombic lattice is stable for magnetic fields above the critical value.

Derived the vibration spectrum of the vortex lattice.

Identified the critical field for lattice transition.

Abstract

Use is made of Onsager's hydrodynamic equation to derive the vibration spectrum of the vortex lattice in d-wave superconductor. In particular the rhombic lattice (i.e. the $45^\circ$ tilted square lattice) is found to be stable for $B>H_{cr}(t)$. Here $H_{cr}(t)$ denotes the critical field at which the vortex lattice transition takes place.