Elasticity and melting of vortex crystals in anisotropic superconductors: Beyond the continuum regime

TL;DR

This paper analyzes the harmonic eigenvalues of vortex crystals in anisotropic superconductors beyond the continuum approximation, providing insights into their phase diagram, thermal fluctuations, and melting behavior.

Contribution

It introduces an analytic correction to nonlocal continuum formulas and applies it to compute melting lines and thermal fluctuations in anisotropic vortex lattices.

Findings

Transverse modes are energetically less costly than longitudinal modes.

Eigenvalues exhibit angular dependence near the Brillouin zone boundary.

The proposed correction fits numerical data well and improves melting line predictions.

Abstract

The elastic moduli of vortex crystals in anisotropic superconductors are frequently involved in the investigation of their phase diagram and transport properties. We provide a detailed analysis of the harmonic eigenvalues (normal modes) of the vortex lattice for general values of the magnetic field strength, going beyond the elastic continuum regime. The detailed behavior of these wavevector-dependent eigenvalues within the Brillouin zone (BZ), is compared with several frequently used approximations that we also recalculate. Throughout the BZ, transverse modes are less costly than their longitudinal counterparts, and there is an angular dependence which becomes more marked close to the zone boundary. Based on these results, we propose an analytic correction to the nonlocal continuum formulas which fits quite well the numerical behavior of the eigenvalues in the London regime. We use this approximate expression to calculate thermal fluctuations and the full melting line (according to Lindeman's criterion) for various values of the anisotropy parameter.