Supercooled vortex liquid and quantitative theory of melting of the flux line lattice in type II superconductors

TL;DR

This paper develops a quantitative theory of vortex liquid and melting in type II superconductors, using a metastable liquid state concept, large N models, and resummation techniques, with results matching experimental data.

Contribution

It introduces a new theoretical framework for vortex liquid behavior and melting in type II superconductors, incorporating metastable states and advanced mathematical methods.

Findings

The vortex liquid has a higher Madelung constant than the solid by about the latent heat of melting.

The theory predicts magnetization, entropy, and heat capacity jumps at melting.

Comparison with experiments and simulations shows good agreement with the model.

Abstract

A metastable homogeneous state exists down to zero temperature in systems of repelling objects. Zero ''fluctuation temperature'' liquid state therefore serves as a (pseudo) ''fixed point'' controlling the properties of vortex liquid below and even around melting point. There exists Madelung constant for the liquid in the limit of zero temperature which is higher than that of the solid by an amount approximately equal to the latent heat of melting. This picture is supported by an exactly solvable large $N$ Ginzburg - Landau model in magnetic field. Based on this understanding we apply Borel - Pade resummation technique to develop a theory of the vortex liquid in type II superconductors. Applicability of the effective lowest Landau level model is discussed and corrections due to higher levels is calculated. Combined with previous quantitative description of the vortex solid the melting line is located. Magnetization, entropy and specific heat jumps along it are calculated. The magnetization of liquid is larger than that of solid by $% 1.8%$ irrespective of the melting temperature. We compare the result with experiments on high $T_{c}$ cuprates $YBa_{2}Cu_{3}O_{7}$, $DyBCO$, low $% T_{c}$ material $(K,Ba)BiO_{3}$ and with Monte Carlo simulations.