Quantum Melting of a Two-Dimensional Vortex Lattice at Zero Temperature

TL;DR

This paper investigates the quantum melting of a two-dimensional vortex lattice at zero temperature, proposing criteria for melting based on vortex density ratios and energy comparisons, with implications for low- and high-Tc superconductors.

Contribution

It introduces two criteria for quantum melting of a 2D vortex lattice at T=0, using Lindemann and wave function energy comparisons, applicable to various superconducting materials.

Findings

Melting occurs when vortex density exceeds a critical ratio.

The Lindemann and energy criteria yield similar melting points.

Implications for low-Tc and high-Tc superconductor layers.

Abstract

We consider the quantum melting of a two-dimensional flux lattice at temperature T = 0 in the ``superclean limit.'' In this regime, we find that vortex motion is dominated by the Magnus force. A Lindemann criterion predicts melting when $n_v/n_p \geq \beta$, where $n_v$ and $n_p$ are the areal number densities of vortex pancakes and Cooper pairs, and $\beta \approx 0.1$. A second criterion is derived by using Wigner crystal and Laughlin wave functions for the solid and liquid phases respectively, and setting the two energies equal. This gives a melting value similar to the Lindemann result. We discuss the numerical value of the melting field at $T = 0$ for thin layers of low-T$_c$ superconductor, such as $a-MoGe$, and single layers of high-T$_c$ materials.