Quantum melting of a two-dimensional vortex lattice at zero temperature.

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 $\frac{{n}_{v}}{{n}_{p}}>~\ensuremath{\beta}$, where ${n}_{v}$ and ${n}_{p}$ are the areal number densities of vortex pancakes and Cooper pairs, and $\ensuremath{\beta}\ensuremath{\approx}0.1$. 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 $T=0$ melting field for thin layers of a low-${T}_{c}$ superconductor, such as $a$-MoGe, and single layers of high-${T}_{c}$ materials.