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

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 nᵥnₚ>~β, where nᵥ and nₚ are the areal number densities of vortex pancakes and Cooper pairs, and β≈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-Tc superconductor, such as a-MoGe, and single layers of high-Tc materials.