Quantum Vortex Melting and Superconductor Insulator Transition in a 2D Josephson Junction Array in a Perpendicular Magnetic Field via Diffusion Monte Carlo

In this study [1], we simulated a quantum rotor model describing a Josephson junction array (JJA) in the phase representation at zero temperature in a perpendicular magnetic field B=0.1,0.2,0.3,0.4 (in units of h/4πea²) on a LxL square lattice with spacing a for L=6,8,10,12. The superconductor-insulator transition (SIT) is tuned by the ratio of charging energy to Josephson coupling, U/J. Abrupt drops in the magnetization values were observed in the bigger lattices at certain values of B and U/J caused by the formation of vortices. Increasing U/J at a fixed B field causes quantum vortex melting. The magnetization drops to zero around U/J ∼ 5 indicating SIT. For B=0.1 the SIT occurs without an intermediate vortex state and the magnetization scales as M ∼ L⁴, whereas for B=0.4 the scaling is M ∼ L⁴ during the vortex melting. For B between 0.1 and 0.4 the scaling is not clear. We used the diffusion Monte Carlo (DMC) method with a guiding wavefunction optimized using the variational Monte Carlo (VMC) method.

[1] P. Karki and Y. L. Loh, Journal of Physics: Condensed Matter 30, 385901 (2018).