Superconductor-semiconductor Josephson junction arrays are a uniquely tunable platform for studying collective quantum phenomena, particularly in the regime where localized Andreev bound states can hybridize across the lattice when the physical separation between adjacent junctions is smaller than their coherence length (
ξABS>dJJ). Here, we investigate three distinct Al-InAs Josephson junction arrays: a square array and super-honeycomb array fabricated within this
ξABS>dJJ regime, as well as a larger-spacing super-honeycomb control device designed such that
ξABS≲ dJJ. Under an out-of-plane field, critical current peaks emerge at rational filling factors, reflecting stable vortex configurations in the lattices. In the super-honeycomb lattice, vortices localize to distinct non-identical plaquettes at different filling factors, as predicted by frustrated XY model simulations. A rotating in-plane field yields periodic critical current oscillations that reflect the Rashba spin-orbit coupling inherent to the InAs quantum well. Surprisingly, at
f=1, the closely spaced super-honeycomb array exhibits a distinct critical current minimum as the magnitude of the in-plane field increases, a signature absent in the square array and large-spacing super-honeycomb array. These results indicate that this signature is jointly influenced by the unique geometry of the super-honeycomb vortex lattice and by long-range inter-junction hybridization.
In this study, we simulated a quantum rotor model describing a Josephson junction array (JJA) in the phase representation at zero temperature in a perpendicular magnetic field [Formula: see text] (in units of [Formula: see text]) on a [Formula: see text] square lattice with spacing a for [Formula: see text]. 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 [Formula: see text] indicating SIT. For B = 0.1 the SIT occurs without an intermediate vortex state and the magnetization scales as [Formula: see text], whereas for B = 0.4 the scaling is [Formula: see text] 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. The ground state energy is calculated easily in DMC and its error estimates were generally smaller than [Formula: see text], both with and without the guiding wavefunction. Quantities like magnetization and vorticity that do not commute with the Hamiltonian were calculated using an efficient forward walking algorithm. Their estimates are affected severely in absence of the guiding wavefunction. With the guiding wavefunction, errors for the magnetization were generally less than [Formula: see text] and going up to [Formula: see text] percent around the phase transition from the Meissner to the vortex state, and without the guiding wavefunction errors were generally higher than [Formula: see text] and going up to [Formula: see text] around the critical point.