Numerical identification of three distinct phases in a
(2+1)D array of quantum dissipative Josephson junctions
We have performed large-scale Monte Carlo simulations on a model describing a (2+1)-dimensional array of dissipative Josephson junctions. We find three distinct stable quantum phases of the system. The most ordered state features long-range spatial ordering in the phase $\ensuremath{\theta}$ of the superconducting order parameter, but temporal ordering only in spatial gradients $\ensuremath{\Delta}\ensuremath{\theta}$, not in $\ensuremath{\theta}$. Significantly, the most ordered state therefore does not have three-dimensional (3D)
XY ordering. Rather, it features two-dimensional (2D) spin waves coexisting with temporally disordered phases $\ensuremath{\theta}$. There is also an intermediate phase featuring quasi-long-range spatial order in $\ensuremath{\theta}$ coexisting with a gas of instantons in $\ensuremath{\Delta}\ensuremath{\theta}$. We briefly discuss possible experimental signatures of such a state, which may be viewed as a local metal and a global superconductor. The most disordered state has phase disorder in all spatio-temporal directions, and may be characterized as a gas of proliferated vortices coexisting with a gas of $\ensuremath{\Delta}\ensuremath{\theta}$ instantons. The phase transitions between these phases are discussed. The transition from the most ordered state to the intermediate state is driven by proliferation of instantons in $\ensuremath{\Delta}\ensuremath{\theta}$. The transition from the intermediate state to the most disordered state is driven by the proliferation of spatial point vortices in the background of a proliferated $\ensuremath{\Delta}\ensuremath{\theta}$-instanton gas, and constitutes a Berezinskii-Kosterlitz-Thouless phase transition. The model also features a direct phase transition from the most ordered state to the most disordered state, and this transition is neither in the 2D
XY nor in the 3D
XY universality class. It comes about via a simultaneous proliferation of point vortices in two spatial dimensions and $\ensuremath{\Delta}\ensuremath{\theta}$ instantons, with a complicated interplay between them. The results are compared to, and differ in a fundamental way from, the results that are found in dissipative quantum rotor systems. The difference originates with the difference in the values that the fundamental degrees of freedom can take in the latter systems compared to dissipative Josephson junction arrays.
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.
We show that dissipative Josephson junction arrays, an extended system, have an unusual ``floating'' metal phase in which the states of local
(0+1)-dimensional elements (single junctions) can slide past each other despite arbitrary range spatial couplings among them. The zero-temperature metal-to-superconductor quantum phase transition is controlled in any dimension by a locus of critical points fixed only by the local lattice topology. Our theory can be tested by measuring $I\text{\ensuremath{-}}V$ characteristics. This may be the simplest and most natural example of a floating phase.