Magnetic flux induce dissipation effect on the quantum phase diagram of mesoscopic SQUID array

TL;DR

This paper explores how magnetic flux-induced dissipation affects the quantum phase diagram of mesoscopic SQUID arrays, revealing complex phase boundaries, special points, and the influence of co-tunneling effects.

Contribution

It provides a detailed analysis of magnetic flux effects on the phase diagram, deriving an analytical relation between dissipation and Luttinger liquid parameters, and highlighting deviations from standard Josephson relations.

Findings

Magnetic flux induces dissipation that alters phase boundaries.

Derived analytical relation between dissipation strength and Luttinger liquid parameter.

Observed unique behaviors at half-integer magnetic flux quantum.

Abstract

We present the quantum phase diagram of mesoscopic SQUID array. We predict different quan- tum phases and the phase boundaries along with several special points. We present the results of magnetic flux induced dissipation on these points and also on the phase boundaries. The Josephson couplings at these points are dependant on the system parameter in a more complicated fashion and differ from the Ambegaokar and Baratoff relation. We derive the analytical relation between the dissipation strength and Luttinger liquid parameter of the system. We observe some interesting behaviour at the half-integer magnetic flux quantum and also the importance of co-tunneling effect.