Quantum Phase Transition in Coupled Superconducting Quantum Dots Array with Charge Frustration

TL;DR

This paper investigates the quantum phase transition in coupled arrays of superconducting quantum dots with charge frustration, revealing the importance of additional co-tunneling processes for accurate phase boundary determination.

Contribution

It introduces a new understanding of quantum phases in coupled SQD arrays by including extra co-tunneling processes and employs Bethe-ansatz and bosonization methods for analysis.

Findings

Correct phase boundaries require considering additional co-tunneling processes.

No evidence of supersolid phase was found.

Charge frustration influences quantum phase transitions.

Abstract

We present the quantum phase transition in two capacitively coupled arrays of superconducting quantum dots (SQD). We consider the presence of gate voltage in each superconducting island. We show explicitly that the co-tunneling process involves with two coupled SQD arrays, near the maximum charge frustration line is not sufficient to explain the correct quantum phases with physically consistent phase boundaries. We consider another extra co-tunneling process along each chain to explain the correct quantum phases with physically consistent phase boundaries. There is no evidence of supersolid phase in our study. We use Bethe-ansatz and Abelian bosonization method to solve the problem