Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions

TL;DR

This paper challenges the traditional view of a universal dissipative quantum phase transition in Josephson junctions, showing through nonperturbative RG analyses that the transition depends on the regime and identifying overlooked factors affecting the phase diagram.

Contribution

It provides a nonperturbative analysis revealing the absence of a universal transition at R_Q and introduces a dangerously irrelevant term explaining previous misunderstandings.

Findings

The insulator phase is suppressed in the deep charge regime.

The system remains superconducting in the transmon regime.

Traditional perturbative arguments are invalid in nonperturbative regimes.

Abstract

Dissipative quantum phase transition has been widely believed to occur in a Josephson junction coupled to a resistor despite a lack of concrete experimental evidence. Here, on the basis of both numerical and analytical nonperturbative renormalization group (RG) analyses, we reveal breakdown of previous perturbative arguments and defy the common wisdom that the transition always occurs at the quantum resistance $R_{Q} \!=\! h/(4e^2)$. We find that RG flows in nonperturbative regimes induce nonmonotonic renormalization of the charging energy and lead to a qualitatively different phase diagram, where the insulator phase is strongly suppressed to the deep charge regime (Cooper pair box), while the system is always superconducting in the transmon regime. We identify a previously overlooked dangerously irrelevant term as an origin of the failure of conventional understandings. Our predictions can be tested in recent experiments realizing high-impedance long superconducting waveguides and would provide a solution to the long-standing controversy about the fate of dissipative quantum phase transition in the resistively shunted Josephson junction.