Josephsonic diagnostic of competing orders in quantum critical multiband superconductors

TL;DR

This paper derives a general expression for Josephson current in multiband superconductors near quantum critical points, explaining experimental observations of nonmonotonic supercurrent behavior under pressure or doping.

Contribution

It introduces a universal formula for Josephson current in superconductors with coexisting orders, linking quantum criticality to supercurrent peaks and providing a theoretical framework for recent experiments.

Findings

Critical current peaks at quantum critical points.

Nonmonotonic supercurrent dependence on pressure and doping.

Applicability to heavy fermion and iron-based superconductors.

Abstract

Motivated by the recent experimentally observed manifestations of the quantum critical point fluctuations in the thermodynamic properties of multiband superconductors, we derive a general expression for the Josephson current of various junctions between two superconductors in the phase of superconductivity coexistence with the spin-density-wave. We demonstrate that the critical current peaks at the quantum critical point that separates pure and mixed superconducting phases. We argue that our results are generic and, in particular, can be adopted to explain the recent observations of a nonmonotonic dependence of the supercurrent on the external pressure in the heavy fermion superconductor CeRhIn$_5$, and on the chemical doping in iron-based superconductors such as Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$.