First- and Second-Order Phase Transitions, Fulde-Ferrel Inhomogeneous State and Quantum Criticality in Ferromagnet/Superconductor Double Tunnel Junctions

TL;DR

This paper investigates phase transitions, quantum criticality, and inhomogeneous superconducting states in ferromagnet/superconductor/ferromagnet junctions, revealing the nature of various phase transitions and critical points through theoretical analysis.

Contribution

It introduces a detailed phase diagram and identifies quantum critical points, highlighting the behavior of superconducting gaps and free energies near criticality in these junctions.

Findings

First-order transition from homogeneous BCS to FF state at bias voltage V*

Second-order transitions from BCS and FF states to normal state at Vc

Identification of a quantum critical point VQCP with specific critical exponents

Abstract

First- and second-order phase transitions, Fulde-Ferrel (FF) inhomogeneous superconducting (SC) state and quantum criticality in ferromagnet/superconductor/ferromagnet double tunnel junctions are investigated. For the antiparallel alignment of magnetizations, it is shown that a first-order phase transition from the homogeneous BCS state to the inhomogeneous FF state occurs at a certain bias voltage $V^{\ast}$; while the transitions from the BCS state and the FF state to the normal state at $% V_{c}$ are of the second-order. A phase diagram for the central superconductor is presented. In addition, a quantum critical point (QCP), $% V_{QCP}$, is identified. It is uncovered that near the QCP, the SC gap, the chemical potential shift induced by the spin accumulation, and the difference of free energies between the SC and normal states vanish as $% |V-V_{QCP}|^{z\nu}$ with the quantum critical exponents $z\nu =1/2$, 1 and 2, respectively. The tunnel conductance and magnetoresistance are also discussed.