First- and second-order phase transitions, Fulde-Ferrel inhomogeneous state, and quantum criticality in ferromagnet/superconductor double tunnel junctions
Biao Jin, Gang Su, Qing-Rong Zheng
DOI 10.1103/PhysRevB.71.144514 · Physical Review B
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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*, while the transitions from the BCS state and the FF state to the normal state at Vc are of the second-order. A phase diagram for the central superconductor is presented. In addition, a quantum critical point (QCP), VQCP, 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 the free energies between the SC and the normal states vanish as ∣V−VQCP∣zν with the quantum critical exponents zν=12, 1, and 2, respectively. The tunnel conductance and magnetoresistance are also discussed.
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