In-plane Fulde-Ferrel-Larkin-Ovchinnikov instability in a superconductor–normal metal bilayer system under nonequilibrium quasiparticle distribution

Abstract

It is predicted that a new class of systems -superconductor/normal metal (S/N) heterostructures can reveal the in-plane Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) instability under nonequilibrium conditions at temperatures close to the critical temperature. It does not require any Zeeman interaction in the system. For S/N heterostructures under non-equilibrium distribution there is a natural easily adjustable parameter -voltage, which can control the FFLO-state. This FFLO-state can be of different types: plane wave, stationary wave and, even, 2D-structures are possible. Some types of the FFLO-state are accompanied by the magnetic flux, which can be observed experimentally. All the types of the FFLO-state can be revealed through the temperature dependence of the linear response of the system on the applied magnetic field near Tc, which strongly differs from that one for the homogeneous state.PACS numbers: 74.45.+c, 74.40.Gh There are two mechanisms of superconductivity destruction by a magnetic field: orbital effect and the Zeeman interaction of electron spins with the magnetic field. Usually the orbital effect is more restrictive. However there are several classes of systems, where the orbital effect is strongly weakened (systems with large effective mass of electrons 1,2 , thin films and layered superconductors under in-plane magnetic field 3 ) or even completely absent (superconductor/ferromagnet (S/F) heterostructures 4,5 ). Then the Zeeman interactions of electron spins with a magnetic or an exchange field is responsible for the superconductivity destruction.The behavior of a superconductor with a homogeneous exchange field h was studied long ago 6-9 . It was found that homogeneous superconducting state becomes energetically unfavorable above the paramagnetic (Pauli) limit h = ∆ 0 / √ 2, where ∆ 0 is the zero-temperature superconducting gap. As it was predicted by Larkin and Ovchinnikov 6 and by Fulde and Ferrell 7 , in a narrow region of exchange fields exceeding this value superconductivity can appear as an inhomogeneous state with a spatially modulated Cooper pair wave function (FFLOstate).Now there is a growing body of experimental evidence for the FFLO phase, generated by the applied magnetic field, reported from various measurements 10-24 . However, any unambiguous experimental results, which can be interpreted only as a fingerprint of the FFLO-state, are not reported by now.On the other hand, it has been predicted recently 25 that the FFLO-state can be realized in S/F heterostructures, where S is a singlet s-wave superconductor. Here we mean the so-called in-plane FFLO-state, where the superconducting order parameter profile is modulated along the layers. It should be distinguished from the normal to the S/F interface oscillations of the condensate wave function in the ferromagnetic layer, which are well investigated as theoretically, so as experimentally 4,5,26 .In this paper we show that the in-plane FFLO-state can be the most energetically favorable state in S/N heterostructures under the non-equili...

Paramagnetic Meissner effect in voltage-biased proximity systems

“…While no such effect was detected in Ref. [31], they focused on high temperatures and thin superconductors, while the opposite limit may be the relevant one. Even if it is not possible to realize the effect in a dirty S/N structure, the prospect of a voltage-controllable Meissner effect in dirty S/F devices may still be of interest.…”

“…A similar setup to ours was investigated in Ref. [31], where they calculated the Meissner response of S/N structures driven out of equilibrium using a voltage-controlled quasiparticle injector. However, they did not find a paramagnetic response, and the main reason appears to be their parameters.…”

“…In contrast, Ref. [31] considered dirty materials, thin superconductors, and high temperatures. This suppresses the subgap peaks in the DOS, which we will see are essential for a paramagnetic response.…”

Paramagnetic Meissner, vortex and 'onion' ground states in Fulde-Ferrell finite-size superconductor

“…If thickness of the superconductor in hybrid SF or SN bilayers is small the paramagnetic response of proximity induced odd-frequency superconductivity in F or N layer may exceed the diamagnetic response of the host superconductor which leads to global paramagnetism. It may signal about instability and appearance of modulated, along hybrid structure, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like superconducting state 12,13 which has zero magnetic response (λ −2 → 0 in Eq. [1]).…”

“…In Larkin-Ovchinnikov state the modulated state corresponds to the standing wave (superconducting order parameter Ψ ∼ cos(q LO r)) while in Fulde-Ferrell state Ψ ∼ exp(iq F F r). Note that in the FF state spontaneous currents can flow in the ground state 13,14 which are absent in LO state.…”