Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures

Bergeret, F. S.; Volkov, A. N.; Efetov, K. B.

doi:10.1103/revmodphys.77.1321

Cited by 1,528 publications

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“…Although this type of pairing does not occur there, it is possible in certain FSF systems [1,2,13,14] with ordinary singlet pairing in S. This arrangement can induce, via proximity effects, triplet correlations with m = 0 and m = ±1 projections of the total spin. If the magnetization orientations in both F layers are unidirectional and along the quantization axis, symmetry arguments show that only the m = 0 projection along that axis can exist.Odd triplet pairing in F/S structures has been studied in the dirty limit through linearized Usadel-type quasiclassical equations [2,13,14,15]. In this case, it was found that m = 0 triplet pairs always exist.…”

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confidence: 99%

“…The m = ±1 components, for which the exchange field is not pair-breaking, can be long ranged, and were found to exist for nonhomogeneous magnetization. For FSF trilayers [2,16,17], the quasiclassical methods predict that the structure contains a superposition of all three spin triplet projections except when the magnetizations of the F layers are collinear, in which case the m = ±1 components along the magnetization axis vanish. It is noted in Ref.…”

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Odd Triplet Pairing in Clean Superconductor/Ferromagnet Heterostructures

2007

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We study triplet pairing correlations in clean Ferromagnet (F)/Superconductor (S) nanojunctions, via fully self consistent solution of the Bogoliubov-de Gennes equations. We consider FSF trilayers, with S being an s-wave superconductor, and an arbitrary angle α between the magnetizations of the two F layers. We find that contrary to some previous expectations, triplet correlations, odd in time, are induced in both the S and F layers in the clean limit. We investigate their behavior as a function of time, position, and α. The triplet amplitudes are largest at times on the order of the inverse "Debye" frequency, and at that time scale they are long ranged in both S and F. The zero temperature condensation energy is found to be lowest when the magnetizations are antiparallel.PACS numbers: 74.45.+c, 74.25.Bt, 74.78.Fk The proximity effects in superconductor/ferromagnet (SF) heterostructures lead to the coexistence of ferromagnetic and superconducting ordering and to novel transport phenomena [1,2]. Interesting effects that arise from the interplay between these orderings have potential technological applications in fields such as spintronics [3]. For example, the relative orientation of the magnetizations in the F layers in FSF trilayers can have a strong influence on the conductivity [4,5,6,7,8], making them good spin valve candidates. Such trilayers were first proposed[9] for insulating F layers and later for metallic [10,11] ones. This interplay also results in fundamental new physics. An outstanding example is the existence of "odd" triplet superconductivity. This is an s-wave pairing triplet state that is even in momentum, and therefore not destroyed by nonmagnetic impurities, but with the triplet correlations being odd in frequency, so that the equal time triplet amplitudes vanish as required by the Pauli principle. This exotic pairing state with total spin one was proposed long ago [12] as a possible state in superfluid 3 He. Although this type of pairing does not occur there, it is possible in certain FSF systems [1,2,13,14] with ordinary singlet pairing in S. This arrangement can induce, via proximity effects, triplet correlations with m = 0 and m = ±1 projections of the total spin. If the magnetization orientations in both F layers are unidirectional and along the quantization axis, symmetry arguments show that only the m = 0 projection along that axis can exist.Odd triplet pairing in F/S structures has been studied in the dirty limit through linearized Usadel-type quasiclassical equations [2,13,14,15]. In this case, it was found that m = 0 triplet pairs always exist. They are suppressed in F over short length scales, just as the singlet pairs. The m = ±1 components, for which the exchange field is not pair-breaking, can be long ranged, and were found to exist for nonhomogeneous magnetization. For FSF trilayers [2,16,17], the quasiclassical methods predict that the structure contains a superposition of all three spin triplet projections except when the magnetizations of the F layers are collinear, in wh...

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Odd Triplet Pairing in Clean Superconductor/Ferromagnet Heterostructures

2007

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“…22,23 We also note that the spin-orbitassisted proximity-effect scenario considered here is different from the diffusive ferromagnet case, where the likely mechanism for proximity effect is believed to be the odd-frequency pairing. 23,24 The main argument for the odd-frequency superconductivity is that any anisotropic pairing would decay fast into a disordered metal on a length-scale of order a mean-freepath, while the odd-frequency isotropic pairing is immune from non-magnetic static disorder. This result follows from the Usadel equation if we assume that the non-s-wave part of the disorder-averaged condensate wave-function is small.…”

Section: Discussionmentioning

confidence: 99%

“…[56][57][58][59] The information available to us is insufficient to determine the nature of proximity-induced superconductivity in the nanowire. As we have mentioned above, odd-frequency s-wave proximity effect, 23,24 studied in the context of diffusive ferromagnets, remains a realistic scenario here. It is well-known that the conversion from singlet to triplet superconductivity within this scenario occurs due to some form of inhomogeneous magnetic moments near the interface.…”

Section: Introductionmentioning

confidence: 91%

“…In one case, the long-ranged proximity effect is attributed to spin-triplet oddfrequency s-wave pairing which can be induced when magnetization inhomogeneity is present near the interface. 23,24 This beautiful theory, which predicts an exotic odd-frequency (even-momentum) symmetry for the triplet component of the condensate, was originally suggested by Berenzinskii as a possible phase in superfluid 3 He. 25 Other theoretical works have investigated Josephson coupling between two conventional superconductors separated by a half-metallic ferromagnet and studied singlet-triplet conversion due to a spin-active interface.…”

Section: Introductionmentioning

confidence: 95%

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Microscopic theory for a ferromagnetic nanowire/superconductor heterostructure: Transport, fluctuations, and topological superconductivity

Takei

Galitski

2012

Phys. Rev. B

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Motivated by the recent experiment of Wang et al. [Nature Physics 6, 389 (2010)], who observed a highly unusual transport behavior of ferromagnetic Cobalt nanowires proximity-coupled to superconducting electrodes, we study proximity effect and temperature-dependent transport in such a mesoscopic hybrid structure. It is assumed that the asymmetry in the tunneling barrier gives rise to the Rashba spin-orbit-coupling in the barrier that enables induced p-wave superconductivity in the ferromagnet to exist. We first develop a microscopic theory of Andreev scattering at the spin-orbit-coupled interface, derive a set of self-consistent boundary conditions, and find an expression for the p-wave mini-gap in terms of the microscopic parameters of the contact. Second, we study temperature-dependence of the resistance near the superconducting transition and find that it should generally feature a fluctuation-induced peak. The upturn in resistance is related to the suppression of the singleparticle density of states due to the formation of fluctuating pairs, whose tunneling is suppressed. In conclusion, we discuss this and related setups involving ferromagnetic nanowires in the context of one-dimensional topological superconductors. It is argued that to realize unpaired end Majorana modes, one does not necessarily need a half-metallic state, but a partial spin polarization may suffice. Finally, we propose yet another related class of material systems -ferromagnetic semiconductor wires coupled to ferromagnetic superconductors -where direct realization of Kitaev-Majorana model should be especially straightforward.

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