Odd triplet superconductivity in a superconductor/ferromagnet system with a spiral magnetic structure

Abstract

We analyze a superconductor-ferromagnet (S/F) system with a spiral magnetic structure in the ferromagnet F for a weak and strong exchange field. The long-range triplet component (LRTC) penetrating into the ferromagnet over a long distance is calculated for both cases. In the dirty limit (or weak ferromagnetism) we study the LRTC for conical ferromagnets. Its spatial dependence undergoes a qualitative change as a function of the cone angle ϑ. At small angles ϑ the LRTC decays in the ferromagnet exponentially in a monotonic way. If the angle ϑ exceeds a certain value, the exponential decay of the LRTC is accompanied by oscillations with a period that depends on ϑ. This oscillatory behaviour leads to a similar dependence of the Josephson critical current in SFS junctions on the thickness of the F layer. In the case of a strong ferromagnet the LRTC decays over the length which is determined by the wave vector of the magnetic spiral and by the exchange field.

Unconventional superconductivity in double quantum dots

“…For noncollinear magnetizations, e.g., due to domain walls [11][12][13][14][15][16][17], spin-active interfaces [18,19], multiple noncollinear magnetized ferromagnetic layers [17,20,21], helical magnets [22][23][24], or spin-orbit coupling [25], odd-frequency correlations with finite spin polarization can penetrate deeply into ferromagnets, as confirmed in several experiments [26][27][28][29][30][31][32].…”

“…By a similar mechanism, Majorana fermions can also be generated in double quantum dots [7,8]. The idea of odd-frequency pairing has first been brought up by Berezinskii [9] as a possible explanation of superfluid 3 He but has experienced a revival in the context of superconductor-ferromagnet heterostructures [10].For noncollinear magnetizations, e.g., due to domain walls [11][12][13][14][15][16][17], spin-active interfaces [18,19], multiple noncollinear magnetized ferromagnetic layers [17,20,21], helical magnets [22][23][24], or spin-orbit coupling [25], odd-frequency correlations with finite spin polarization can penetrate deeply into ferromagnets, as confirmed in several experiments [26][27][28][29][30][31][32].Odd-frequency triplet pairing also appears in diffusive normal metals contacted by an even-frequency triplet superconductor [33].Finally, odd-frequency singlet superconductivity has only been theoretically predicted [34] without experimental confirmation so far. Quantum dots coupled to conventional superconductors show an interesting interplay of proximity effect and Coulomb interaction [35,36].…”

Anomalous current in diffusive ferromagnetic Josephson junctions

“…Studies, based on quasiclassics, of the diffusive Josephson junctions through various noncoplanar structures, including a helix [40], magnetic vortex [41], and skyrmion [42], have shown no AJE. In contrast, in diffusive systems with half-metallic elements [29,31] and in junctions between magnetic superconductors with spin filters [35,36] a finite anomalous current has been predicted.…”

Spin-triplet supercurrent through inhomogeneous ferromagnetic trilayers

“…One of the most intriguing phenomena in the context of this interplay is the generation of a long-ranged spin-triplet supercurrent flowing through a Josephson junction with magnetic elements. The main criterion for generation of such a current is that some form of magnetic inhomogeneity must be present in the junction, as first shown by Bergeret et al [20][21][22] and Volkov et al [23][24][25] . In the diffusive limit of transport, being often the experimentally most relevant regime, such a nonuniform magnetization can induce exotic long-range superconducting correlations which are odd under time-reversal: the so-called odd-frequency superconducting state.…”