Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

Abstract

We investigate the proximity effect in diffusive superconducting hybrid structures with a spin-orbit (SO) coupling. Our study is focused on the singlet-triplet conversion and the generation of long-range superconducting correlations in ferromagnetic elements. We derive the quasiclassical equations for the Green's functions including the SO coupling terms in form of a background SU(2) field. With the help of these equations, we first present an interesting complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superconducting structure in the presence of SO coupling. From this analogy it turns out naturally that the SO coupling is an additional source of the long-range triplet component (LRTC) besides the magnetic inhomogeneities studied in the past. This analogy opens a range of possibilities for the generation and manipulation of the triplet condensate in hybrid structures. In particular we demonstrate that a normal metal with a SO coupling can be used as source of LRTC if attached to a S/F bilayer. We also demonstrate an explicit connection between an inhomogeneous exchange field and SO coupling mechanisms for the generation of the LRTC and establish the conditions for the appearance of the LRTC in different geometries. Our work gives a global description of the singlet-triplet conversion in hybrids structures in terms of generic spin-fields and our results are particularly important for the understanding of the physics underlying spintronic devices with superconductors.

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].…”

Theory of current-induced spin polarization in an electron gas

“…(1) is the SU (2) approach, where the SOC is described in terms of a spin-dependent gauge field [43]. This formalism, introduced in the context of quarkgluon kinetic theory [53,54], was recently also extended to superconducting structures with SOC [55,56]. For a recent pedagogical introduction, see Ref.…”

Modulation of pure spin currents with a ferromagnetic insulator

“…(1) in the z direction and use the BrataasNazarov-Bauer boundary condition at the NM/FMI interface [5]. From the solution one can obtain an expression for the nonlocal resistance at the FM detector that reads [37,42,43]…”