Quasiclassical theory of magnetoelectric effects in superconducting heterostructures in the presence of spin-orbit coupling

Abstract

The quasiclassical theory in terms of equations for the Green's functions (Eilenberger equations) is generalized in order to allow for quantitative description of the magneto-electric effects and proximity-induced triplet correlations in the presence of spin-orbit coupling in hybrid superconducting systems. The formalism is valid under the condition that the spin-orbit coupling is weak with respect to the Fermi energy, but exceeds the superconducting energy scale considerably. On the basis of the derived formalism it is shown that the triplet correlations in the spin-orbit coupled normal metal can be induced by proximity to a singlet superconductor without any exchange or external magnetic field. They contain an odd-frequency even-momentum component, which is stable against disorder. The value of the proximity-induced triplet correlations is of the order of ∆so/εF , that is absent in the framework of the standard quasiclassical approximation, but can be described by our theory. The spin polarization, induced by the Josephson current flowing through the superconductor/Rashba metal/superconductor junction, is also calculated.

Cryogenic Memory Element Based on an Anomalous Josephson Junction

“…Here, σ is the width and I max is the intensity, in units of I c , of the pulse, so that a value I max > 1 indicates a bias current larger than the critical value. Because of the magnetoelectric effect in a ϕ 0 -junction, the charge current induces an in-plane magnetic moment [27,28,[36][37][38][39], which in turn acts as a torque on the out-of plane magnetization of the F layer and eventually leads to its switching [20,22].…”

Odd-frequency superconducting pairing in junctions with Rashba spin-orbit coupling

“…In this regard, it is important to men-tion that even such odd-frequency pair correlations can arise due to intrinsic properties of the system, as found for example in multiband superconductors, [3][4][5][6][7] or even due to more exotic mechanisms. 2, [8][9][10][11][12] Odd-frequency pairing has also been extensively studied in hybrid systems that include superconductorferromagnet junctions, normal-superconducror (NS) junctions, 21,[40][41][42][43][44][45][46][47][48] topological insulators-superconductor junctions, [49][50][51][52][53][54][55][56][57][58] as well as in inhomogeneous systems under time-dependent fields. 59,60 In NS junctions, oddfrequency pairing is generated due to the interface breaking the spatial parity, which allows the transformation from even s-wave to odd p-wave symmetry, while conserving the spin structure.…”

“…[75][76][77][78] Only very few and recent works have so far investigated this possibility of SO coupling generating significant odd-frequency pairing and then with their major findings focused on twodimensional situations. 44,45,79,80 Additional studies are thus desirable for a better understanding of the induced odd-frequency superconducting pairing in systems with SO coupling. In particular, one-dimensional systems are highly interesting in this regard as they both provide possibilities for analytical treatment within a fully quantum picture without any notable approximations and because of the huge recent experimental interest in SO coupled one-dimensional nanowires.…”

Signature of odd-frequency equal-spin triplet pairing in the Josephson current on the surface of Weyl nodal loop semimetals

“…However, for the long-range equal-spin triplet pairing to appear in any of these previously studied structures, two magnetization directions have to be present: one magnetization direction rotates the spin-singlet state to a mixedspin triplet state, while the second direction, not parallel to the first, generates equal-spin pairing. Alternatively, spin-orbit coupling can substitute for one of the magnetic fields, where for example an FM-SC interface with spinorbit coupling has been shown to be sufficient to generate equal-spin triplet pairing 56,58,59 . In contrast, for a Josephson junction on the surface of a WNLS, the DSS is only polarized in only a single direction, here along the −z-direction, but still equal-spin triplet pairing completely dominates.…”