Skew Andreev reflection in ferromagnet/superconductor junctions

Abstract

Andreev reflection (AR) in ferromagnet/superconductor junctions is an indispensable spectroscopic tool for measuring spin polarization. We study theoretically how the presence of a thin semiconducting interface in such junctions, inducing Rashba and Dresselhaus spin-orbit coupling, modifies AR processes. The interface gives rise to a momentum-and spin-dependent scattering potential, making the AR probability strongly asymmetric with respect to the sign of the incident electrons' transverse momenta. This skew AR creates spatial charge carrier imbalances and transverse Hall currents in the ferromagnet. We show that the effect is giant, compared to the normal regime. We provide a quantitative analysis and a qualitative picture of this phenomenon, and finally show that skew AR also leads to a widely tunable transverse supercurrent response in the superconductor. strate that, analogously to the tunneling picture in the normalconducting case, skew reflection [49] of spin-polarized carriers at the barrier leads to TAHEs in the F. Due to the presence of a S electrode, we distinguish two skew reflection processes: skew specular reflection (SR) and skew Andreev reflection (AR). By formulating a qualitative physical picture including both processes, we assert that skew SR and skew AR can act together and significantly enhance the TAHE compared to all previously studied (normal) systems. Special attention must be paid to skew AR, which transfers Cooper pairs across the barrier into the S. The electrons forming one Cooper pair are thereby also subject to the proposed skew reflection mechanism. We discuss that the result is a transverse supercurrent response, initially deduced from a phenomenological Ginzburg-Landau treatment [50], with widely tunable characteristics. Both findings, relatively giant TAHE conductances in the F and transverse supercurrents in the S, are distinct fingerprints to experimentally detect skew AR and characterize the junctions' interfacial SOC.We consider a biased ballistic F/SC/S junction grown along theẑ-direction, in which the two semi-infinite F and S regions are separated by an ultrathin SC barrier [see Fig. 1(a)]. The barrier may be composed of a thin layer of zincblende materials (e.g., GaAs or InAs) and introduces potential scattering, as well as strong interfacial Rashba [16] and Dresselhaus [17] SOC [18,19].The system can be modeled by means of the stationary Bogoljubov-de Gennes (BdG) Hamiltonian [51],SCσ0 δ(z)+Ĥ SOC SC δ(z) represents the single-electron Hamiltonian andĤ h = −σ yĤ * eσy its holelike counterpart (σ 0 andσ i indicate the 2 × 2 identity and the ith Pauli matrix; σ = [σ x ,σ y ,σ z ] is the vector of Pauli matrices). The F is described within the Stoner model with exchange energy ∆ XC and magnetization directionm = [cos Φ, sin Φ, 0] , where Φ is measured with respect to thex-axis. Following earlier studies [52-56], the ultrathin SC layer is included into our model as a δ-like barrier with height V SC and width d SC ; its SOC enters the Hamiltonian [18, 19]Ĥ SOC SC = α (k yσx ...

Anomalous Josephson Hall effect charge and transverse spin currents in superconductor/ferromagnetic-insulator/superconductor junctions

“…Let us first discuss the dependence of the AJHE currents on the in-plane magnetization angle, Φ, and at zero superconducting phase difference (φ S = 0). The apparent sinelike (cosinelike) variations of I x (I y ) with respect to Φ are a direct consequence of the intriguing interplay of ferromagnetism and the interfacial SOC [42], and a distinct (experimental) fingerprint for the junction's magnetoanisotropic charge transport properties [37]. To be more specific, we deduced I x ∼ −(α + β) sin Φ and I y ∼ (α − β) cos Φ in an earlier work [42].…”

“…We just focus on (spin-conserving) AR since this scattering process essentially drives the supercurrents we are predominantly interested in. Earlier studies [42] showed that the contributions of spin-flip AR, i.e., the triplet Cooper pair currents are small within the considered limit and can be neglected when formulating a qualitative picture. The dashed black line indicates the tunneling parameters λ SC = (2mλ SC )/( 2 q F ) = 2 and λ MA = (2mλ MA )/( 2 q F ) = 0.25, which combine to λ SC + λ MA for up-spin electrons.…”

“…withĤ e = [− 2 /(2m) ∇ 2 − µ]σ 0 +Ĥ F-I representing the single-electron Hamiltonian andĤ h = −σ yĤ * eσy its holelike counterpart (σ 0 andσ i indicate the two-by-two identity and the ith Pauli matrix). Analogously to previous studies [42,67,[79][80][81][82], the ultrathin F-I region is included into our model as an effective potential-and SOC-dependent deltalike barrier, H F-I = λ SCσ0 + λ MA (m ·σ) + α (k yσx − k xσy ) − β (k yσx + k xσy ) δ(z), (2) where the first two parts describe scalar and magnetic tunneling with amplitudes λ SC and λ MA , respectively. The unit vector along the magnetization direction in the F-I, m = [cos Φ, sin Φ, 0 , is determined with respect to thê x [110]-reference direction [see Fig.…”

“…Although first experiments carried out on granular nanojunctions [41] essentially confirmed the theoretical expectations, the effect is typically weak in normal-state junctions. More sizable TAHE conductances, coming along with a spontaneous transverse supercurrent response, were predicted for superconducting junctions [42], opening several novel perspectives, e.g., the possibility to experimentally verify superconducting magnetoelectric effects [43,44]. * E-Mail: andreas.costa@physik.uni-regensburg.de From that viewpoint, integrating TAHEs into Josephson junctions could likewise attract considerable interest.…”

Superconducting triplet pairings and anisotropic magnetoresistance effects in ferromagnet/superconductor/ferromagnet double-barrier junctions

“…Following earlier studies [26,[65][66][67][68][69][70], the ultrathin semiconducting interface layers are included into our model as deltalike barriers with heights (widths) V L (d L ) at the left and V R (d R ) at the right interface, respectively. Their SOCs enter through the effective spin-orbit fields…”