Intrinsic spin-orbit interaction in diffusive normal wire Josephson weak links: Supercurrent and density of states

Abstract

We study the effect of the intrinsic (Rashba or Dresselhaus) spin-orbit interaction in superconductor-nanowiresuperconductor (SNS) weak links in the presence of a spin-splitting field that can result either from an intrinsic exchange field or the Zeeman effect of an applied field. We solve the full nonlinear Usadel equations numerically [The code used for calculating the results in this paper is available in https://github.com/wompo/Usadel-fornanowires] and analyze the resulting supercurrent through the weak link and the behavior of the density of states in the center of the wire. We point out how the presence of the spin-orbit interaction gives rise to a long-range spin triplet supercurrent, which remains finite even in the limit of very large exchange fields. In particular, we show how rotating the field leads to a sequence of transitions between the 0 and π states as a function of the angle between the exchange field and the spin-orbit field. Simultaneously, the triplet pairing leads to a zero-energy peak in the density of states. We proceed by solving the linearized Usadel equations, showing the correspondence to the solutions of the full equations and detail the emergence of the long-range supercurrent components. Our studies are relevant for ongoing investigations of supercurrent in semiconductor nanowires in the limit of several channels and in the presence of disorder.

Magnetoanisotropic Josephson effect due to interfacial spin-orbit fields in superconductor/ferromagnet/superconductor junctions

“…Instead, the junctions are in stable 0 states in the former and stable π states in the latter case for all regarded magnetization orientations. Similar phenomena are predicted to occur in lateral S/N/S junctions with Zeeman splitting and uniform Rashba coupling [41][42][43]. In Appendix C we provide a detailed analysis of the interlayer thickness dependence of the transitions.…”

“…Spin-orbit fields can even induce superconducting proximity effects in half metals [31]. Moreover, magnetic anisotropies of the critical current with respect to the orientation of the present spin-orbit fields have been predicted to occur in lateral S/nanowire/S Josephson junctions with a Zeeman splitting [41][42][43], as well as in diffusive vertical S/F/S Josephson junctions [44].…”

Supercurrent vortex pinball via a triplet Cooper pair inverse Edelstein effect

“…In the study of a 1D Josephson junction with spin-orbit coupling, it was recently discovered that the critical current varies greatly with the direction of an applied exchange field, even creating 0-π transitions 8,13 . It is therefore reasonable to presume that the current density distribution becomes nontrivial.…”

“…4c and 4d, which show the current density distribution for αL = 1.2 and αL = 1.6, respectively. It is noted that for large enough Rashba parameter α, no 0-π transition will take place 8 , and vortices will only appear for large exchange fields where the conventional contribution to the current, J I , is sufficiently suppressed relative to J tt .…”

“…If the exchange field is spatially varying, or the system contains spin-orbit coupling, the triplet Cooper pairs may rotate between different triplet states where the electron spins are parallel, making tunable superconducting spin transport possible [2][3][4] . In light of this discovery, the effect of spin-orbit coupling on proximitized materials has recently been investigated in several works [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] . In this paper, we consider a spin-orbit coupled superconducting hybrid which is found to display novel, inherently two-dimensional, physical phenomena which are hidden in effective one-dimensional models.…”