Controlling superconducting spin flow with spin-flip immunity using a single homogeneous ferromagnet

Gapped triplet $p$-wave superconductivity in strong spin-orbit-coupled semiconductor quantum wells in proximity to $s$-wave superconductor

“…In recent years, triplet superconductivity has attracted much attention, which provides the possibility to realize the nondissipative spin transport and hence has potential application in spintronics. [1][2][3][4][5][6][7][8][9][10][11] To confirm or realize the triplet superconductivity, much efforts have been made to several potential systems, including the unconventional superconductor Sr 2 RuO 4 , [12][13][14][15][16][17][18][19] the conventional superconductor-ferromagnet (S-F) interface with induced odd-frequency and even-momentum triplet pairings, [2][3][4][20][21][22][23][24] conventional superconductors with induced spin-orbit coupling (SOC) in the surface or interface which possess even-frequency and odd-momentum triplet pairings, 20,[25][26][27][28][29][30] and the non-centrosymmetric superconductors including the heavy fermion system. [31][32][33] Specifically, Sr 2 RuO 4 was suggested to be the triplet p-wave superconductor which may arise from the spinfluctuation-induced attractive potential between the triplet states, 14,[34][35][36] whose experimental confirmation is still in progress.…”

“…We point out here that with the momentum-independent attractive potential between electrons from the s-wave channel, no triplet gap or triplet order parameter arises in the superconductor. As a natural extension, much efforts are focused on the system with the SOC in proximity to the s-wave superconductors, including spin-orbitcoupled metals 22,[26][27][28][29] and even semiconductors. 30 Finally, in the non-centrosymmetric superconductor, with the SOC naturally existing in the superconductor itself, it is shown that if proper forms of attractive effective electron-electron (e-e) interaction potential are realized from the symmetry analysis, triplet gap or triplet order parameter can be realized.…”

“…14,31,32 However, their experimental confirmations are still in progress. [12][13][14][15][16][17][18][19]31,32 In contrast to this, the triplet superconductivity in the system with the Zeeman field or SOC, [2][3][4][21][22][23][24][26][27][28][29][30] which is in proximity to the s-wave superconductor, is relatively easy to be realized and manipulated with the flexible manipulation of the strength and type of the SOC. [38][39][40] Specifically, the triplet superconductivity in conventional S-F interface or the S-F-S Josephson junction has been experimentally confirmed by observing the structure of the energy gap 23,24 or 0-π transition of Josephson effect.…”

“…Furthermore, the blue dashed and purple chain curves denote the calculated results from Eqs. (28) and(29), respectively, in which the longitudinal polarization function is also taken to be constant. The inset zooms the density dependencies of the chemical potential and effective polarization function [Eq (27)…”