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Register a new userTheory of tunneling spectroscopy of normal metal/ferromagnet/spin-triplet superconductor junctions
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We study the tunneling conductance of a ballistic normal metal / ferromagnet / spin-triplet superconductor junction using the extended Blonder-Tinkham-Klapwijk formalism as a model for a $c$-axis oriented Au / SrRuO$_{3}$ / Sr$_{2}$RuO$_{4}$ junction. We compare chiral $p$-wave (CPW) and helical $p$-wave (HPW) pair potentials, combined with ferromagnet magnetization directions parallel and perpendicular to the interface. For fixed $theta_{M}$, where $theta_{M}$ is a direction of magnetization in the ferromagnet measured from the $c$-axis, the tunneling conductance of CPW and HPW clearly show different voltage dependencies. It is found that the cases where the $d$-vector is perpendicular to the magnetization direction (CPW with $theta_{M} = pi/2$ and HPW with $theta_{M} = 0$) are identical. The obtained results serve as a guide to determine the pairing symmetry of the spin-triplet superconductor Sr$_{2}$RuO$_{4}$.
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On the basis of the Keldysh method of non-equilibrium systems, we develop a theory of electron tunneling in normal-metal/superconductor junctions. By using the tunneling Hamiltonian model (being appropriate for the tight-binding systems), the tunneling current can be exactly obtained in terms of the equilibrium Green functions of the normal metal and the superconductor. We calculate the conductance of various junctions. The discrepancy between the present treatment and the well-known scheme by Blonder, Tinkham, and Klapwijk is found for some junctions of low interfacial potential barrier.
We theoretically study the electronic transport through a ferromagnet-Ising superconductor junction. A tight-binding Hamiltonian describing the Ising superconductor is presented. Then by combing the non-equilibrium Greens function method, the expressions of Andreev reflection coefficient and conductance are obtained. A strong magnetoanisotropic spin-triplet Andreev reflection is shown, and the magnetoanisotropic period is $pi$ instead of $2pi$ as in the conventional magnetoanisotropic system. We demonstrate a significant increase of the spin-triplet Andreev reflection for the single-band Ising superconductor. Furthermore, the dependence of the Andreev reflection on the incident energy and incident angle are also investigated. A complete Andreev reflection can occur when the incident energy is equal to the superconductor gap, regardless of the Fermi energy (spin polarization) of the ferromagnet. For the suitable oblique incidence, the spin-triplet Andreev reflection can be strongly enhanced. In addition, the conductance spectroscopies of both zero bias and finite bias are studied, and the influence of gate voltage, exchange energy, and spin-orbit coupling on the conductance spectroscopy are discussed in detail. The conductance reveals a strong magnetoanisotropy with period $pi$ as the Andreev reflection coefficient. When the magnetization direction is parallel to the junction plane, a large conductance peak always emerges at the superconductor gap. This work offers a comprehensive and systematic study of the spin-triplet Andreev reflection, and has underlying application of $pi$-periodic spin valve in spintronics.
Ferromagnetic spin valves offer the key building blocks to integrate giant- and tunneling-magnetoresistance effects into spintronics devices. Starting from a generalized Blonder--Tinkham--Klapwijk approach, we theoretically investigate the impact of interfacial Rashba and Dresselhaus spin-orbit couplings on the tunneling conductance, and thereby the tunneling-magnetoresistance characteristics, of ferromagnet/superconductor/ferromagnet spin-valve junctions embedding thin superconducting spacers between the either parallel or antiparallel magnetized ferromagnets. We focus on the unique interplay between usual electron tunnelings -- that fully determine the tunneling magnetoresistance in the normal-conducting state -- and the peculiar Andreev reflections in the superconducting state. In the presence of interfacial spin-orbit couplings, special attention needs to be paid to the spin-flip (unconventional) Andreev-reflection process that is expected to induce superconducting triplet correlations in proximitized regions. As a transport signature of these triplet pairings, we detect conductance double-peaks around the singlet-gap energy, reflecting the competition between the singlet and the newly emerging triplet gap. We thoroughly analyze the Andreev reflections role in connection with superconducting tunneling-magnetoresistance phenomena, and eventually unravel huge conductance and tunneling-magnetoresistance magnetoanisotropies -- easily exceeding their normal-state counterparts by several orders of magnitude -- as another experimentally accessible fingerprint of unconventional Andreev reflections. Our results provide an important contribution to establish superconducting magnetic spin valves as an essential ingredient for future superconducting-spintronics concepts.
We calculate the superconducting critical temperature $T_c$, the singlet pair function $Psi^+(x)$, and triplet pair function $Psi^-(x)$ of superconductor/normal metal/ferromagnet (S/N/F) trilayers using the linearized Usadel equation near $T_c$. The Greens function method developed by Fominov $et al.$ for the S/F bilayers is extended to the S/N/F trilayer systems. The S of the trilayers is taken to be an s-wave singlet pairing superconductor, and the S/N and N/F interfaces are modeled in terms of the interface resistances parameterized, respectively, by $gamma_b^{SN}$ and $gamma_b^{NF}$. We present the $T_c$, $Psi^+(x)$, and $Psi^-(x)$ for typical $gamma_b^{SN}$, $gamma_b^{NF}$, and the exchange energy $ E_{ex}$: (a) For a small (large) $gamma_b^{NF}$, $T_c$ of S/N/F trilayers, as $d_N$ is increased, increases (decreases) on the length scale of N coherence length $xi_N$ with a discontinuity at $d_N=0$ due to a boundary condition mismatch. (b) $T_c(d_F)$ shows a non-monotonic behavior like S/F bilayers with a weakened shallow dip. (c) The odd frequency triplet component $Psi^-(x)$, induced by $E_{ex}$ and proximity effects, has a maximum near the N/F interface and decreases on the length scale $xi_{ex}$ in F. It also penetrates into N and S regions on the length scale $xi_N$ and $xi_S$, respectively. Based on these results we make comments on the experimental observation of the odd triplet components and the recent $T_c$ measurements in Nb/Au/CoFe trilayer systems.
In s-wave superconductors the Cooper pair wave function is isotropic in momentum space. This property may also be expected for Cooper pairs entering a normal metal from a superconductor due to the proximity effect. We show, however, that such a deduction is incorrect and the pairing function in a normal metal is surprisingly anisotropic because of quasiparticle interference. We calculate angle resolved quasiparticle density of states in NS bilayers which reflects such anisotropic shape of the pairing function. We also propose a magneto-tunneling spectroscopy experiment which could confirm our predictions.
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