Quantum Interference and the Spin Orbit Interaction in Mesoscopic Normal-Superconducting Junctions

Slevin, Keith; Pichard, Jean‐Louis; Mello, Pier A.

doi:10.1051/jp1:1996228

Cited by 13 publications

(18 citation statements)

References 37 publications

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“…The results are for a metal without spin-orbit scattering (Brouwer and Beenakker, 1995b). In the presence of strong spin-orbit scattering each entry is to be multiplied by −1/2 (Slevin, Pichard, and Mello, 1996). For comparison, the corresponding result in the normal state is listed between {· · ·}.…”

Section: Weak Localizationmentioning

confidence: 99%

Random-matrix theory of quantum transport

1997

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This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects to two reservoirs, either directly, or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is Dyson's circular ensemble for ballistic point contacts, or the Poisson kernel for point contacts containing a tunnel barrier. In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation. The equivalence is discussed with the non-linear σ model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction. To be published in Rev. Mod. Phys. (1997).

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Section: Weak Localizationmentioning

confidence: 99%

Random-matrix theory of quantum transport

1997

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“…With this convention, used for example in Refs. [39,40], the second-quantized Bogoliubov-de Gennes Hamiltonian is 1 2 c † Hc, where…”

Section: The Ten-fold Waymentioning

confidence: 99%

Onsager relations in coupled electric, thermoelectric, and spin transport: The tenfold way

et al. 2012

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Hamiltonian systems can be classified into ten classes, in terms of the presence or absence of timereversal symmetry, particle-hole symmetry and sublattice/chiral symmetry. We construct a quantum coherent scattering theory of linear transport for coupled electric, heat and spin transport; including the effect of Andreev reflection from superconductors. We derive a complete list of the Onsager reciprocity relations between transport coefficients for coupled electric, spin, thermoelectric and spin caloritronic effects. We apply these to all ten symmetry classes, paying special attention to specific additional relations that follow from the combination of symmetries, beyond microreversibility. We discuss these relations in several illustrative situations. We show the reciprocity between spin-Hall and inverse spin-Hall effects, and the reciprocity between spin-injection and magnetoelectric spin currents. We discuss the symmetry and reciprocity relations of Seebeck, Peltier, spin-Seebeck and spin-Peltier effects in systems with and without coupling to superconductors. PACS numbers: 73.23.-b,85.75.-d,72.15.Jf,74.25.fg arXiv:1207

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“…Furthermore, research in spintronics has sparked renewed interest in the effects of the spin-orbit interaction on quantum transport. 11,12) In this proceeding, we report precise analyses of the critical phenomena at the Anderson transition in the SU(2) model 13,14) and the three dimensional generalization of the Ando model, 15,16) both of which have spinorbit coupling and have symplectic symmetry. We also extend our finite size scaling analysis beyond the critical region and present a numerical estimate of the β function.…”

Section: 3)mentioning

confidence: 99%