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Volumn 54, Issue 10, 1996, Pages 7406-7420

Diagrammatic theory of random scattering matrices for normal-metal-superconducting mesoscopic junctions

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EID: 0000142729     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.54.7406     Document Type: Article
Times cited : (15)

References (32)
  • 7
    • 0000401963 scopus 로고
    • Yu.V. Nazarov, Phys. Rev. Lett. 73, 1420 (1994).
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 1420
  • 12
    • 0000005829 scopus 로고
    • A.F. Andreev, Zh. Éksp. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)]; 51, 1510 (1966) [ 24, 1019 (1967)].
    • (1964) Zh. Éksp. Teor. Fiz. , vol.46 , pp. 1823
    • Andreev, A.1
  • 13
    • 33744692902 scopus 로고
    • For an early application of Andreev scattering to mesoscopic N-S structures, see G.E. Blonder, M. Tinkham and T.M. Klapwijk, Phys. Rev. B 25, 4515 (1982).
    • (1982) Phys. Rev. B , vol.25 , pp. 4515
    • Blonder, G.1    Tinkham, M.2    Klapwijk, T.3
  • 14
    • 0000142334 scopus 로고    scopus 로고
    • There the depression in the density of states was short ranged, and disappeared at energies a few level spacings above the Fermi level, because the system considered was not perfectly time-reversal symmetric. In contrast, here the density of states remains depressed through a range in energies of the order of the correlation energy, which is much larger than the level spacing, as explained in Sec. II
    • We postpone a detailed discussion of the density of states and its relationship with reduced conductances to Ref. 16 (this reduction of the density of states is also obtained in the context of the Usadel equations, as mentioned, e.g., in Ref. 7). Note that it is much stronger (corresponding to a "leading-order" correction) than the reduction due to the "edge" of the spectrum, discussed, e.g., in A. Altland and M.R. Zirnbauer, Phys. Rev. Lett. 76, 3420 (1996). There the depression in the density of states was short ranged, and disappeared at energies a few level spacings above the Fermi level, because the system considered was not perfectly time-reversal symmetric. In contrast, here the density of states remains depressed through a range in energies of the order of the correlation energy, which is much larger than the level spacing, as explained in Sec. II.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 3420
    • Altland, A.1    Zirnbauer, M.2
  • 16
    • 0005457776 scopus 로고
    • Although the majority of recent work uses the transmission matrix, there are also exceptions in which the scattering matrix was used directly, e.g., K. Frahm and J.-L. Pichard, J. Phys. (France) I 5, 847 (1995).
    • (1995) J. Phys. (France) I , vol.5 , pp. 847
    • Frahm, K.1
  • 18
    • 0001233362 scopus 로고
    • A.I. Larkin and Yu.N. Ovchinnikov, Zh. Éksp. Teor. Fiz. 68, 1915 (1975) [Sov. Phys. JETP 41, 960 (1975)]. For a review of the early work on superconducting weak links, see K.K. Likharev, Rev. Mod. Phys. 51, 101 (1979).
    • (1975) Zh. Éksp. Teor. Fiz. , vol.68 , pp. 1915
    • Larkin, A.1
  • 19
    • 3643066333 scopus 로고
    • this context, the semiclassical approximation should be understood as implying propagation along distinct classical orbits, with definite expressions for the contribution of each orbit (and an underlying chaotic classical dynamics for each specific realization of the impurity potential or the shape of the cavity). Unfortunately, confusion may arise because the word "semiclassical" is often used to imply other ℏ→0 approximations, e.g., those in which the impurity averaging has been performed before the ℏ→0 limit is taken
    • See, e.g., R. Blumel and U. Smilansky, Phys. Rev. Lett. 60, 477 (1988). In this context, the semiclassical approximation should be understood as implying propagation along distinct classical orbits, with definite expressions for the contribution of each orbit (and an underlying chaotic classical dynamics for each specific realization of the impurity potential or the shape of the cavity). Unfortunately, confusion may arise because the word "semiclassical" is often used to imply other ℏ→0 approximations, e.g., those in which the impurity averaging has been performed before the ℏ→0 limit is taken.
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 477
    • Blumel, R.1    Smilansky, U.2
  • 21
    • 0642340331 scopus 로고    scopus 로고
    • Note that, depending on the convention, an extra minus sign may appear in all of the Andreev reflection amplitudes; this is of no importance as interference can only occur between amplitudes differing by an even number of Andreev reflections
    • For a detailed exposition, see K. Slevin, J.-L. Pichard and P.A. Mello, J. Phys. (France) I 6, 529 (1996). Note that, depending on the convention, an extra minus sign may appear in all of the Andreev reflection amplitudes; this is of no importance as interference can only occur between amplitudes differing by an even number of Andreev reflections.
    • (1996) J. Phys. (France) I , vol.6 , pp. 529
    • Slevin, K.1    Mello, P.2
  • 26
    • 33744543538 scopus 로고
    • The Large N Expansion in Quantum Field Theory and Statistical Physics: From spin systems to 2-dimensional gravity, edited by E. Brezin and S. R. Wadia (World Scientific, Singapore, 1993)
    • G. 't Hooft, Nucl. Phys. B72, 461 (1974); in The Large N Expansion in Quantum Field Theory and Statistical Physics: From spin systems to 2-dimensional gravity, edited by E. Brezin and S. R. Wadia (World Scientific, Singapore, 1993).
    • (1974) Nucl. Phys. , vol.B72 , pp. 461
    • 't Hooft, G.1
  • 27
    • 0001511611 scopus 로고
    • Note that here the times considered, or the lengths of the corresponding orbits, are of the order of the escape time (Formula presented) and much shorter than the Heisenberg time ℏ/Δ. The fact that Δ, the single-particle level spacing in the cavity, is much smaller than ℏ/(Formula presented), i.e., that the cavity has a continuous rather than a discrete spectrum, follows from the fact that the total number of modes, N, is large
    • See, e.g., M.V. Berry, Proc. R. Soc. London, A 400, 229 (1985). Note that here the times considered, or the lengths of the corresponding orbits, are of the order of the escape time (Formula presented) and much shorter than the Heisenberg time ℏ/Δ. The fact that Δ, the single-particle level spacing in the cavity, is much smaller than ℏ/(Formula presented), i.e., that the cavity has a continuous rather than a discrete spectrum, follows from the fact that the total number of modes, N, is large.
    • (1985) Proc. R. Soc. London , vol.400 , pp. 229
    • Berry, M.1
  • 28
    • 36749105566 scopus 로고
    • See also Ref. 26, and especially Chap. 8 in M.J. Creutz, Quarks, Gluons and Lattices (Cambridge University Press, Cambridge, England, 1983). Although our results are certainly contained in those of the large-N QCD literature, we are not aware of an analog in the literature to our simple expression for the couplings defined below, Eq. (17)
    • S. Samuel, J. Math. Phys. 21, 2695 (1980); See also Ref. 26, and especially Chap. 8 in M.J. Creutz, Quarks, Gluons and Lattices (Cambridge University Press, Cambridge, England, 1983). Although our results are certainly contained in those of the large-N QCD literature, we are not aware of an analog in the literature to our simple expression for the couplings defined below, Eq. (17).
    • (1980) J. Math. Phys. , vol.21 , pp. 2695
    • Samuel, S.1


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