Abstract
The theory of superconducting tunneling is extended to treat superconducting junctions with arbitrarily thin, but structureless tunnel barriers. An exact expression for the tunneling current is obtained, using standard, many-body, nonequilibrium Green's function techniques, assuming Fermi distributions in each electrode. The tunneling current result agrees with the recent theory of Blonder, Tinkham, and Klapwijk, but extends their results to treat strong coupling superconductors, proximity effect tunneling, and the effects of tunneling angle. Results for the Josephson critical current in S' INS (superconductor S', insulator I, metal N, superconductor S) junctions, where NS is a proximity effect double layer, are presented for barrier thicknesses ranging from zero to barrier thicknesses for which the tunneling Hamiltonian approach is correct, and for varying N metal thicknesses. Results forI-V curves are presented for normal metal (M)-INS junctions for a similar range of barrier thicknesses and N metal thicknesses. It is shown that the tunneling currentI is the sum of a supercurrentI SUP carried solely by Cooper pairs through S, and a quasiparticle currentI QP carried solely by quasiparticles. The influence of leakage on phonon structure observed on tunneling into strong coupling superconductors is described. The nonoscillating portion of the Josephson current is plotted as a function of voltage for the S' INS junction in the tunneling Hamiltonian limit.
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References
G. B. Arnold,Phys. Rev. B17, 3576 (1978).
T. M. Klapwijk, G. E. Blonder, and M. Tinkham,Physica 109+110B, 1157 (1982).
G. E. Blonder, M. Tinkham, and T. M. Klapwijk,Phys. Rev. B 25, 4515 (1982); see also A. V. Zaitsev,Zh. Eksp. Teor. Fiz. 78, 221 (1980) [Sov. Phys. JETP 51, 111 (1980)].
J. Demers and A. Griffin,Can. J. Phys. 49, 285 (1970); A. Griffin and J. Demers,Phys. Rev. B 4, 2202 (1971).
T. E. Feuchtwang,Phys. Rev. B 10, 4121 (1974).
G. B. Arnold,Phys. Rev. B 18, 1076 (1978).
S. N. Artemenko, A. F. Volkov, and A. V. Zaitsev,Zh. Eksp. Teor. Fiz. 76, 1816 (1979) [Sov. Phys. JETP 49, 924 (1979)].
M. Tinkham, inIntroduction to Superconductivity (McGraw-Hill, New York, 1975), p. 44.
E. L. Wolf and G. B. Arnold,Phys. Rep. 91, 31 (1982), and references cited therein.
S. T. Ruggiero, E. Track, G. B. Arnold, and D. E. Prober,Bull. Am. Phys. Soc. 29(3), 407 (1984).
A. Baratoff, Ph. D. Thesis, Cornell University, Ithaca, New York (1964).
I. O. Kulik and A. N. Omel'yanchuk,Sov. J. Low Temp. Phys. 4, 142 (1978).
W. J. Gallagher,Physica 108B, 825 (1981).
P. G. DeGennes and D. Saint-James,Phys. Lett. 4, 151 (1963).
E. L. Wolf, R. J. Noer, and G. B. Arnold,J. Low Temp. Phys. 40, 419 (1980).
W. L. McMillan and J. M. Rowell, inSuperconductivity, R. Parks, eds. (Marcel Dekker, New York, 1979), p. 561.
S. T. Ruggiero, G. B. Arnold, E. Track, and D. E. Prober, in Proceedings of the 17th International Conference on Low Temperature Physics, to be published.
V. Z. Kresin,Phys. Rev. B 28, 1294 (1983).
A. F. Andreev,Zh. Eksp. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)].
M. A. Peshkin and R. A. Buhrman,Phys. Rev. B 28, 161 (1983).
T. R. Lemberger,Phys. Rev. Lett. 52, 1029 (1984).
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Arnold, G.B. Superconducting tunneling without the tunneling Hamiltonian. J Low Temp Phys 59, 143–183 (1985). https://doi.org/10.1007/BF00681510
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DOI: https://doi.org/10.1007/BF00681510