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Abstract

If an electron-like (k>kF) or a hole-like (k<kF) excitation is added to a superconductor, a charge imbalance is created. Charge imbalance is of practical importance first, because it gives rise to a measureable steady-state voltage in a superconductor, and second, because it provides a tool for measuring various electron-relaxation rates. The importance of the disequilibrium of the electron- and hole-like branches was first pointed out by Pippard et al. (1971) who measured the electrical resistance of superconductor-normal metal-superconductor (SNS) sandwiches as a function of temperature. Near the superconducting transition temperature, Tc, they found that the resistance increased with increasing temperature. They ascribed this increase to the propagation of quasiparticles having a branch imbalance distribution into or out of the superconductor, a process that, at the time, they believed generated a potential step at each NS interface, and thus produced an additional boundary resistance. However, the first quantitative understanding of charge imbalance arose from experiments in which electrons were injected via a tunnel junction into a superconducting film (Clarke 1972); at the time this experiment was performed, its connection with the NS interface resistance was not apparent.

Keywords

Boltzmann Equation Elastic Scattering Tunnel Junction Charge Imbalance Charge Relaxation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Abrikosov, A. A., and Gor’kov, L. P., 1960, Contribution to the theory of superconducting alloys with paramagnetic impurities, Zh. Eksp. Teor. Fiz., 39:1781 [Sov. Phys. JETP, 12:1243].Google Scholar
  2. Anderson, P. W., 1959, Theory of dirty superconductors, J. Phys. Chem. Solid., 11:26.ADSCrossRefGoogle Scholar
  3. Andréev, A. F., 1964, The thermal conductivity of the intermediate state in superconductors, Zh. Eksp. Teor. Fiz., 46:182 [Sov. Phys. JETP, 19:1228].Google Scholar
  4. Aronov, A. G., 1974, The influence of condensate motion on the thermoelectric effects in superconductors, Zh. Eksp. Teor. Fiz., 67:178 [Sov. Phys. JETP, 40:90].ADSGoogle Scholar
  5. Artemenko, N., and Volkov, A. F., 1977, Andréev reflection and the electric resistance of superconductors in the intermediate state, Zh. Eksp. Teor. Fiz., 72:1018 [Sov. Phys. JETP, 45:533].ADSGoogle Scholar
  6. Artemenko, N., Volkov, A. F., and Zaiteev, A. V., 1978, On the contribution of the superconductor resistance of a superconductor-normal metal system, J. Low Temp. Phys., 30:487.ADSCrossRefGoogle Scholar
  7. Bergmann, G., 1971, Eliashberg function α2 (E)F(E) and the strong-coupling behavior of a disordered superconductor, Phys. Rev., B3:3797.ADSGoogle Scholar
  8. Beyer Nielsen, J., Ono, Y. A., Pethick, C. J., and Smith, H., 1980, The effect of impurity scattering on the thermally induced charge imbalance in a clean superconductor, Solid State Comm., 33:925.CrossRefGoogle Scholar
  9. Blackford, B. L., 1976, A tunneling investigation of energy-gap anisotropy in superconducting bulk aluminum crystals, J. Low Temp. Phys., 23:43.ADSCrossRefGoogle Scholar
  10. Chambers, R. G., 1952, The anomalous skin effect, Proc. Roy. Soc. Lond., 215:481.ADSCrossRefGoogle Scholar
  11. Chang, J-J, 1979, Relaxation of the quasiparticle charge imbalance in superconductors, Phys. Rev., B19:1420.ADSGoogle Scholar
  12. Chang, J-J, and Scalapino, D. J., 1977, Kinetic-equation approach to nonequilibrium superconductivity, Phys. Rev., B15:2651.ADSGoogle Scholar
  13. Chi, C. C., and Clarke, J., 1979, Quasiparticle branch mixing rates in superconducting aluminum, Phys. Rev., B19:4495.ADSGoogle Scholar
  14. Chi, C. C., and Clarke, J., 1980, Addendum to “Quasiparticle branch mixing rates in superconducting aluminum,” Phys. Rev., B21:333.ADSGoogle Scholar
  15. Chi, C. C., and Langenberg, D. N., 1976, Microwave response of non-equilibrium superconductors, Bull. Am. Phys. Soc., 21:403.Google Scholar
  16. Clarke, J., 1972, Experimental observation of pair-quasiparticle potential difference in nonequilibrium superconductors, Phys. Rev. Lett., 28:1363.ADSCrossRefGoogle Scholar
  17. Clarke, J., 1976, Superconducting quantum interference devices for low frequency measurements in: “Superconductor Applications: SQUIDS and Machines,” B. B. Schwartz and S. Foner, eds., Plenum, New York.Google Scholar
  18. Clarke, J., Eckern, U., Schmid, A., Schon, G., and Tinkham, M., 1979, Branch-imbalance relaxation times in superconductors, Phys. Rev., B20:3933.ADSGoogle Scholar
  19. Clarke, J., Fjordbøge, B. R., and Lindelof, P. E., 1979a, Super-current induced charge imbalance measured in a superconductor in the presence of a thermal gradient, Phys. Rev. Lett., 43:642.ADSCrossRefGoogle Scholar
  20. Clarke, J., and Paterson, J. L., 1974, Measurements of the relaxation of quasiparticle branch imbalance in superconductors, J. Low Temp. Phys., 15:491.ADSCrossRefGoogle Scholar
  21. Clarke, J., and Tinkham, M., 1980, Theory of quasiparticle charge imbalance induced in a superconductor by a supercurrent in the presence of a thermal gradient, Phys. Rev. Lett., 44:106.ADSCrossRefGoogle Scholar
  22. Craven, R. A., Thomas, G. A., and Parks, R. D., 1971, Sharpening of the resistive transition of a superconductor with the addition of paramagnetic impurities, Phys. Rev., B4:2185.ADSGoogle Scholar
  23. DeGennes, P. G., 1964, Boundary effects in superconductors, Rev. Mod. Phys., 36:225.ADSCrossRefGoogle Scholar
  24. DeGennes, P. G., 1966, “Superconductivity of metals and alloys,” Benjamin, New York.Google Scholar
  25. Dolan, G. J., and Jackel, L. D., 1977, Voltage measurements within the non-equilibrium region near phase slip centers, Phys. Rev. Lett., 39:1628.ADSCrossRefGoogle Scholar
  26. Entin-Wohlman, O., and Orbach, R., 1979, Effect of pair breaking on branch relaxation in nonequilibrium superconductors, Phys. Rev., B19:4510.ADSGoogle Scholar
  27. Fickett, F. R., 1971, Cryogenics, 11:349.CrossRefGoogle Scholar
  28. Galperin, Yu. M., Gurevich, V. L., and Kozub, V. I., 1974, Thermoelectric effects in superconductors, Zh. Eksp. Teor. Fiz., 66:1387 [Sov. Phys. JETP, 39:680].ADSGoogle Scholar
  29. Ginzburg, V. L., and Landau, L. D., 1950, Zh. Eksp. Teor. Fiz., 20:1064.Google Scholar
  30. Gray, K. E., Long, A. R., and Adkins, C. J., 1969, Measurements of the lifetime of excitations in superconducting aluminum, Phil. Mag., 20:273.ADSCrossRefGoogle Scholar
  31. Gschneidner, K. A., 1964, Physical properties and interrelationships of metallic and semi-metallic elements, Solid State Phys., 16:275.CrossRefGoogle Scholar
  32. Harding, G. L., Pippard, A. B., and Tomlinson, J. R., 1974, Resistance of superconducting-normal interfaces, Proc. Roy. Soc. Lond., A340: l.Google Scholar
  33. Heidel, D. F., and Garland, J. C., 1980, Thermoelectric potentials in superconducting aluminum films, Bull. Am. Phys. Soc., 25:411.Google Scholar
  34. Hsiang, T-Y, 1980, Magnetic field dependence of the superconductor-normal metal boundary resistance, Phys. Rev., B21:956.ADSGoogle Scholar
  35. Hsiang, T-Y, and Clarke, J., 1980, Boundary resistance of the superconducting-normal interface, Phys. Rev., B21:945.ADSGoogle Scholar
  36. Kadin, A. M., Skocpol, W. J., and Tinkham, M., 1978, J. Low Temp. Phys., 33:481.Google Scholar
  37. Kadin, A. M., Smith, L. N., and Skocpol, W. J., 1980, Charge imbalance waves and nonequilibrium dynamics near a superconducting phase-slip center, J. Low Temp. Phys., 38:497.ADSCrossRefGoogle Scholar
  38. Kaplan, S. B., Chi, C. C., Langenberg, D. N., Chang, J. J., Jafarey, S., and Scalapino, D. J., 1976, Quasiparticle and phonon lifetimes in superconductors, Phys. Rev., B14:4854.ADSGoogle Scholar
  39. Kittel, C., 1976, “Introduction to Solid State Physics,” 5th edition, Wiley, New York.Google Scholar
  40. Knorr, K., and Barth, N., 1970, Superconductivity and phonon spectra of disordered thin films, Solid State Comm., 8:1085.ADSCrossRefGoogle Scholar
  41. Krahenbuhl, Y., and Watts-Tobin, R. J., 1979, Microscopic theory of the current-voltage relationship across a normal-superconducting interface, J. Low. Temp. Phys., 35:569.ADSCrossRefGoogle Scholar
  42. Lawrence, W. E., and Meador, A. N., 1978, Calculation of the order-parameter relaxation times in superconducting aluminum, Phys. Rev., B18:1154.ADSGoogle Scholar
  43. Leavens, C. R., and Carbotte, J. P., 1971, Contribution to the theory of weak coupling superconductors, Can J. Phys., 49:724;ADSCrossRefGoogle Scholar
  44. Leavens, C. R., and Carbotte, J. P., 1972, Gap anisotropy in a weak coupling superconductor, Annals of Physics, 70:338.ADSCrossRefGoogle Scholar
  45. Lemberger, T. R., and Clarke, J., 1980, Charge-imbalance relaxation in the presence of a pair-breaking interaction in superconducting AlEr films, submitted to Phys. Rev. B.Google Scholar
  46. Lemberger, T. R., and Clarke, J., 1980a, Charge imbalance relaxation in the presence of a pair-breaking supercurrent in dirty, superconducting films, submitted to Phys. Rev. B.Google Scholar
  47. Long, A. R., 1973, The attenuation of high frequency phonons in metals, J. Phys., F3:2023.ADSCrossRefGoogle Scholar
  48. Maki, K., 1969, Gapless superconductivity, in: “Superconductivity,” R. D. Parks, ed., Marcel Dekker, New York.Google Scholar
  49. Markowitz, D., and Kadanoff, L. P., 1963, Effect of impurities upon critical temperature of anisotropic superconductors, Phys. Rev., 131:563.ADSCrossRefGoogle Scholar
  50. Meservey, R., and Schwartz, B. B., 1969, Equilibrium properties: comparison of experimental results with predictions of the BCS theory, in: “Superconductivity,” R. D. Parks, ed., Marcel Dekker, New York.Google Scholar
  51. Moody, M. V., and Paterson, J. L., 1979, Relaxation of the distribution function branch imbalance Q* in Sn and Sn-In alloys, J. Low Temp. Phys., 34:83.ADSCrossRefGoogle Scholar
  52. Ovchinnikov, Yu. N., 1977, Penetration of an electrical field into a superconductor, J. Low Temp. Phys., 28:43.ADSCrossRefGoogle Scholar
  53. Pethick, C. J., and Smith, H., 1979, Relaxation and collective motion in superconductors: a two-fluid description, Annals of Physics, 119:133.ADSCrossRefGoogle Scholar
  54. Pethick, C. J., and Smith, H., 1979a, Generation of charge imbalance in a superconductor by a temperature gradient, Phys. Rev. Lett., 43:640.ADSCrossRefGoogle Scholar
  55. Pethick, C. J., and Smith, H., 1980, Charge imbalance in nonequili-brium superconductors, to be published in J. Phys. C.Google Scholar
  56. Pippard, A. B., 1965, “The Dynamics of Conduction Electrons,” Gordon and Breach, New York.Google Scholar
  57. Pippard, A. B., Shephard, J. G., and Tindall, D. A., 1971, Resistance of superconducting-normal interfaces, Proc. Roy. Soc. Lond., A324:17.ADSGoogle Scholar
  58. Rieger, T. J., Scalapino, D. J., and Mercereau, J. E., 1971, Charge conservation and chemical potentials in time-dependent Ginzburg-Landau theory, Phys. Rev. Lett., 27:1787.ADSCrossRefGoogle Scholar
  59. Rothwarf, A., and Taylor, B. N., 1967, Measurement of recombination lifetimes in superconductors, Phys. Rev. Lett., 19:27.ADSCrossRefGoogle Scholar
  60. Schmid, A., and Schön, G., 1975, Linearized kinetic equations and relaxation processes of a superconductor near Tc, J. Low Temp. Phys., 20:207.ADSCrossRefGoogle Scholar
  61. Schmid, A., and Schön, G., 1979, Generation of branch imbalance by the interaction between supercurrent and thermal gradient, Phys. Rev. Lett., 43:793.ADSCrossRefGoogle Scholar
  62. Schön, G., 1980, unpublished.Google Scholar
  63. Schuller, I., and Gray, K. E., 1977, Temperature dependence of the relaxation time of the superconducting order parameter, Solid State Comm., 23:337.ADSCrossRefGoogle Scholar
  64. Skocpol, W. J., Beasley, M. R., and Tinkham, M., 1974, Phase-slip centers and nonequilibrium processes in superconducting tin microbridges, J. Low Temp. Phys., 16:145.ADSCrossRefGoogle Scholar
  65. Smith, L. N., and Mochel, J. M., 1976, Phonon and quasiparticle dynamics in superconducting aluminum tunnel junctions, Phys. Rev. Lett., 35:1597.ADSCrossRefGoogle Scholar
  66. Tinkham, M., 1972, Tunneling generation, relaxation, and tunneling detection of hole-electron imbalance in superconductors, Phys. Rev., B6:1747.ADSGoogle Scholar
  67. Tinkham, M., 1975, “Introduction to Superconductivity,” McGraw-Hill, Inc., New York.Google Scholar
  68. Tinkham, M., and Clarke, J., 1972, Theory of pair-quasiparticle potential difference in non-equilibrium superconductors, Phys. Rev. Lett., 28:1366.ADSCrossRefGoogle Scholar
  69. Van Harlingen, D. J., 1980, Thermoelectric generation of charge imbalance at superconductor interfaces, Bull. Am. Phys. Soc., 25:411.Google Scholar
  70. Waldram, J. R., 1975, Chemical potential and boundary resistance at normal-superconducting interfaces, Proc. Roy. Soc. Lond., A345:231.ADSGoogle Scholar
  71. Yu, M. L., and Mercereau, J. E., 1972, Electric potentials near a superconducting-normal bondary, Phys. Rev. Lett., 28:1117.ADSCrossRefGoogle Scholar
  72. Zavaritzkii, N. V., 1969, Increase of the critical temperature of superconductors condensed at low temperatures, Zh. Eksp. Teor. Fiz., 57:752 [Sov. Phys. JETP, 30:412].Google Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • John Clarke
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Materials and Molecular Research DivisionLawrence Berkeley LaboratoryBerkeleyUSA

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