Advertisement

Charge Imbalance: Its Relaxation, Diffusion and Oscillation

  • C. J. Pethick
  • H. Smith
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 65)

Abstract

Broadly speaking, one can distinguish three different levels of description which have made decisive contributions to our understanding of condensed matter. On the coarsest time and length scales phenomena may be described in terms of a limited number of variables. This leads to descriptions such as hydrodynamics for liquids (two-fluid hydrodynamics for superfluids), elasticity theory for solids, and the Landau-Ginzburg equations for superconductors. At the other extreme one has fully microscopic descriptions, which are able to take into account rapid spatial and temporal variations. The price one pays for the increase in generality is the increased complexity of the formalism, and a large increase in the number of degrees of freedom that must be considered. For example, distribution functions must be used, rather than simply the total density. At this microscopic level the theory of superconductors, the BCS theory, has been spectacularly successful in making possible the understanding of a vast range of phenomena. By comparison, microscopic theories have had relatively little impact on work on the helium liquids.

Keywords

Boltzmann Equation Collective Mode Collision Term Charge Imbalance Coherence Factor 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, P.W., 1959, Theory of dirty superconductors, J. Phys. Chem. Solids, 11:26.ADSCrossRefGoogle Scholar
  2. Aronov, A.G., 1974, The influence of condensate motion on the thermoelectric effects in superconductors, Zh. Eksp. Teor. Fiz., 67:178 [1975, Sov. Phys. JETP, 40:90].ADSGoogle Scholar
  3. Artemenko, S.N. and Volkov, A.F., 1975, Collective excitations with a sound spectrum in superconductors, Zh. Eksp. Teor. Fiz., 69:1764 [1976, Sov. Phys. JETP, 42:896].ADSGoogle Scholar
  4. Artemenko, S.N., Volkov, A.F., and Zaitsev, A.V., 1978, On the contribution of the superconductor to the resistance of a superconductor-normal metal system, J. Low Temp. Phys., 30:487.ADSCrossRefGoogle Scholar
  5. Betbeder-Matibet, O. and Nozières, P., 1969, Transport equations in clean superconductors, Ann. Phys. (N.Y.), 51:392.ADSCrossRefGoogle Scholar
  6. 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 Commun., 33:925.CrossRefGoogle Scholar
  7. Bray, A.J. and Schmidt, H., 1975, Collective modes in charged superconductors near Tc, Solid State Commun., 17:1175.ADSCrossRefGoogle Scholar
  8. Carlson, R.V. and Goldman, A.M., 1975, Propagating order-parameter collective modes in superconducting films, Phys. Rev. Lett., 34:11.ADSCrossRefGoogle Scholar
  9. Carlson, R.V. and Goldman, A.M., 1976, Dynamics of the order parameter of superconducting aluminum films, J. Low Temp. Phys., 25:67.ADSCrossRefGoogle Scholar
  10. Chang, J.J., 1978, Gap enhancement in superconducting thin films due to quasiparticle tunnel injection, Phys. Rev., B17:2137.ADSGoogle Scholar
  11. Chi, C.C. and Clarke, J., 1979, Quasiparticle branch mixing rates in superconducting aluminum, Phys. Rev., B19:4495.ADSGoogle Scholar
  12. Chi, C.C. and Clarke, J., 1980, Addendum to “Quasiparticle branch mixing rates in superconducting aluminum”, Phys. Rev., B21:333.ADSGoogle Scholar
  13. Clarke, J., 1972, Experimental observation of pair-quasiparticle potential difference in nonequilibrium superconductors, Phys. Rev. Lett., 28:1363.ADSCrossRefGoogle Scholar
  14. Clarke, J., Fjordbøge, B., and Lindelof, P.E., 1979, Supercurrent-induced charge imbalance measured in a superconductor in the presence of a thermal gradient, Phys. Rev. Lett., 43:642.ADSCrossRefGoogle Scholar
  15. 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
  16. Dolan, G.J. and Jackel, L.D., 1977, Voltage measurements within the nonequilibrium region near phase-slip centers, Phys. Rev. Lett., 39:1628.ADSCrossRefGoogle Scholar
  17. Entin-Wohlman, O. and Orbach, R., 1979, Effect of pair breaking on branch relaxation in nonequilibrium superconductors, Phys. Rev., B19:4510.ADSGoogle Scholar
  18. Hsiang, T.Y. and Clarke, J., 1980, Boundary resistance of the superconducting-normal interface, Phys. Rev., B21:945.ADSGoogle Scholar
  19. Kadin, A.M., Skocpol, W.J., and Tinkham, M., 1978, Magnetic field dependence of relaxation times in nonequilibrium superconductors, J. Low Temp. Phys., 33:481.ADSCrossRefGoogle Scholar
  20. 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
  21. Leggett, A.J. and Takagi, S., 1977, Orientational dynamics of super-fluid 3He: A two-fluid model. I. Spin dynamics with relaxation, Ann. Phys. (N.Y.), 106:79-ADSCrossRefGoogle Scholar
  22. 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
  23. Pethick, C.J. and Smith, H., 1978, Relaxation and collective motion in superconductors, a two-fluid description, J. Physique Supplement, 39:C6–488.Google Scholar
  24. Pethick, C.J. and Smith, H., 1979a, Relaxation and collective motion in superconductors: a two-fluid description, Ann. Phys. (N.Y.), 119:133.ADSCrossRefGoogle Scholar
  25. Pethick, C.J. and Smith, H., 1979b, Generation of charge imbalance in a superconductor by a temperature gradient, Phys. Rev. Lett., 43:640.ADSCrossRefGoogle Scholar
  26. Pethick, C.J. and Smith, H., 1980, Charge imbalance in non-equilibrium superconductors, J. Phys. C., to be published.Google Scholar
  27. Pippard, A.B., Shepherd, J.G., and Tindall, B.A., 1971, Resistance of superconducting-normal interfaces, Proc. Roy. Soc. Lond., A324:17.ADSGoogle Scholar
  28. Putterman, S.J., 1977, Phenomenological theory of collective modes and relaxation effects in type II. superconductors, J. Low Temp. Phys., 28:339.ADSCrossRefGoogle Scholar
  29. Schmid, A. and Schön, G., 1975a, Linearized kinetic equations and relaxation processes of a superconductor near Tc, J. Low Temp. Phys., 20:207.ADSCrossRefGoogle Scholar
  30. Schmid, A. and Schön, G., 1975b, Collective oscillations in a dirty superconductor, Phys. Rev. Lett., 34:941.ADSCrossRefGoogle Scholar
  31. 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
  32. Schön, G., 1980, private communication, this summer school.Google Scholar
  33. Skocpol, W.J., Beasley, M.R., and Tinkham, M., 1974, Phase-slip centers and non-equilibrium processes in superconducting tin microbridges, J. Low Temp. Phys., 16:145.ADSCrossRefGoogle Scholar
  34. Tinkham, M., 1972, Tunneling generation, relaxation, and tunneling detection of hole-electron imbalance in superconductors, Phys. Rev., B6:1747.ADSGoogle Scholar
  35. Tinkham, M. and Clarke, J., 1972, Theory of pair-quasiparticle potential difference in non-equilibrium superconductors, Phys. Rev. Lett., 28:1366.ADSCrossRefGoogle Scholar
  36. Waldram, J.R., 1975, Chemical potential and boundary resistance at normal-superconducting interfaces, Proc. Roy. Soc. Lond., A345:231.ADSGoogle Scholar
  37. Ziman, J.M., 1960, “Electrons and Phonons,” Oxford University Press, London.MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • C. J. Pethick
    • 1
    • 2
  • H. Smith
    • 3
  1. 1.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.NorditaCopenhagen ØDenmark
  3. 3.Physics Laboratory I, H.C. Ørsted InstituteUniversity of CopenhagenCopenhagen ØDenmark

Personalised recommendations