About this Journal Submit a Manuscript Table of Contents
Advances in Condensed Matter Physics
Volume 2013 (2013), Article ID 104379, 25 pages
http://dx.doi.org/10.1155/2013/104379
Review Article

Electrodynamics of Metallic Superconductors

1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

Received 11 April 2013; Revised 23 May 2013; Accepted 9 June 2013

Academic Editor: Victor V. Moshchalkov

Copyright © 2013 M. Dressel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. London, Superfluids, vol. 1 of Macroscopic Theory of Superconductivity, John Wiley & Sons, New York, NY, USA, 1950.
  2. J. Bardeen, “Theory of the Meissner effect in superconductors,” Physical Review, vol. 97, no. 6, pp. 1724–1725, 1955. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Bardeen, “Theory of Supercondgctivity,” in Handbuch der Physik, vol. 15, pp. 274–369, Springer, Berlin, Germany, 1956.
  4. H. Welker, “Supraleitung und magnetische Austauschwechselwirkung,” Zeitschrift für Physik, vol. 114, no. 9-10, pp. 525–551, 1939. View at Publisher · View at Google Scholar · View at Scopus
  5. L. N. Cooper, “Bound electron pairs in a degenerate fermi gas,” Physical Review, vol. 104, no. 4, pp. 1189–1190, 1956. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of superconductivity,” Physical Review, vol. 108, no. 5, pp. 1175–1204, 1957. View at Publisher · View at Google Scholar · View at Scopus
  7. L. C. Hebel and C. P. Slichter, “Nuclear relaxation in superconducting aluminum,” Physical Review, vol. 107, no. 3, p. 901, 1957.
  8. L. C. Hebel and C. P. Slichter, “Nuclear spin relaxation in normal and superconducting aluminum,” Physical Review, vol. 113, no. 6, pp. 1504–1519, 1959. View at Publisher · View at Google Scholar · View at Scopus
  9. R. W. Morse and H. V. Bohm, “Superconducting energy gap from ultrasonic attenuation measurements,” Physical Review, vol. 108, no. 4, pp. 1094–1096, 1957. View at Publisher · View at Google Scholar · View at Scopus
  10. R. E. Glover III and M. Tinkham, “Transmission of superconducting films at millimeter-microwave and far infrared frequencies,” Physical Review, vol. 104, no. 3, pp. 844–845, 1956. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Tinkham, “Energy gap interpretation of experiments on infrared transmission through superconducting films,” Physical Review, vol. 104, no. 3, pp. 845–846, 1956. View at Publisher · View at Google Scholar · View at Scopus
  12. R. E. Glover III and M. Tinkham, “Conductivity of superconducting films for photon energies between 0.3 and 40kTc,” Physical Review, vol. 108, no. 2, pp. 243–256, 1957. View at Publisher · View at Google Scholar · View at Scopus
  13. M. J. Buckingham, “Very high frequency absorption in superconductors,” Physical Review, vol. 101, no. 4, pp. 1431–1432, 1956. View at Publisher · View at Google Scholar · View at Scopus
  14. G. S. Blevins, W. Gordy, and W. M. Fairbank, “Superconductivity at millimeter wave frequencies,” Physical Review, vol. 100, no. 4, pp. 1215–1216, 1955. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Tinkham and R. E. Glover III, “Superconducting energy gap inferences from thin-film transmission data,” Physical Review, vol. 110, no. 3, pp. 778–779, 1958. View at Publisher · View at Google Scholar · View at Scopus
  16. A. T. Forrester, “Superconducting energy gap inferences from thin-film transmission data,” Physical Review, vol. 110, no. 3, pp. 776–778, 1958. View at Publisher · View at Google Scholar · View at Scopus
  17. M. A. Biondi, A. T. Forrester, M. P. Garfunkel, and C. B. Satterthwaite, “Experimental evidence for an energy gap in superconductors,” Reviews of Modern Physics, vol. 30, no. 4, pp. 1109–1136, 1958. View at Publisher · View at Google Scholar · View at Scopus
  18. M. A. Biondi, M. P. Garfunkel, and A. O. McCoubrey, “Millimeter wave absorption in superconducting aluminum,” Physical Review, vol. 101, no. 4, pp. 1427–1429, 1956. View at Publisher · View at Google Scholar · View at Scopus
  19. M. A. Biondi, M. P. Garfunkel, and A. O. McCoubrey, “Microwave measurements of the energy gap in superconducting aluminum,” Physical Review, vol. 108, no. 2, pp. 495–497, 1957. View at Publisher · View at Google Scholar · View at Scopus
  20. M. A. Biondi, A. T. Forrester, and M. P. Garfunkel, “Millimeter wave studies of superconducting tin,” Physical Review, vol. 108, no. 2, pp. 497–498, 1957. View at Publisher · View at Google Scholar · View at Scopus
  21. M. A. Biondi and M. P. Garfunkel, “Measurement of the temperature variation of the energy gap in superconducting aluminum,” Physical Review Letters, vol. 2, no. 4, pp. 143–145, 1959. View at Publisher · View at Google Scholar · View at Scopus
  22. M. A. Biondi and M. P. Garfunkel, “Millimeter wave absorption in superconducting aluminum. I. Temperature dependence of the energy gap,” Physical Review, vol. 116, no. 4, pp. 853–861, 1959. View at Publisher · View at Google Scholar · View at Scopus
  23. M. A. Biondi and M. P. Garfunkel, “Millimeter wave absorption in superconducting aluminum. II. Calculation of the skin depth,” Physical Review, vol. 116, no. 4, pp. 862–867, 1959. View at Publisher · View at Google Scholar · View at Scopus
  24. M. Tinkham, “Absorption of electromagnetic radiation in superconductors,” Physica, vol. 24, supplement 1, pp. S35–S41, 1958. View at Scopus
  25. R. A. Ferrell and R. E. Glover III, “Conductivity of superconducting films: a sum rule,” Physical Review, vol. 109, no. 4, pp. 1398–1399, 1958. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Tinkham and R. A. Ferrell, “Determination of the superconducting skin depth from the energy gap and sum rule,” Physical Review Letters, vol. 2, no. 8, pp. 331–333, 1959. View at Publisher · View at Google Scholar
  27. D. C. Mattis and J. Bardeen, “Theory of the anomalous skin effect in normal and superconducting metals,” Physical Review, vol. 111, no. 2, pp. 412–417, 1958. View at Publisher · View at Google Scholar · View at Scopus
  28. W. Zimmermann, E. H. Brandt, M. Bauer, E. Seider, and L. Genzel, “Optical conductivity of BCS superconductors with arbitrary purity,” Physica C, vol. 183, no. 1–3, pp. 99–104, 1991. View at Scopus
  29. K. Steinberg, M. Scheffler, and M. Dressel, “Quasiparticle response of superconducting aluminum to electromagnetic radiation,” Physical Review B, vol. 77, no. 21, Article ID 214517, 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. D. M. Ginsberg, P. L. Richards, and M. Tinkham, “Apparent structure on the far infrared energy gap in superconducting lead and mercury,” Physical Review Letters, vol. 3, no. 7, pp. 337–338, 1959. View at Publisher · View at Google Scholar · View at Scopus
  31. D. M. Ginsberg and M. Tinkham, “Far infrared transmission through superconducting films,” Physical Review, vol. 118, no. 4, pp. 990–1000, 1960. View at Publisher · View at Google Scholar · View at Scopus
  32. P. L. Richards and M. Tinkham, “Far-infrared energy gap measurements in bulk superconducting in, Sn, Hg, Ta, V, Pb, and Nb,” Physical Review, vol. 119, no. 2, pp. 575–590, 1960. View at Publisher · View at Google Scholar · View at Scopus
  33. L. H. Palmer and M. Tinkham, “Far-infrared absorption in thin superconducting lead films,” Physical Review, vol. 165, no. 2, pp. 588–595, 1968. View at Publisher · View at Google Scholar · View at Scopus
  34. M. Tinkham, “The electromagnetic properties of superconductors,” Reviews of Modern Physics, vol. 46, no. 4, pp. 587–596, 1974. View at Publisher · View at Google Scholar · View at Scopus
  35. P. Wyder, “Far-infrared and superconductivity,” Infrared Physics, vol. 16, no. 1-2, pp. 243–251, 1976. View at Scopus
  36. K. Holczer, O. Klein, and G. Grüner, “Observation of the conductivity coherence peak in superconducting Pb,” Solid State Communications, vol. 78, no. 10, pp. 875–877, 1991. View at Scopus
  37. O. Klein, E. J. Nicol, K. Holczer, and G. Grüner, “Conductivity coherence factors in the conventional superconductors Nb and Pb,” Physical Review B, vol. 50, no. 9, pp. 6307–6316, 1994. View at Publisher · View at Google Scholar · View at Scopus
  38. A. B. Pippard, “Metallic conduction at high frequencies and low temperatures,” Advances in Electronics and Electron Physics, vol. 6, pp. 1–45, 1954. View at Publisher · View at Google Scholar · View at Scopus
  39. A. B. Pippard, “The anomalous skin effect in anisotropic metals,” Proceedings of the Royal Society of London A, vol. 224, no. 1157, pp. 273–282, 1954.
  40. J. R. Waldram, “Surface impedance of superconductors,” Advances in Physics, vol. 13, no. 49, pp. 1–88, 1964.
  41. M. Tinkham, Introduction to Superconductivity, Mc-Graw Hill, New York, NY, USA, 1st edition, 1975.
  42. M. Tinkham, Introduction to Superconductivity, Mc-Graw Hill, New York, NY, USA, 2nd edition, 1996.
  43. M. Tinkham, Introduction to Superconductivity, Dover Publication, Mineola, NY, USA, 2nd edition, 2004.
  44. G. Rickayzen, Theory of Superconductivity, Interscience Publishers, New York, NY, USA, 1965.
  45. R. D. Parks, Ed., Superconductivity, Vol. I and II, Marcel Dekker, New York, NY, USA, 1969.
  46. M. Dressel and G. Grüner, Electrodynamics of Solids, Cambridge University Press, Cambridge, UK, 2002.
  47. D. N. Basov, R. D. Averitt, D. van der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Reviews of Modern Physics, vol. 83, no. 2, pp. 471–541, 2011. View at Publisher · View at Google Scholar · View at Scopus
  48. D. Sherman, G. Kopnov, D. Shahar, and A. Frydman, “Measurement of a superconducting energy gap in a homogeneously amorphous insulator,” Physical Review Letters, vol. 108, no. 17, Article ID 177006, 2012. View at Publisher · View at Google Scholar · View at Scopus
  49. B. Sacépé, C. Chapelier, T. I. Baturina, V. M. Vinokur, M. R. Baklanov, and M. Sanquer, “Pseudogap in a thin film of a conventional superconductor,” Nature Communications, vol. 1, no. 9, article 140, 2010. View at Publisher · View at Google Scholar · View at Scopus
  50. Y. Mizukami, H. Shishido, T. Shibauchi et al., “Extremely strong-coupling superconductivity in artificial two-dimensional Kondo lattices,” Nature Physics, vol. 7, no. 11, pp. 849–853, 2011. View at Publisher · View at Google Scholar · View at Scopus
  51. S. P. Chockalingam, M. Chand, A. Kamlapure et al., “Tunneling studies in a homogeneously disordered s-wave superconductor: NbN,” Physical Review B, vol. 79, no. 9, Article ID 094509, 2009. View at Publisher · View at Google Scholar · View at Scopus
  52. T. Timusk and B. Statt, “The pseudogap in high-temperature superconductors: an experimental survey,” Reports on Progress in Physics, vol. 62, no. 1, pp. 61–122, 1999. View at Publisher · View at Google Scholar · View at Scopus
  53. N. D. Basov and T. Timusk, “Electrodynamics of high—Tc superconductors,” Reviews of Modern Physics, vol. 77, no. 2, pp. 721–729, 2005. View at Publisher · View at Google Scholar · View at Scopus
  54. U. S. Pracht, M. Scheffler, M. Dressel, D. F. Kalok, C. Strunk, and T. I. Baturina, “Direct observation of the superconducting gap in a thin film of titanium nitride using terahertz spectroscopy,” Physical Review B, vol. 86, no. 18, Article ID 184503, 2012.
  55. E. F. C. Driessen, P. C. J. J. Coumou, R. R. Tromp, P. J. de Visser, and T. M. Klapwijk, “Strongly disordered tin and nbtin s-wave superconductors probed by microwave electrodynamics,” Physical Review Letters, vol. 109, no. 10, Article ID 107003, 2012.
  56. M. R. Vissers, M. P. Weides, J. S. Kline, M. Sandberg, and D. P. Pappas, “Identifying capacitive and inductive loss in lumped element superconducting hybrid titanium nitride/aluminum resonators,” Applied Physics Letters, vol. 101, Article ID 022601, 2012.
  57. D. Henrich, S. Dörner, M. Hofherr et al., “Broadening of hotspot response spectrum of superconducting NbN nanowire singlephoton detector with reduced nitrogen content,” Journal of Applied Physics, vol. 112, no. 7, Article ID 074511, 2012.
  58. K. Il'in, M. Hofherr, D. Rall et al., “Ultra-thin TaN films for superconducting nanowire single-photon detectors,” Journal of Low Temperature Physics, vol. 167, pp. 809–814, 2011. View at Publisher · View at Google Scholar · View at Scopus
  59. A. Engel, A. Schilling, K. Ilin, and M. Siegel, “Dependence of count rate on magnetic field in superconducting thin-film TaN single-photon detectors,” Physical Review B, vol. 86, Article ID 140506, 2012.
  60. A. J. Kerman, E. A. Dauler, W. E. Keicher et al., “Kinetic-inductance-limited reset time of superconducting nanowire photon counters,” Applied Physics Letters, vol. 88, no. 11, Article ID 111116, 2006. View at Publisher · View at Google Scholar · View at Scopus
  61. G. Gol'Tsman, O. Okunev, G. Chulkova et al., “Fabrication and properties of an ultrafast NbN hot-electron single-photon detector,” IEEE Transactions on Applied Superconductivity, vol. 11, no. 1, pp. 574–577, 2001. View at Publisher · View at Google Scholar · View at Scopus
  62. J. Zhang, W. Slysz, A. Verevkin et al., “Response time characterization of NbN superconducting single-photon detectors,” IEEE Transactions on Applied Superconductivity, vol. 13, no. 2, pp. 180–183, 2003. View at Publisher · View at Google Scholar · View at Scopus
  63. C. M. Natarajan, M. G. Tanner, and R. H. Hadfields, “Superconducting nanowire single-photon detectors: physics and applications,” Superconductor Science and Technology, vol. 25, no. 6, Article ID 063001, 2012.
  64. P. B. Miller, “Surface impedance of superconductors,” Physical Review, vol. 118, no. 4, pp. 928–934, 1960. View at Publisher · View at Google Scholar · View at Scopus
  65. A. A. Abrikosov, L. P. Gorkov, and I. M. Khalatnikov, “A Superconductor in a high frequency field,” Soviet Physics: JETP, vol. 8, no. 1, pp. 182–189, 1959.
  66. A. A. Abrikosov, L. P. Gorkov, and I. M. Khalatnikov, “Analysis of experimental data relating to the surface impedance of superconductors,” Soviet Physics: JETP, vol. 10, no. 1, pp. 132–134, 1960.
  67. J.-J. Chang and D. J. Scalapino, “Gap enhancement in superconducting thin films due to microwave irradiation,” Journal of Low Temperature Physics, vol. 29, no. 5-6, pp. 477–485, 1977. View at Publisher · View at Google Scholar · View at Scopus
  68. J.-J. Chang and D. J. Scalapino, “Kinetic-equation approach to nonequilibrium superconductivity,” Physical Review B, vol. 15, no. 5, pp. 2651–2670, 1977. View at Publisher · View at Google Scholar · View at Scopus
  69. J.-J. Chang and D. J. Scalapino, “Nonequilibrium superconductivity,” Journal of Low Temperature Physics, vol. 31, no. 1-2, pp. 1–32, 1978. View at Publisher · View at Google Scholar · View at Scopus
  70. D. N. Langenberg and A. L. Larkin, Eds., Nonequilibrium Superconductivity, North-Holland, Amserdam, The Netherlands, 1986.
  71. N. Kopnin, Theory of Nonequilibrium Superconductivity, Oxford University Press, Oxford, UK, 2009.
  72. U. S. Pracht, E. Heintze, C. Clauss et al., “Electrodynamics of the superconducting state in ultra-thin films at THz frequencies,” IEEE Transactions on Terahertz Science and Technology, vol. 3, no. 3, pp. 269–280, 2013.
  73. L. Leplae, “Derivation of an expression for the conductivity of superconductors in terms of the normal-state conductivity,” Physical Review B, vol. 27, no. 3, pp. 1911–1912, 1983. View at Publisher · View at Google Scholar · View at Scopus
  74. J.-J. Chang and D. J. Scalapino, “Electromagnetic response of layered superconductors,” Physical Review B, vol. 40, no. 7, pp. 4299–4305, 1989. View at Publisher · View at Google Scholar · View at Scopus
  75. A. J. Berlinsky, C. Kallin, G. Rose, and A.-C. Shi, “Two-fluid interpretation of the conductivity of clean BCS superconductors,” Physical Review B, vol. 48, no. 6, pp. 4074–4079, 1993. View at Publisher · View at Google Scholar · View at Scopus
  76. S. B. Nam, “Theory of electromagnetic properties of superconducting and normal systems. I,” Physical Review, vol. 156, no. 2, pp. 470–486, 1967. View at Publisher · View at Google Scholar · View at Scopus
  77. S. B. Nam, “Theory of electromagnetic properties of strong-coupling and impure superconductors. II,” Physical Review, vol. 156, no. 2, pp. 487–493, 1967. View at Publisher · View at Google Scholar · View at Scopus
  78. O. Klein, S. Donovan, M. Dressel, and G. Grüner, “Microwave cavity perturbation technique: part I: principles,” International Journal of Infrared and Millimeter Waves, vol. 14, no. 12, pp. 2423–2457, 1993. View at Publisher · View at Google Scholar · View at Scopus
  79. S. Donovan, O. Klein, M. Dressel, K. Holczer, and G. Grüner, “Microwave cavity perturbation technique: part II: experimental scheme,” International Journal of Infrared and Millimeter Waves, vol. 14, no. 12, pp. 2459–2487, 1993. View at Publisher · View at Google Scholar · View at Scopus
  80. M. Dressel, O. Klein, S. Donovan, and G. Grüner, “Microwave cavity perturbation technique: part III: applications,” International Journal of Infrared and Millimeter Waves, vol. 14, no. 12, pp. 2489–2517, 1993. View at Publisher · View at Google Scholar · View at Scopus
  81. M. Scheffler and M. Dressel, “Broadband microwave spectroscopy in Corbino geometry for temperatures down to 1.7 K,” Review of Scientific Instruments, vol. 76, no. 7, Article ID 074702, 2005. View at Publisher · View at Google Scholar · View at Scopus
  82. M. Scheffler, S. Kilic, and M. Dressel, “Strip-shaped samples in a microwave Corbino spectrometer,” Review of Scientific Instruments, vol. 78, no. 8, Article ID 086106, 2007. View at Publisher · View at Google Scholar · View at Scopus
  83. K. Steinberg, M. Scheffler, and M. Dressel, “Broadband microwave spectroscopy in Corbino geometry at 3He temperatures,” Review of Scientific Instruments, vol. 83, no. 2, Article ID 024704, 2012. View at Publisher · View at Google Scholar · View at Scopus
  84. R. P. S. M. Lobo, J. D. LaVeigne, D. H. Reitze et al., “Photoinduced time-resolved electrodynamics of superconducting metals and alloys,” Physical Review B, vol. 72, no. 2, Article ID 024510, 2005. View at Publisher · View at Google Scholar · View at Scopus
  85. K. E. Kornelsen, M. Dressel, J. E. Eldridge, M. J. Brett, and K. L. Westra, “Far-infrared optical absorption and reflectivity of a superconducting NbN film,” Physical Review B, vol. 44, no. 21, pp. 11882–11887, 1991. View at Publisher · View at Google Scholar · View at Scopus
  86. D. Karecki, R. E. Peña, and S. Perkowitz, “Far-infrared transmission of superconducting homogeneous NbN films: scattering time effects,” Physical Review B, vol. 25, no. 3, pp. 1565–1571, 1982. View at Publisher · View at Google Scholar · View at Scopus
  87. M. Šindler, R. Tesař, J. Koláček, L. Skrbek, and Z. ŠimŠa, “Far-infrared transmission of a superconducting NbN film,” Physical Review B, vol. 81, no. 18, Article ID 184529, 2010.
  88. R. Tesař, M. Šindler, K. Ilin, J. Koláček, M. Siegel, and L. Skrbek, “Terahertz thermal spectroscopy of a NbN superconductor,” Physical Review B, vol. 84, no. 13, Article ID 132506, 2011.
  89. M. W. Coffey and J. R. Clem, “Theory of high-frequency linear response of isotropic type-II superconductors in the mixed state,” Physical Review B, vol. 46, no. 18, pp. 11757–11764, 1992. View at Publisher · View at Google Scholar · View at Scopus
  90. M. W. Coffey and J. R. Clem, “Theory of microwave transmission and reflection in type-II superconductors in the mixed state,” Physical Review B, vol. 48, no. 1, pp. 342–350, 1993. View at Publisher · View at Google Scholar · View at Scopus
  91. B. P. Gorshunov, G. V. Kozlov, A. A. Volkov et al., “Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges,” International Journal of Infrared and Millimeter Waves, vol. 14, no. 3, pp. 683–702, 1993. View at Publisher · View at Google Scholar · View at Scopus
  92. B. P. Gorshunov, I. V. Fedorov, G. V. Kozlov, A. A. Volkov, and A. D. Semenov, “Dynamic conductivity and the coherence peak in the submillimeter spectra of superconducting NbN films,” Solid State Communications, vol. 87, no. 1, pp. 17–21, 1993. View at Scopus
  93. B. Gorshunov, A. Volkov, I. Spektor et al., “Terahertz BWO-spectrosopy,” International Journal of Infrared and Millimeter Waves, vol. 26, no. 9, pp. 1217–1240, 2005. View at Publisher · View at Google Scholar · View at Scopus
  94. B. P. Gorshunov, A. A. Volkov, A. S. Prokhorov et al., “Terahetz BWO spectroscopy of conductors and superconductors,” Quantum Electronics, vol. 37, no. 10, pp. 916–923, 2007. View at Publisher · View at Google Scholar · View at Scopus
  95. M. Dressel, N. Drichko, B. Gorshunov, and A. Pimenov, “THz spectroscopy of superconductors,” IEEE Journal on Selected Topics in Quantum Electronics, vol. 14, no. 2, pp. 399–406, 2008. View at Publisher · View at Google Scholar · View at Scopus
  96. M. C. Nuss, K. W. Goossen, J. P. Gordon, P. M. Mankiewich, M. L. O'Malley, and M. Bhushan, “Terahertz time-domain measurement of the conductivity and superconducting band gap in niobium,” Journal of Applied Physics, vol. 70, no. 4, pp. 2238–2241, 1991. View at Publisher · View at Google Scholar · View at Scopus
  97. A. V. Pronin, M. Dressel, A. Pimenov, A. Loidl, I. V. Roshchin, and L. H. Greene, “Direct observation of the superconducting energy gap developing in the conductivity spectra of niobium,” Physical Review B, vol. 57, no. 22, pp. 14416–14421, 1998. View at Scopus
  98. U. Pracht, M. Scheffler, M. Dressel, K. S. Ilin, and M. Siegel, unpublished.
  99. A. Semenov, B. Günther, U. Böttger et al., “Optical and transport properties of ultrathin NbN films and nanostructures,” Physical Review B, vol. 80, no. 5, Article ID 054510, 2009. View at Publisher · View at Google Scholar · View at Scopus
  100. E. Burstein, D. N. Langenberg, and B. N. Taylor, “Superconductors as quantum detectors for microwave and sub-millimeter-wave radiation,” Physical Review Letters, vol. 6, no. 3, pp. 92–94, 1961. View at Publisher · View at Google Scholar · View at Scopus
  101. D. M. Ginsberg, “Upper limit for quasi-particle recombination time in a superconductor,” Physical Review Letters, vol. 8, no. 5, pp. 204–207, 1962. View at Publisher · View at Google Scholar · View at Scopus
  102. J. R. Schrieffer and D. M. Ginsberg, “Calculation of the quasiparticle recombination time in a superconductor,” Physical Review Letters, vol. 8, no. 5, pp. 207–208, 1962. View at Publisher · View at Google Scholar · View at Scopus
  103. A. Rothwarf and M. Cohen, “Rate of capture of electrons injected into superconducting lead,” Physical Review, vol. 130, no. 4, pp. 1401–1405, 1963. View at Publisher · View at Google Scholar · View at Scopus
  104. A. Rothwarf and B. N. Taylor, “Measurement of recombination lifetimes in superconductors,” Physical Review Letters, vol. 19, no. 1, pp. 27–30, 1967. View at Publisher · View at Google Scholar · View at Scopus
  105. L. R. Testardi, “Destruction of superconductivity by laser light,” Physical Review B, vol. 4, no. 7, pp. 2189–2196, 1971. View at Publisher · View at Google Scholar · View at Scopus
  106. J. F. Federici, B. I. Greene, P. N. Saeta, D. R. Dykaar, F. Sharifi, and R. C. Dynes, “Direct picosecond measurement of photoinduced Cooper-pair breaking in lead,” Physical Review B, vol. 46, no. 17, pp. 11153–11156, 1992. View at Publisher · View at Google Scholar · View at Scopus
  107. Experiments on NbN films by R. Kaindl, M. Carnahan, and D. Chemla at the Advanced Light Source of the Lawrance Berkeley National Laboratory. Figure reproduced from N. Gedik: THz spectroscopy of quasiparticle dynamics in complex materials, https://portal.slac.stanford.edu/sites/conf_public/THz_2012_09/presentations/gedik_Frontiers_of_THz_Science.pdf.
  108. M. Beck, M. Klammer, S. Lang et al., “Energy-gap dynamics of superconducting NbN thin films studied by time-resolved terahertz spectroscopy,” Physical Review Letters, vol. 107, no. 17, Article ID 177007, 2011. View at Publisher · View at Google Scholar · View at Scopus
  109. R. Matsunaga and R. Shimano, “Nonequilibrium BCS state dynamics induced by intense terahertz pulses in a superconducting NbN film,” Physical Review Letters, vol. 109, no. 18, Article ID 187002, 1 pages, 2012.
  110. J.-J. Chang and D. J. Scalapino, “New instability in superconductors under external dynamic pair breaking,” Physical Review B, vol. 10, no. 9, pp. 4047–4049, 1974. View at Publisher · View at Google Scholar · View at Scopus
  111. D. J. Scalapino and B. A. Huberman, “Onset of an inhomogeneous state in a nonequilibrium superconducting film,” Physical Review Letters, vol. 39, no. 21, pp. 1365–1368, 1977. View at Publisher · View at Google Scholar · View at Scopus
  112. P. W. Anderson, “Theory of dirty superconductors,” Journal of Physics and Chemistry of Solids, vol. 11, no. 1-2, pp. 26–30, 1959. View at Scopus
  113. M. Strongin, R. S. Thompson, O. F. Kammerer, and J. E. Crow, “Destruction of superconductivity in disordered near-monolayer films,” Physical Review B, vol. 1, no. 3, pp. 1078–1091, 1970. View at Publisher · View at Google Scholar · View at Scopus
  114. R. C. Dynes, A. E. White, J. M. Graybeal, and J. P. Garno, “Breakdown of eliashberg theory for two-dimensional superconductivity in the presence of disorder,” Physical Review Letters, vol. 57, no. 17, pp. 2195–2198, 1986. View at Publisher · View at Google Scholar · View at Scopus
  115. D. B. Haviland, Y. Liu, and A. M. Goldman, “Onset of superconductivity in the two-dimensional limit,” Physical Review Letters, vol. 62, no. 18, pp. 2180–2183, 1989. View at Publisher · View at Google Scholar · View at Scopus
  116. J. M. Valles Jr., R. C. Dynes, and J. P. Garno, “Electron tunneling determination of the order-parameter amplitude at the superconductor-insulator transition in 2D,” Physical Review Letters, vol. 69, no. 24, pp. 3567–3570, 1992. View at Publisher · View at Google Scholar · View at Scopus
  117. A. Yazdani and A. Kapitulnik, “Superconducting-insulating transition in two-dimensional a-MoGe thin films,” Physical Review Letters, vol. 74, no. 15, pp. 3037–3040, 1995. View at Publisher · View at Google Scholar · View at Scopus
  118. A. M. Goldman and N. Marković, “Superconductor-insulator transitions in the two-dimensional limit,” Physics Today, vol. 51, no. 11, pp. 39–44, 1998. View at Scopus
  119. M. A. Paalanen, A. F. Hebard, and R. R. Ruel, “Low-temperature insulating phases of uniformly disordered two-dimensional superconductors,” Physical Review Letters, vol. 69, no. 10, pp. 1604–1607, 1992. View at Publisher · View at Google Scholar · View at Scopus
  120. V. F. Gantmakher, M. V. Golubkov, V. T. Dolgopolov, G. E. Tsydynzhapov, and A. A. Shashkin, “Destruction of localized electron pairs above the magnetic-field-driven superconductor-insulator transition in amorphous In-O films,” JETP Letters, vol. 68, no. 4, pp. 363–369, 1998. View at Publisher · View at Google Scholar · View at Scopus
  121. V. Y. Butko and P. W. Adams, “Quantum metallicity in a two-dimensional insulator,” Nature, vol. 409, no. 6817, pp. 161–164, 2001. View at Publisher · View at Google Scholar · View at Scopus
  122. V. F. Gantmakher, S. N. Ermolov, G. E. Tsydynzhapov, A. A. Zhukov, and T. I. Baturina, “Suppression of 2D superconductivity by the magnetic field: quantum corrections vs. the superconductor-insulator transition,” JETP Letters, vol. 77, no. 8, pp. 424–428, 2003. View at Publisher · View at Google Scholar · View at Scopus
  123. N. Hadacek, M. Sanquer, and J.-C. Villégier, “Double reentrant superconductor-insulator transition in thin TiN films,” Physical Review B, vol. 69, no. 2, Article ID 024505, 2004. View at Scopus
  124. G. Sambandamurthy, L. W. Engel, A. Johansson, and D. Shahar, “Superconductivity-Related Insulating Behavior,” Physical Review Letters, vol. 92, no. 10, Article ID 107005, 2004. View at Publisher · View at Google Scholar · View at Scopus
  125. G. Sambandamurthy, L. W. Engel, A. Johansson, E. Peled, and D. Shahar, “Experimental evidence for a collective insulating state in two-dimensional superconductors,” Physical Review Letters, vol. 94, no. 1, Article ID 017003, 2005. View at Publisher · View at Google Scholar · View at Scopus
  126. M. Steiner and A. Kapitulnik, “Superconductivity in the insulating phase above the field-tuned superconductor-insulator transition in disordered indium oxide films,” Physica C, vol. 422, no. 1-2, pp. 16–26, 2005. View at Publisher · View at Google Scholar · View at Scopus
  127. T. I. Baturina, J. Bentner, C. Strunk, M. R. Baklanov, and A. Satta, “From quantum corrections to magnetic-field-tuned superconductor-insulator quantum phase transition in TiN films,” Physica B, vol. 359-361, pp. 500–502, 2005. View at Publisher · View at Google Scholar · View at Scopus
  128. T. I. Baturina, C. Strunk, M. R. Baklanov, and A. Satta, “Quantum metallicity on the high-field side of the superconductor-insulator transition,” Physical Review Letters, vol. 98, no. 12, Article ID 127003, 2007. View at Publisher · View at Google Scholar · View at Scopus
  129. B. Sacépé, C. Chapelier, T. I. Baturina, V. M. Vinokur, M. R. Baklanov, and M. Sanquer, “Disorder-induced inhomogeneities of the superconducting state close to the superconductor-insulator transition,” Physical Review Letters, vol. 101, no. 15, Article ID 157006, 2008. View at Publisher · View at Google Scholar · View at Scopus
  130. B. Sacépé, T. Dubouchet, C. Chapelier et al., “Localization of preformed Cooper pairs in disordered superconductors,” Nature Physics, vol. 7, no. 3, pp. 239–244, 2011. View at Publisher · View at Google Scholar · View at Scopus
  131. S. M. Hollen, H. Q. Nguyen, E. Rudisaile et al., “Cooper-pair insulator phase in superconducting amorphous Bi films induced by nanometer-scale thickness variations,” Physical Review B, vol. 84, no. 6, Article ID 064528, 2011. View at Publisher · View at Google Scholar · View at Scopus
  132. V. M. Vinokur, T. I. Baturina, M. V. Fistul, A. Y. Mironov, M. R. Baklanov, and C. Strunk, “Superinsulator and quantum synchronization,” Nature, vol. 452, no. 7187, pp. 613–615, 2008. View at Publisher · View at Google Scholar · View at Scopus
  133. S. Poran, E. Shimshoni, and A. Frydman, “Disorder-induced superconducting ratchet effect in nanowires,” Physical Review B, vol. 84, no. 1, Article ID 014529, 2011. View at Publisher · View at Google Scholar · View at Scopus
  134. Y. Dubi, Y. Meir, and Y. Avishai, “Theory of the magnetoresistance of disordered superconducting films,” Physical Review B, vol. 73, no. 5, Article ID 054509, 2006. View at Publisher · View at Google Scholar · View at Scopus
  135. Y. Dubi, Y. Meir, and Y. Avishai, “Nature of the superconductor-insulator transition in disordered superconductors,” Nature, vol. 449, no. 7164, pp. 876–880, 2007. View at Publisher · View at Google Scholar · View at Scopus
  136. D. Kowal and Z. Ovadyahu, “Disorder induced granularity in an amorphous superconductor,” Solid State Communications, vol. 90, no. 12, pp. 783–786, 1994. View at Scopus
  137. D. Kowal and Z. Ovadyahu, “Scale dependent superconductor-insulator transition,” Physica C, vol. 468, no. 4, pp. 322–325, 2008. View at Publisher · View at Google Scholar · View at Scopus
  138. N. Trivedi, R. T. Scalettar, and M. Randeria, “Superconductor-insulator transition in a disordered electronic system,” Physical Review B, vol. 54, no. 6, pp. R3756–R3759, 1996. View at Scopus
  139. Y. Imry, M. Strongin, and C. C. Homes, “An inhomogeneous Josephson phase in thin-film and high-Tc superconductors,” Physica C, vol. 468, no. 4, pp. 288–293, 2008. View at Publisher · View at Google Scholar · View at Scopus
  140. M. V. Feigei'man, L. B. Ioffe, V. E. Kravtsov, and E. A. Yuzbashyan, “Eigenfunction fractality and pseudogap state near the superconductor-insulator transition,” Physical Review Letters, vol. 98, no. 2, Article ID 027001, 2007. View at Publisher · View at Google Scholar · View at Scopus
  141. M. V. Feigel'man, L. B. Ioffe, V. E. Kravtsov, and E. Cuevas, “Fractal superconductivity near localization threshold,” Annals of Physics, vol. 325, no. 7, pp. 1390–1478, 2010. View at Publisher · View at Google Scholar · View at Scopus
  142. K. Bouadim, Y. L. Loh, M. Randeria, and N. Trivedi, “Single- and two-particle energy gaps across the disorder-driven superconductor-insulator transition,” Nature Physics, vol. 7, no. 11, pp. 884–889, 2011. View at Publisher · View at Google Scholar · View at Scopus