Do electrons change their c-axis kinetic energy upon entering the superconducting state?

European Physical Journal B

Volumn 5, Issue 3, 1998, Pages 337-343

  Chakravarty, S ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

74.20. z Theories and models of superconducting state; 74.25.Gz Optical properties; 74.72. hHigh Tc compounds

Indexed keywords

BINDING ENERGY; ELECTRODYNAMICS; ELECTRON TUNNELING; HIGH TEMPERATURE SUPERCONDUCTORS; KINETIC ENERGY; MATHEMATICAL MODELS; OPTICAL PROPERTIES; SUPERCONDUCTIVITY;

INTERLAYER TUNNELING;

OXIDE SUPERCONDUCTORS;

EID: 0032295249     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510050451     Document Type: Article

References (38)

1. c cuprates (Princeton University Press, Princeton, 1997).
2. This is only true for higher energy processes. For lower energy processes, there is incoherent hopping of electrons between the planes that gives rise to zero frequency conductivity at finite temperatures.
3. M. Tinkham, Introduction to Superconductivity, second edition (McGraw-Hill, New York, 1996).
4. J.M. Kosterliz, D.J. Thouless, Progress in low temperature, physics, VIIB, edited by D. Brewer (North-Holland, Amsterdam, 1978).
5. T. Tsuzuki, T. Matsubara, Phys. Lett. 37A, 13 (1971); W.E. Lawrence, S. Doniach, Proc. 12th Int. Conf. Low Temp. Phys., 361, edited by E. Kanda (Keigaku, Tokyo, 1971).
6. T. Tsuzuki, T. Matsubara, Phys. Lett. 37A, 13 (1971); W.E. Lawrence, S. Doniach, Proc. 12th Int. Conf. Low Temp. Phys., 361, edited by E. Kanda (Keigaku, Tokyo, 1971).
7. The phase across a large area, large capacitance, Josephson junction is a macroscopic variable obeying classical dynamical equation with the Hamiltonian determined from the coupling energy. For small capacitance junctions, quantum fluctuations of the phase become important (See Ref. [3] and references therein.)
8. S. Chakravarty, P.W. Anderson, Phys. Rev. Lett. 72, 3859 (1994).
9. A.J. Leggett, Science 274, 587 (1996).
10. V.J. Emery, S. Kivelson, Nature 374, 434 (1995).
11. The actual hopping matrix elements between the planes are known from electronic structure calculations (O.K. Andersen et al., J. Phys. Chem. Solids 56, 1573 (1995).), including those pertinent to single layer materials (O.K. Andersen, private communications.). The realistic model is a little more complex, as it involves hopping to nearest and next-nearest sites of the adjacent layers as well. Moreover, for multilayer materials, one must modify the model by distinguishing hopping between close pairs of planes and those between the unit cells. These modifications are not difficult to incorporate as long as the interlayer tunneling is described by a single particle hopping Hamiltonian.
12. The actual hopping matrix elements between the planes are known from electronic structure calculations (O.K. Andersen et al., J. Phys. Chem. Solids 56, 1573 (1995).), including those pertinent to single layer materials (O.K. Andersen, private communications.). The realistic model is a little more complex, as it involves hopping to nearest and next-nearest sites of the adjacent layers as well. Moreover, for multilayer materials, one must modify the model by distinguishing hopping between close pairs of planes and those between the unit cells. These modifications are not difficult to incorporate as long as the interlayer tunneling is described by a single particle hopping Hamiltonian.
13. B.S. Shastry, B. Sutherland, Phys. Rev. Lett. 65, 243 (1990), and references therein; see also D.J. Scalapino, S.R. White, S.C. Zhang, Phys. Rev. B 47, 7995 (1993); A similar sum rule was invoked by J.E. Hirsch, Physica C 199, 305 (1992), to argue for a change in the kinetic energy in the superconducting state. Beyond this, there are no similarities with our work, either in philosophy or in content.
14. B.S. Shastry, B. Sutherland, Phys. Rev. Lett. 65, 243 (1990), and references therein; see also D.J. Scalapino, S.R. White, S.C. Zhang, Phys. Rev. B 47, 7995 (1993); A similar sum rule was invoked by J.E. Hirsch, Physica C 199, 305 (1992), to argue for a change in the kinetic energy in the superconducting state. Beyond this, there are no similarities with our work, either in philosophy or in content.
15. B.S. Shastry, B. Sutherland, Phys. Rev. Lett. 65, 243 (1990), and references therein; see also D.J. Scalapino, S.R. White, S.C. Zhang, Phys. Rev. B 47, 7995 (1993); A similar sum rule was invoked by J.E. Hirsch, Physica C 199, 305 (1992), to argue for a change in the kinetic energy in the superconducting state. Beyond this, there are no similarities with our work, either in philosophy or in content.
16. See, for example, P.C. Martin, in Many-Body Physics, edited by C. De Witt, R. Balian (Gordon and Breach, New York, 1967).
17. W. Kohn, Phys. Rev. 133, A171 (1964).
18. c(ω) calculated from this effective Hamiltonian cannot be the physical conductivity for scales of the order or larger than the high energy cutoff implied in the effective Hamiltonian. This makes it problematic to accurately estimate the missing area as only the order of magnitude of the cutoff is known.
19. c are enormous. There are other notable exceptions as well, such as optimally doped T12201 and YBCO for which the c-axis resistivity is approximately linear with temperature. Nonetheless, even in these exceptional cases, the temperature dependence can be assumed to persist if superconductivity could be suppressed.
20. c are enormous. There are other notable exceptions as well, such as optimally doped T12201 and YBCO for which the c-axis resistivity is approximately linear with temperature. Nonetheless, even in these exceptional cases, the temperature dependence can be assumed to persist if superconductivity could be suppressed.
21. Y. Ando et al., Phys. Rev. Lett. 75, 4662 (1995); G.S. Boebinger et al., Phys. Rev. Lett. 77, 5417 (1996).
22. Y. Ando et al., Phys. Rev. Lett. 75, 4662 (1995); G.S. Boebinger et al., Phys. Rev. Lett. 77, 5417 (1996).
23. M.J. Graf et al., Phys. Rev. B 52, 10588 (1995); P.J. Hirschfeld, S.M. Quinlan, D.J. Scalapino, Phys. Rev. B 55, 12742 (1997).
24. M.J. Graf et al., Phys. Rev. B 52, 10588 (1995); P.J. Hirschfeld, S.M. Quinlan, D.J. Scalapino, Phys. Rev. B 55, 12742 (1997).
25. 1/2.
26. P.W. Anderson, Science 279, 1196 (1998). For example, for doping level of 17-20% in LSCO, the calculated c-axis penetration depth is 3 ± 1μ. Similarly, for Hg1201, it is 1 ± 0.5μ.
27. J.W. Loram et al., Physica C 235-240, 134 (1994).
28. S. Uchida, K. Tamasaku, S. Tajima, Phys. Rev. B 53, 14558 (1996); see also D.N. Basov et al., Phys. Rev. B 52, R13141 (1995).
29. S. Uchida, K. Tamasaku, S. Tajima, Phys. Rev. B 53, 14558 (1996); see also D.N. Basov et al., Phys. Rev. B 52, R13141 (1995).
30. -1 in LSCO. Finally, because the gap is likely to be a d-wave gap, the specification of the finite upper limit of the integral in terms of the gap is ambiguous. It is important to note that such redistribution of spectral weight over enormously large energy range is impossible in any Fermi liquid based theories, with or without impurities, because the c-axis single particle hopping bandwidth is small, especially in the single layer materials. The spectral weight redistribution must be due to strong correlation effects. All conventional theories that purportedly explains the experimental measurements of the c-axis penetration depth suffer from this criticism and cannot be trusted.
31. T. Shibauchi et al., Phys. Rev. Lett. 72, 2263 (1994).
32. C. Panagopoulos et al., Phys. Rev. Lett. 72, 2320 (1994).
33. K.A. Moler et al., Science 279, 1193 (1998).
34. For a brief review of the materials aspects, see J.D. Jorgensen et al., Physica C 282-287, 97 (1997) and references therein.
35. This is also true for classical statistical mechanical problems discussed in Section 2.
36. S. Chakravarty, A. Sudbø, P.W. Anderson, S. Strong, Science 261, 337 (1993).
37. The momentum diagonal pair tunneling Hamiltonian is infinitely long ranged in real space and must be understood as a mean field Hamiltonian. The long ranged nature renders the mean field theory exact. The BCS reduced Hamiltonian has the same property in its real space form. S. Chakravarty, to be published.
38. See Ref. [1], and also L. Yin, S. Chakravarty, Int. J. Mod. Phys. B 10, 805 (1996).