Inter-Layer Tunneling (ILT) in "high-Tc" cuprate systems

One of the most exciting unconventional mechanisms which has been suggested for the superconductivity in the "high-Tc" cuprate systems has been the Inter-Layer Tunneling (ILT) Model of Sudbo, Chakravarty and P.W. Anderson(Ref. 1). In this model superconductivity is created by interlayer pair tunneling (whereas in conventional superconductivity it must first be created by pairing within each plane), giving a linear relation between Tc and the Josephson plasma resonance, wJ.

Figure 1: Schematic of the experimental techniques: a) Grazing incidence reflectivity. The p-polarized  light incident at a grazing angle sets up a periodic electric field pattern, which is polarized perpendicular to the sample surface, and decays exponentially inside the solid. b) Scanning SQUID microscopy. The octagonal  picup loop detects the magnetic flux perpendicular to the a-c face

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Figure 3. a) Images of the magnetic field perpendicular to an a-c face of a Tl2Ba2CuO6 single crystal in two different locations, showing two different interlayer Josephson vortices. The dashed lines indicate the longitudinal cross-sections. Inset: sketch of the 4 mm octagonal pickup loop. b) The flux through the SQUID pickup loop along the longitudinal cross-sections. The solid curves are fits which determine the c-axis penetration depths of these two vortices to be (I) lc = 17±4 mm and (II) lc =19±1 mm. The straight lines indicate the extent of lc for each vortex.

 

Figure 2. a} P-polarized reflectivity at 80o angle of incidence of Tl2Ba2CuO6 (Tc=85 K) at 4 K (uppercurve) and 100 K (lower curve). b) The same on an expanded frequency scale. From top to bottom: 4K, 10 K, 20 K, 30 K, 40 K, 50 K, 60 K, 75 K, and 90 K. The curves have been given incremental 3% vertical offsets for clarity. The solid curves are 3-parameter fits to the data as described in the text. c) Temperature dependence the c-axis (squares) and a-axis (diamonds) penetration depth displayed as l(0)2/l(T)2.  d)  Temperature dependence of sc(wJ).

 
 Source: A.A. Tsvetkov, D. van der Marel, K.A. Moler, J.R. Kirtley, et al., Global and local measures of the intrinsic Josephson coupling in Tl2Ba2CuO6 as a test of the interlayer tunnelling model , Nature 395 (1998) 360-362.

In the ILT model the superconducting condensation energy (Econd) is precisely the gain in kinetic energy (EJ) due to the tunneling of pairs: Econd = EJ. Both Econd and EJ are experimentally accessible quantities, thus allowing the experimental verification of the ILT hypothesis. EJ can be calculated directly from our value for wJ. To avoid the complexity of having \em two possible Josephson junctions per unit cell of different strength, single layer cuprates had to be considered. Among those Tl2201 had one of the highest Tc's (~ 80 K), and relatively large (though thin along the c-direction) crystals and thin films were available. In the spring of 1996 the first experimental results were presented (Refs. 2, and 4 ),showing that EJ was at least two orders of magnitude too small to account for the condensation energy. Although these results seemed to rule out ILT as the main mechanism of superconductivity (in Ref.4 Leggett discussed the negative implications of those data for the ILT model), they relied on the non-observance of a plasma-resonance where it should have been in the superconducting state (800 cm-1). The issue remained dormant until first lc of 17 mm and next the Josephson plasma resonance (JPR) at 28 cm-1 had been observed experimentally:

In Figure 2 we show the grazing angle of incidence reflectivity spectra of  Tl2Ba2CuO6 with Tc=80 K. All prominent absorption lines for frequencies larger than 50 cm-1 correspond to infrared active lattice vibrations, without strong temperature dependence. In the 4K spectrum we observe a clear absorption at 27.8 cm-1. This resonance exhibits a strong shift upon raising the temperature. Above 70 K it has shifted outside our spectral window. This absorption is due to to a Josephson plasmon, a collective oscillation of the superconducting charge carriers perpendicular to the coupled superconducting planes, with a frequency wJ = ecs-1/2 wpc. This value agrees with scanning SQUID experiments by K.A. Moler (Princeton) and J. Kirtley (IBM) of the shape of vortices penetrating between the planes (see Fig. 3). (Ref. 5,6,7) , allowing a precise determination of EJ~0.25 meV in Tl2201 with Tc=80 K. This is a factor 400 lower than Econd ~ 100 meV per copper, based on specific heat experimental data (Ref. 8).
A c-axis kinetic energy change even smaller than EJ is obtained by estimating the amount of high energy spectral weight transferred to the condensate at zero energy (Ref. 9). In the examples studied so far this gives change of c-axis kinetic energy wich is  at least ten times smaller than EJ and three orders of magnitude smaller than the condensation energy.
 

  1. P. W. Anderson, Interlayer Tunneling Mechanism for High-Tc Superconductivity: Comparison with c Axis Infrared Experiments, Science 268, 1154-1155 (1995).

  2. D. van der Marel, J. Schuetzmann, H.S. Somal, and J.W. van der Eb, Electrodynamical properties of High- Tc superconductors studied with polarized angle resolved infrared spectroscopy, Proceedings of the 10th Anniversary HTS Workshop on Physics, Materials & Applications p 357 (World Scientific, Rivers Edge, NJ, 1996).
  3. A. J. Leggett, Interlayer Tunneling Models: Implications of a Recent Experiment, Science 274, 587-590 (1996).
  4. J. Schuetzmann, H.S. Somal, A.A. Tsvetkov, D. van der Marel,et al, Experimental Test of the Inter-Layer Pairing Models for High-Tc Superconductivity Using Grazing Incidence Infrared Reflectometry, Phys. Rev. B 55 (1997) 11118.
  5. K.A. Moler, J.R. Kirtley, D.G. Hinks, T.W. Li, and M. Xu, Images of interlayer Josephson vortices in Tl2Ba2CuO6+d, Science 279, 1193-1195 (1998).
  6. P.W. Anderson, c-Axis Electrodynamics as Evidence for the Interlayer Theory of High-Temperature Superconductivity, Science 279, 1196-1197 (1998).
  7. A.A. Tsvetkov, D. van der Marel, K.A. Moler, J.R. Kirtley, et al., Global and local measures of the intrinsic Josephson coupling in Tl2Ba2CuO6 as a test of the interlayer tunnelling model, Nature 395 (1998) 360-362.
  8. J. Loram, K.A. Mirza, J.M.Wade, J.R. Cooper, and W.Y. Liang, The Electronic Specific Heat of Cuprate Superconductors, Physica C 235, 134-137 (1994).
  9. D. N. Basov, S. I. Woods, A. S. Katz, E. J. Singley et al, Sum Rules and Interlayer Conductivity of High-Tc Cuprates, Science 283, 49-52 (1999).