Josephson Plasma Resonance in High Temperature Superconductors: A Test of Interlayer Tunneling Theory

Josephson plasma frequency is computed within the interlayer tunneling theory and compared against the experimental results in Tl2Ba2CuOy and La2−xSrxCuO4. It is shown that the theoretical estimates are fully consistent with the recent experiments. Typeset using REVTEX 1 In the Josephson effect [1], the quantum mechanical phases of two superconductors are coupled by the tunneling of the Cooper pairs between them. The coupling energy is a measure of the phase coherence, and the lowest energy is achieved when the phase difference is zero. However, if a phase difference is imposed and the system is released, the phase, to a good approximation, oscillates harmonically. Because the time derivative of the phase is proportional to the voltage difference between the superconductors by the Josephson relation, the voltage also oscillates harmonically, and the frequency of the oscillation is called the Josephson plasma frequency, ωJ [2]. This is a collective mode that has the character of a longitudinal plasma wave. The frequency of this wave is much smaller than the bulk plasma frequency, which is due to the fact that the junction region has a low density of charge carriers characteristic of the weak superconductivity of a Josephson junction. Because ωJ is smaller than the bulk plasma frequency, these oscillations are entirely confined within the junction region. Such oscillations are well documented and were first measured by Dahm et al. [3]. It has been shown [4] that the interlayer tunneling theory can predict the frequency of the Josephson plasma frequency in high temperature superconductors, where the plasma oscillations are confined between the two neighboring layers. In addition, the magnitude of the plasma frequency contains important information about the coupling between the layers, which is an important ingredient to the interlayer tunneling theory of these superconductors [5]. This theory is applicable to both s-wave and d-wave symmetries of the order parameter, as was stated in Ref. [5]; for explicit calculations involving d-symmetry, see Refs. [6,7]. In very recent optical experiments [8], it has been found that the Josephson plasma frequency in Tl2Ba2CuOy is smaller than 50 cm . This is much smaller than the earlier estimate 1500 cm based on the interlayer tunneling theory [4], which did not fully take into account the highly anisotropic nature of the tunneling matrix element and the gap. When this anisotropy is taken into account, I find that ωJ ≤ 282 cm. The same calculation applied to La2−xSrxCuO4 leads to ωJ ≤ 80 cm as compared to the measured value 50 cm [8,9]. Thus, given the uncertainty in the value of the dielectric constant, ǫ, I perceive no difficulty with the interlayer tunneling theory [10]. Note that because the Josephson 2 plasma oscillations are confined between the layers, the relevant dielectric constant is that of the material between the CuO planes. In addition, the present theory can be tested on other unconventional layered superconductors, such as the layered organic superconductors [11], as well. It is also worth noting that the conventional BCS dirty limit theory predicts ωJ to be 230 cm −1 for Tl2Ba2CuOy [8], while the same dirty limit formula yields 200 cm −1 for La2−xSrxCuO4. The Josephson plasma frequency in the interlayer tunneling theory [5] is given by (k is the in-plane wavevector.) 1 2 mω J = ∑