Aspects of tunneling in high-T_c superconductors: WKB revisited

We discuss the merits of WKB for calculating I-V characteristics of high-resistance contacts to high-T_c superconductors. The I-V curves of these contacts (kΩ regime) formed with at least one high-T_c superconductor show a parabolic shape above and below T_c which is remarkably similar for many different type of contacts. This similarity can be attributed to normal electrons tunneling through a trapezoidal potential barrier. Usually the probability of electrons tunneling through such a barrier is calculated using the WKB method. We will show that the barrier width, height and shape as well as densities of states involved do not justify the use of a WKB approach. We therefore advocate the transmission-reflection formalism (TRF), which has the additional advantage of being applicable to a wide range of contacts.