Current-phase relation in a short clean josephson junction model: application to MgB2

Motivated by recent data on high-quality MgB 2 thin films implying that the smaller energy gap has l = 6 (i-wave) symmetry, we consider a simple model for an all-MgB 2 symmetric Josephson Junction (JJ). The model assumes an arbitrary-strength delta-function barrier and one-dimensional current conduction. It is shown that in this context a nodal energy gap with i-wave symmetry acts as an isotropic energy gap (s-wave) with an amplitude modified by the energy-gap misalignment-angle with respect to the crystal principal axes. The corresponding exact Green’s function in momentum space is derived employing a novel approach. The ensuing current-phase relations in the strong and weak barrier-strengths limits are calculated and found to confirm known results, e.g., the Ambegaokar-Baratoff current-phase relation. Inspired by an HTS experiment that established the d-wave energy-gap symmetry, we propose a JJ-related experiment with a MgB 2 bicrystal to confirm our premise that the smaller energy has i-wave symmetry.