Josephson effect in the strontium titanate/lanthanum aluminate junction

We report theoretical studies on the newly discovered novel Josephson effect and scanning tunneling spectroscopy (STS) at the interface of strontium titanate/lanthanum aluminate (STO/LAO). With a phenomenological boson-fermion model, the density of states is calculated and the results are consistent with the STS experiments. A typical calculation of Josephson effect is performed, and it is in qualitative agreement with the experiments. The calculations indicate that the gap states come from the pairing of quasi-particles with a finite total momentum and the Josephson current comes from the tunneling of quasi-particle pairs with zero momentum. The quasi-particles are Bogoliubov quasi-particles. Moreover, the fits using Kulik's formula imply that the Josephson junction at the STO/LAO interface has a point contact with the clean superconductor limit.