Transport Properties of Superconducting d-wave junctions
At surfaces and interfaces of d-wave superconductors, quasiparticle bound states with zero energy, midgap states (MGS), are necessarily formed as a consequence of the sign change of the d-wave order parameter upon 90° rotation. The MGS can never exist at s-wave superconductor surfaces and are therefore true fingerprints of unconventional superconductivity. In this thesis we have studied the basic properties of d-wave superconducting junctions, the central issue being the role of midgap states.
Within a scattering theory of transport, we calculate both the dc Josephson current in phase-biased junctions and the current-voltage characteristics (IVC) and ac current components in voltage-biased junctions.
We have studied the role of MGS in spontaneous time-reversal symmetry breaking at Josphson tunnel junctions of purely d-wave superconductors. For junction transparencies , where is the superconducting coherence length and is the penetration depth, the driving mechanism of the instability is the splitting of MGS by spontaneous establishment of a phase difference across the junction. For tunnel junctions with , the mechanism is instead self-induced Dopplershifts of MGS.
For the particular orientation when a lobe points towards the junction at one side and a node at the other, we find that the odd ac components disapper, which results in a doubling of the Josephson frequency for this orientation.
We present a detailed study of the IVC of voltage-biased junctions. For low transparency junctions we derive analytical results for the MGS resonances. We also elaborate on how intrinsic broadening of MGS may determine the nature of resonant tranport through MGS: either via single particle tunneling for large broadening or via pair tunneling for negligible broadening. We argue that it may be possible to distinguish between these types of transport by a measurement of either the low-voltage IVC of Josephson junctions or the zero-voltage zero-frequency shot noise in normal metal-superconductor junctions.