Multiple Andreev Reflection - a Microscopic Theory of ac Josephson Effect in Mesoscopic Junctions

Doktorsavhandling, 1998

The mechanism of multiple Andreev reflection (MAR) is a microscopic theory for electron transport in voltage biased superconducting junctions, i.e. the ac Josephson effect. In this thesis we propose a new approach for calculating the dc current from MAR. By rewriting the dc current in terms of the probability current we find that it is the flow of probability current in energy space that determines the dc charge current. The flow in energy space can be mapped onto wave propagation in a one dimensional potential barrier structure. Using this formulation we may separate different n-particle contributions to the current. There is also a detailed balance for probability currents flowing upwards and downwards in energy, which cancels the contribution from probability currents flowing between equally filled states. In this way the Pauli exclusion principle is fulfilled within the Landauer approach also for superconducting junctions. Particularly, at zero temperature only processes creating real excitations contribute to the current. The steps in the subharmonic gap structure of superconductor-insulator- superconductor (SIS) junctions are explained as the onsets of different n-particle currents, and the peaks at these onsets are due to resonant transport in energy space of (n+1) and (n+2) particle currents. In junctions with a double barrier structure in the normal region, resonant transport gives the main contribution to the current. We consider the case of a single resonance close to the chemical potential. A resonance in the normal region contributes with two possible resonances in energy space, one for electrons and one for holes. Depending on the position of the resonance, the pair current may have the same order of magnitude as the single particle current even at large voltages. The subharmonic gap structure is crucially dependent on the position of the resonance. The appearance of so called squeezed resonances, originating from symmetric potential structures in energy space, enhances the current drastically. There is evidence that the gap in some of the high Tc superconductors (HTS) has d-wave symmetry. This influences the transport properties of SIS junctions made of HTS. Due to the sign shift in the d-wave gap a surface state appears at the chemical potential of the superconductor. In voltage biased junctions this state gives rise to resonances in the transport through energy space. The sign shift also results in an effective doubling of the Josephson frequency for a specific orientation of the gaps. The anisotropy of the magnitude of the gap also forces the current to have a component perpendicular to the applied electric field.