Circuit Theory of Mesoscopic Superconducting Components

Abstract

Nazarov's quantum circuit theory is essentially a discretised version of the Usadel equation which describes mesoscopic superconducting systems in the diffusive limit. The focus of this thesis project was to investigate the application of the quantum circuit theory to an Andreev interferometer. The report begins with a review of classical transport theory and then of the full Green's function theory of superconductivity leading to the Usadel equation. Quantum circuit theory is then presented with classical circuit theory as an analogy. Quantum circuit theory is then applied to the SNS and SS'S type Josephson junctions that result when discretising the Andreev interferometer. Two types of SNS junctions were considered: firstly, an STNTS type with very strong tunnel junctions separating the intermediate metal from the reservoirs, and secondly, the short, diffusive SNS junction considered by Kulik-Omel'yanchuk. Finally, the added difficulties of a superconducting intermediate metal in the SS'S type junction are discussed and resolved.