Electrical transport in mesoscopic superconducting devices
Abstract
Among the theoretical methods used to describe mesoscopic devices, one of the most successful is the transmission viewpoint pioneered by Landauer, Buttiker and others. This transmission viewpoint, where particles in thermal equilibrium with a contact are injected into an electrical device, provides the framework for predicting electrical current when inelastic scattering is not present inside the device. In order to generalize this transmission formalism to systems containing a superconductor, one substitutes for the Schrodinger equation a matrix equation, which couples electrons and time reversed electrons (holes) via the superconducting interaction. This matrix equation is known as the Bogoliubov-deGennes (BdG) equation. In this thesis, the BdG equation and transmission formalism are used as a theoretical framework to study one dimensional (1-D) normal-insulator-normal-superconducting (NINS) junctions, self-consistent 1-D SNS and SIS junctions, self-consistent 1-D NS junctions quasi-1D NS junctions with a supercurrent flowing in the superconducting metal, and lastly two-dimensional S$\sb1$ X S$\sb2$ Josephson junctions where S$\sb1$, S$\sb2$ are s-wave or d-wave superconductors and X is either an insulator or normal metal. As a result of this research, a number of new electrical transport phenomenon in mesoscopic superconducting systems are predicted. Among these predictions are: (1) Conductance resonances in NINS junctions. (2) The supercurrent in a 1-D ballistic SNS junction is proportional to the phase gradient in the junction and is carried entirely by continuum states. (3) Excess current carried in quasi-1D NS junctions are larger than the excess current carried by a point contact NS junction. (4) Critical currents proportional to $\sqrt{T}$, where T is the transmission coefficient of the junction, in certain d-wave Josephson junctions.
Degree
Ph.D.
Advisors
Bagwell, Purdue University.
Subject Area
Condensation|Electrical engineering|Materials science
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