ABSTRACT
This chapter describes various theoretical approaches, such as the basic mode-matching technique, the transfer matrix, and the scattering matrix methods, to study electron transport through two-dimensional quantum waveguides. It explains the theory to two-electron waveguide devices. Though many fundamental transport properties of quantum wave-guides have been found in the study of idealized structures, in real waveguides the boundaries are usually defined via electrostatic confinement from metal gates and thus the geometries can be complicated. In this case, realistic lateral guiding potentials shall be taken into account, especially when the electrons are of high energies and would transport beyond the single-mode regime. The solid line is for forward transmission, and the dotted line is for side transmission. The bound energy of the quantum bound state becomes larger with enlargement of the internal junction area.
