THE ENERGY-DEPENDENCE OF THE CONDUCTANCE AND SCATTERING WAVE-FUNCTIONS OF A 2D QUANTUM-DOT

A new wave-function matching formalism is used to calculate wave funct ions psi and the conductance g(12) for a quantum dot as functions of t he Fermi wavelength lambda. The dot is formed in a 2D quantum wire wit h hard walls by pushing in through one wall two identical, hard-wall, rectangular fingers with height h, width d and separation s. Calculati ons of conductance g(12) are made for a structure which exhibits two r esonant tunnelling peaks below the nominal transmission threshold over the tops of the fingers. These peaks are associated with the open-end ed organ pipe modes in the region between the fingers. The two longest organ pipe resonant wavelengths are within 2% and 10% of the calculat ed peak positions, but wave-function spillage over the tops of the fin gers and the space between them has a marked effect on both the resona nt wave functions and the resonant wavelengths. Contour plots of \psi\ (2) for scattering waves are presented and used to elucidate the behav iour of g(12).