WAVE-FUNCTION MATCHING IN SCATTERING MATRIX CALCULATIONS FOR HARD-WALL NANOSTRUCTURES

A nanostructure with hard walls is divided into two regions: the terminals and the 'cavity' that connects them. In the absence of a magnetic field the modes in the terminals may be written down immediately. The modes in the cavity are calculated by extending each terminal mode continuously into the cavity and applying hard-wall boundary conditions elsewhere on the cavity boundary. Then a general wave function psi continuous everywhere may be written down. The relationships between the coefficients of the modes in psi are determined by minimizing the mean square discontinuity in the normal derivative of psi averaged over all the interfaces between the terminals and the cavity. This method has been found to be robust and efficient in calculations of the conductance matrix and scattering wave functions for a to quantum wire with a hard-wall finger of various shapes pushed in through one side.