Quantum transmitting boundary method in a magnetic field

Abstract

A numerical algorithm for the solution of the two-dimensional effective-mass Schrödinger equation for current-carrying states, the quantum transmitting boundary method, is extended to magnetotransport problems where a magnetic field is applied. Boundary conditions appropriate for such states are developed and a solution algorithm based on the finite-element method is constructed. The algorithm is valid for general device shapes, general potential profiles, and multiple leads of general orientations. The technique is applied to a quantum channel with a single scatterer, an antidot, in the channel. Magnetic quasibound states (MQBS) are formed around the scatterer and MQBS-induced resonant reflection is observed.