HALL RESISTANCE ANOMALIES AND QUASI-BOUND STATES WITHIN HALL JUNCTIONS

The Hall resistance is studied by solving the Schrodinger equation for electrons in the presence of a magnetic field. The boundary element method (BEM) has been employed to solve the Schrodinger equation with complicated boundary conditions. The Hall resistance anomalies in low magnetic fields are discussed from the view points of the wave mechanics. The quasi-bound states in the Hall junction, which causes sharp dips in the plot of the Hall resistance as a function of the magnetic induction in high magnetic fields, is studied in terms of the wave functions. It is found that the quasi-bound states are similar to some of the eigenstates confined in a disk with a hole. From this similarity, the quasi-bound state which is responsible for each dip is identified.