FINITE-DIFFERENCE APPROACH TO EDGE-STATE TRANSPORT IN QUANTUM WIRES AND MULTITERMINAL DEVICES

We investigate multimode electronic transport in a quantum wire in the presence of a uniform magnetic field. Using a finite-difference schem e for the evaluation of the free-electron Schrodinger equation, we obt ain Harper's equation, which is transformed into an eigenvalue problem . The resulting scattering states of the wire are used to describe the magnetoconductance for free electrons as well as for a periodic latti ce potential. In the latter case we obtain a conductance pattern that is related to the Hofstadter butterfly. The calculated current distrib ution in a disordered quantum Hall device confirms the edge-state pict ure of the transport in the quantum Hall regime.