DC MAGNETOTRANSPORT AND HALL-EFFECT IN MULTIPLY CONNECTED QUANTUM-WIRE SYSTEMS

In the Landauer-Buttiker approach, the dc-transport properties of a system are expressed in terms of its scattering matrix. We propose a method to sum the multiple-scattering events for an arbitrary ensemble of interconnected scatterers, which leads to a closed analytic expression for the matrix elements of the overall-scattering matrix. This approach is used to investigate the dc magnetotransport of a planar periodic lattice of interconnected quantum wires. The calculated conductance as well as the Hall voltage depend strongly on the Fermi wave vector and on the magnetic field. This behavior is a consequence of the interference between waves traveling along different scattering paths. It is closely related to the eigenvalue spectrum of electrons in a two-dimensional lattice in the presence of a perpendicular magnetic field, which is described by the Hofstadter butterfly. We present a detailed analysis of the observed features of the Hall voltage.