Giant oscillations in the Hall conductivity of weakly coupled quantum wires

Abstract

We find that the Hall conductivity of an array of weakly coupled quantum wires has sharp maxima when the Fermi level is coincident with one of a discrete set of energies at which resonant tunneling between nearby wires is allowed. When only one subband is occupied in the quantum wires, gaps in the density of states of the coupled system open at the resonant energies and the Hall conductivity at the maxima is quantized in units of ${\mathit{e}}^2$/h. For Fermi energies away from the resonant values the Hall conductivity is strongly suppressed and attains a value reflecting the linear response of isolated quantum wires.