Theory of two-dimensional quantum-dot arrays in magnetic fields: Electronic structure and lateral quantum transport

A theory of the electronic structure and lateral quantum transport of finite ballistic two-dimensional arrays of coupled quantum dots in magnetic fields is formulated, based on a scattering-matrix approach. The quantum dots are connected to each other and to leads by constrictions with sufficiently strong transmission to suppress Coulomb blockade effects. The internal degrees of freedom of the quantum dots are taken into account. The leads are modeled realistically, using the properties of magnetic edge states. The ‘‘bulk’’ spectra of ordered quantum-dot arrays at moderate and high B are found to contain gaps of two different types: (a) conducting gaps that, in finite systems, give rise to edge states, and (b) insulating gaps that do not. The fomer gaps exhibit quantum-Hall plateaus modulated by Aharonov-Bohm oscillations; the latter do not. Negative quantum-Hall plateaus associated with counter-rotating edge states, as well as normal positive quantum-Hall plateaus, are found. If each lead is coupled to the array through a single quantum dot, measurements of transmission and Hall resonances may in principle provide a map of the complex magnetic spectra of the quantum-dot arrays. The effects of disorder are modeled, and some criteria of sample quality that need to be met for the observation of the predicted effects are established.