Quantum Interference Effects in Mesoscopic Two - Arrays

In this thesis we present a theoretical and experimental study of quantum interference effects in two dimensional networks. Firstly, the phase distribution of an electron in a magnetic field is derived by using classical quantum theory, and results are derived for a single 1 x 1 network or simple loop geometry, and are described in terms of the AB effect. The calculations are then extended to an mxn network, where we show that interference effects can be significantly enhanced, but that the effects are strongly dependent on the transmission and reflection coefficients of the constituent junctions of the network. To establish practical exploitation of the enhanced effects, transmission and reflection coefficients for specific junction geometry relevant to those fabricated are calculated using a distribution approximation function method, where an electron traversing the junctions is simulated, including relevant electrical parameters such as effective mass and Fermi energies. For the experimental component of this study we describe the synthesis of a new heterojunction combination based on GaSb/Sb, where we propose the semimetal Sb to be a useful candidate for fabrication of such network structures, due to its high carrier concentration and long mean free path. Both 1 x 1 and 2 x 2 nano network structures are fabricated with linewidths below 1000 A, demonstrating the ability to engineer structures from Sb epilayers. Finally magneto-transport measurements on such network structures reveal the manifestation of the AB effect, consistent with theoretical predictions.