The transport properties of electrons and phonons in systems with lateral dimensions less than the dominant phonon wavelength will be studied. Typically, this criterion is met in structures with lateral dimensions less than 100nm and at lattice temperatures below 1K. Wires of these dimensions will be defined on a substrate using electron-beam techniques. In order to avoid the effects of coupling between the substrate phonons and the modes of the wire, the structures will be made free-standing using etching techniques. At sufficiently low temperatures, they expect to observe spatial quantization of the phonons in the wires and so a commensurate reduction in the dimensionality describing the phonon spectrum. Details of the spectrum will be ascertained by studying the conductance variations of metallic wires that are shorter than the inelastic scattering length of the electrons. In longer wires, magneto-conductance measurements will be used to study the electron-phonon interaction in systems of reduced phonon and electron dimensionality. Finally, he will investigate phonon scattering processes and phonon localization effects in free-standing dielectric and semiconducting wires.
