Nanomechanics and nanoscale phonon dynamics
The dynamics of phonons in mesoscopic and nanometer-scale systems is poorly understood compared with its electronic counterpart. We have initiated a new line of investigations into mesoscopic phenomena, such as coherent energy transport, in nanostructures. This field was recently opened up by a beautiful experiment [K. Schwab et al., Nature 404, 974 (2000)] from the group of Michael Roukes at the California Institute of Technology, where a quantization of thermal conductance in freely suspended one-dimensional Si wires was observed. The thermal conductance quantization is analogous to the electrical conductance quantization in one-dimensional conductors.

Our first work in this area was a theory of mesoscopic thermal transport in the weak-tunneling limit, which occurs if there is strong reflection at the boundary between the phonon reservoirs and wire. Kelly Patton and I have shown in this limit that the energy transport is simply determined by the local vibrational DOS at the surface of the bodies acting as reservoirs, and our expression for the thermal current is analogous to the well-known formula for the electrical current through a tunneling barrier. This result suggests the intriguing possibility of a new type of scanning probe, a scanning thermal-conductance microscope, which would be a vibrational analog of the scanning tunneling microscopy that probes the local phonon density of states of a material, either conducting or insulating, with atomic-scale resolution.

We are currently exploring this idea through a variety of theoretical and computational studies. In particular, Sarah Dunning and I are trying to use molecular-mechanics models of DNA to predict the thermal-conductance profile that would be seen by such a microscope.

	download articles:		• Noninertial mechanism for electronic energy relaxation in nanocrystals • Electron-phonon dynamics in an ensemble of nearly isolated nanoparticles • Thermal transport through a mesoscopic weak link • Phonon spectrum in a nanoparticle mechanically coupled to a substrate • Theory of electron-phonon dynamics in insulating nanoparticles

Shi-Xian Qu and I have recently developed a theory of mesoscopic electrical and thermal conduction through curved wires. Our method consists of introducing a local orthogonal coordinate system dictated by the shape of the wire, rewriting the wave equation in this system, identifying an effective scattering potential caused by the local curvature, and solving the associated Lippmann-Schwinger equation. A novel aspect of the phonon transport case is that the reflection probability always vanishes in the long-wavelength limit, allowing a simple perturbative (Born approximation) treatment at low energies. An account of this work is in progress.

Currently we are investigating quantum-optics effects (such as the Hanbury-Brown Twiss effect) and nonlinear phonomena (such as the formation of gap solitons) with coherent phonons in nanostructures, as well as energy loss mechanisms in nanomechanical resonators and electron-phonon interaction in nanostrctures. In particular, Joel Varley and I, in collaboration with Guigen Zhang and Dustin Dyer in the Department of Biological and Agricultural Engineering, are studying energy loss in nanomechanical resonators by sound ratiation into the support subsrate, the so-called clamping loss mechanism. And Shi-Xian Qu and I, in collaboration with Andrew Cleland at UC Santa Barbara, are investigating electron-phonon thermalization in low-dimensional phonon systems.

We have also been interested in experimental work done in the groups of Bill Dennis and Richard Meltzer at the University of Georgia on phonon dynamics in nanometer-scale crystals made from large-band-gap insulators. The nanoparticles are doped with rare-earth ions, resulting in a low concentration of highly localized electronic impurity states. Phonon emission rates between very closely spaced levels are found to be hundreds of times slower than between the same states in bulk crystals, reflecting a diminished phonon density of states at low energies. We have addressed this problem theoretically and have proposed that the observed relaxation rate can be understood by analyzing the broadened vibrational spectrum of a nanoparticle mechanically coupled to its environment. Our results are in good agreement with experiment. We have also studied several other aspects of electron and phonon dynamics in nanoparticles.

Our work in this area is supported by a Petroleum Research Fund type-AC grant from the American Chemical Society, a Research Innovation Award from the Research Corporation, and by a Faculty Research Grant from the University of Georgia.

SELECTED PUBLICATIONS