Abstract. Acoustic phonon modes of a free-standing rectangular quantum wire of cubic crystals are theoretically investigated using an algorithm developed to analyze data from resonant ultrasound spectroscopy. The normal phonon modes are classified by their spatial symmetries into a compressional mode termed the dilatational mode and non-compressional modes referred to as the flexural, torsional and shear modes. The formalism we present is quite general and can be applied to wires of any cubic material. As an example, the dispersion relations are obtained for square and rectangular wires of GaAs, taking into account anisotropic elasticity of the material. The dispersion curves for a rectangular wire are compared with those of the approximate hybrid modes referred to as the thickness and width modes, and the validity of the modes is discussed. The existence of edge modes is confirmed by examining the spatial distribution of displacement vectors.

We report on a molecular dynamics study of the cross-plane lattice thermal conductivity in GaAs/AlAs superlattices. The layers of the superlattice are modelled by a three-dimensional face centred cubic lattice with cubic anharmonicity, and with atomic scale roughness at the interfaces. We perform the simulation of heat flow for a section of a superlattice with high-and lowtemperature thermal reservoirs attached to opposite ends. The calculation reproduces qualitatively the features observed experimentally, i.e., the dramatic reduction of the conductivity relative to the conductivity of the bulk constituent materials, and the variation of the thermal conductivity with the superlattice repeat distance. The results are also in agreement with those obtained previously by Daly et al (2002 Phys. Rev. B 66 024301) who determined the thermal conductivity from the time taken for an initially inhomogeneous temperature distribution to relax.

We analytically study phonon transmission and localization in random superlattices by using a Green's function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the superlattice structure factor. This is done by considering the backscattering of phonons, due to the complex mass density fluctuations, which incorporates all of the forward scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied.

Confined and interface acoustic phonon modes in a cylindrical quantum wire embedded in another material are analytically investigated based on the elastic continuum model by means of the potential theory. Confined acoustic phonon modes are coupled modes of bulk-longitudinal and transverse acoustic waves, classified into torsional, dilatational, and flexural modes due to the rotational symmetry of the modes. Dispersions of the confined modes have subband structures with finite cutoff frequencies owing to quantization of wave vectors in the lateral direction. The density of confined phonon states becomes, as a result, a staircaselike structure. As for the interface modes, regions of material parameters for the possible existence of interface modes are investigated. We found that the existence of interface modes in a quantum wire–surrounding system becomes more sensitive to the combinations of materials than that for a plane interface

We study both analytically and numerically phonon transmission fluctuations and localization in partially ordered superlattices with correlations among neighboring layers. In order to generate a sequence of layers with a varying degree of order we employ a model proposed by Hendricks and Teller as well as partially ordered versions of deterministic aperiodic superlattices. By changing a parameter measuring the correlation among adjacent layers, the Hendricks-Teller superlattice exhibits a transition from periodic ordering, with alternating layers, to the phase separated opposite limit; including many intermediate arrangements and the completely random case. In the partially ordered versions of deterministic superlattices, there is short-range order (among any N consecutive layers) and long range disorder, as in the N-state Markov chains. The average and fluctuations in the transmission, the backscattering rate, and the localization length in these multilayered systems are calculated based on the superlattice structure factors we derive analytically. The standard deviation of the transmission versus the average transmission lies on a universal curve irrespective of the specific type of disorder of the SL. We illustrate these general results by applying them to several GaAs-AlAs superlattices for the proposed experimental observation of phonon universal transmission fluctuations. 62.65.+k, 63.50.+x, 68.65.+g, 71.55.Jv

The gate voltage dependence of a single-electron transistor using the shuttle mechanism in which a vibrating conductive nanoparticle carries charges between the electrodes is studied theoretically and with numerical simulations. Two types of gate voltage effect on the transport properties are demonstrated: one is direct modulation of the current via modification in the tunneling rate, giving rise to shift of ] I/]V peaks on the step-like current, splitting of the current steps and periodic behavior of the current with the change in gate voltage. Another is an indirect effect due to a shift in the range of the nanoparticle vibration induced by the gate voltage. The latter effect stops the shuttle mechanism at a large gate voltage, leading to the conduction gap which widens in proportion to the gate voltage

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Random telegraph noise in the electric current produced by shot noise is predicted for an array of movable colloid particles by Monte Carlo and molecular dynamics calculations. The electron transport is attributed to the shuttle mechanism where moving colloid particles carry charges. The colloid-particle motion induced by the source-drain voltage shows periodic and/or quasiperiodic vibrations, and the current value depends on the vibration modes. Shot noise that is uncorrelated with the colloid-particle motion causes transitions between the periodic and quasiperiodic vibration modes, resulting in random switching between the current levels corresponding to the vibration modes.