A theory of generalized Bloch oscillations.

Bloch oscillations of electrons are shown to occur for cases when the energy spectrum does not consist of the traditional evenly-spaced ladders and the potential gradient does not result from an external electric field. A theory of such generalized Bloch oscillations is presented and an exact calculation is given to confirm this phenomenon. Our results allow for a greater freedom of design for experimentally observing Bloch oscillations. For strongly coupled oscillator systems displaying Bloch oscillations, it is further demonstrated that reordering of oscillators leads to destruction of Bloch oscillations. We stipulate that the presented theory of generalized Bloch oscillations can be extended to other systems such as acoustics and photonics.

Band structure of hydrogenated Si nanosheets and nanotubes.

The band structures of fully hydrogenated Si nanosheets and nanotubes are elucidated by the use of an empirical tight-binding model. The hydrogenated Si sheet is a semiconductor with an indirect band gap of about 2.2 eV. The symmetries of the wavefunctions allow us to explain the origin of the gap. We predict that, for certain chiralities, hydrogenated Si nanotubes represent a new type of semiconductor, one with coexisting direct and indirect gaps of exactly the same magnitude. This behavior is different from that governed by the Hamada rule established for non-hydrogenated carbon and silicon nanotubes. A comparison to the results of an ab initio calculation is made.

Electronic properties of semiconductor nanowires.

This paper provides a review of the state-of-the-art electronic-structure calculations of semiconductor nanowires. Results obtained using empirical k.p, empirical tight-binding, semi-empirical pseudopotential, and with ab initio methods are compared. For conciseness, we will restrict our detailed discussions to free-standing plain and modulated nanowires. Connections to relevant experimental data, particularly band gaps and polarization anisotropy, will be made since these results depend crucially on the electronic properties. For completeness, a brief review on the synthesis of nanowires is included.

Acoustic cavity modes in lens-shaped structures.

A method for solving exactly the Helmholtz equation in parabolic rotational coordinates is presented using separability of the eigenfunctions and the Frobenius power series expansion technique. Two examples of interest in acoustics are considered and analyzed quasianalytically: The acoustic pressure in a cavity defined by two paraboloids (forming a lens-shaped structure) with (I) rigid wall boundary conditions and (II) pressure-release boundaries. The rigid-wall (pressure-release) acoustic enclosure problem is a Neumann (Dirichlet) boundary condition problem. In both cases, eigenfunctions and eigenmodes are calculated and the shape dependence of the eigenvalue for the ground state is examined.