Instanton Calculus of Lifshitz Tails

For noninteracting particles moving in a Gaussian random potential, there exists a disagreement in the literature on the asymptotic expression for the density of states in the tail of the band. We resolve this discrepancy. Further we illuminate the physical facet of instantons appearing in replica and supersymmetric derivations with another derivation employing a Lagrange multiplier field.Comment: 5 page

Strain Modulated Electronic Properties of Ge Nanowires - A First Principles Study

We used density-functional theory based first principles simulations to study the effects of uniaxial strain and quantum confinement on the electronic properties of germanium nanowires along the [110] direction, such as the energy gap and the effective masses of the electron and hole. The diameters of the nanowires being studied are up to 50 {\AA}. As shown in our calculations, the Ge [110] nanowires possess a direct band gap, in contrast to the nature of an indirect band gap in bulk. We discovered that the band gap and the effective masses of charge carries can be modulated by applying uniaxial strain to the nanowires. These strain modulations are size-dependent. For a smaller wire (~ 12 {\AA}), the band gap is almost a linear function of strain; compressive strain increases the gap while tensile strain reduces the gap. For a larger wire (20 {\AA} - 50 {\AA}), the variation of the band gap with respect to strain shows nearly parabolic behavior: compressive strain beyond -1% also reduces the gap. In addition, our studies showed that strain affects effective masses of the electron and hole very differently. The effective mass of the hole increases with a tensile strain while the effective mass of the electron increases with a compressive strain. Our results suggested both strain and size can be used to tune the band structures of nanowires, which may help in design of future nano-electronic devices. We also discussed our results by applying the tight-binding model.Comment: 1 table, 8 figure

Effective medium theory of elastic waves in random networks of rods

We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining novel wavelength-dependent effective elastic moduli, we calculate both the static moduli and the dispersion relations of ultrasonic longitudinal and transverse elastic waves. At finite wave vector $k$ the waves are dispersive, with phase and group velocities decreasing with increasing wave vector. These results are directly applicable to networks with empty pore space. They also describe the solid matrix in two-component (Biot) theories of fluid-filled porous media. We suggest the possibility of low density materials with higher ratios of stiffness and strength to density than those of foams, aerogels or trabecular bone.Comment: 14 pp., 3 fig

Netons: Vibrations of Complex Networks

We consider atoms interacting each other through the topological structure of a complex network and investigate lattice vibrations of the system, the quanta of which we call {\em netons} for convenience. The density of neton levels, obtained numerically, reveals that unlike a local regular lattice, the system develops a gap of a finite width, manifesting extreme rigidity of the network structure at low energies. Two different network models, the small-world network and the scale-free network, are compared: The characteristic structure of the former is described by an additional peak in the level density whereas a power-law tail is observed in the latter, indicating excitability of netons at arbitrarily high energies. The gap width is also found to vanish in the small-world network when the connection range $r = 1$.Comment: 9 pages, 6 figures, to appear in JP

Cooling of cryogenic electron bilayers via the Coulomb interaction

Heat dissipation in current-carrying cryogenic nanostructures is problematic because the phonon density of states decreases strongly as energy decreases. We show that the Coulomb interaction can prove a valuable resource for carrier cooling via coupling to a nearby, cold electron reservoir. Specifically, we consider the geometry of an electron bilayer in a silicon-based heterostructure, and analyze the power transfer. We show that across a range of temperatures, separations, and sheet densities, the electron-electron interaction dominates the phonon heat-dissipation modes as the main cooling mechanism. Coulomb cooling is most effective at low densities, when phonon cooling is least effective in silicon, making it especially relevant for experiments attempting to perform coherent manipulations of single spins.Comment: 9 pages, 5 figure

Tilt-angle landscapes and temperature dependence of the conductance in biphenyl-dithiol single-molecule junctions

Using a density-functional-based transport method we study the conduction properties of several biphenyl-derived dithiol (BPDDT) molecules wired to gold electrodes. The BPDDT molecules differ in their side groups, which control the degree of conjugation of the pi-electron system. We have analyzed the dependence of the low-bias zero-temperature conductance on the tilt angle phi between the two phenyl ring units, and find that it follows closely a cos^2(phi) law, as expected from an effective pi-orbital coupling model. We show that the tilting of the phenyl rings results in a decrease of the zero-temperature conductance by roughly two orders of magnitude, when going from a planar conformation to a configuration in which the rings are perpendicular. In addition we demonstrate that the side groups, apart from determining phi, have no influence on the conductance. All this is in agreement with the recent experiment by Venkataraman et al. [Nature 442, 904 (2006)]. Finally, we study the temperature dependence of both the conductance and its fluctuations and find qualitative differences between the examined molecules. In this analysis we consider two contributions to the temperature behavior, one coming from the Fermi functions and the other one from a thermal average over different contact configurations. We illustrate that the fluctuations of the conductance due to temperature-induced changes in the geometric structure of the molecule can be reduced by an appropriate design.Comment: 9 pages, 6 figures; submitted to Phys. Rev.

Ground-plane screening of Coulomb interactions in two-dimensional systems: How effectively can one two-dimensional system screen interactions in another?

The use of a nearby metallic ground-plane to limit the range of the Coulomb interactions between carriers is a useful approach in studying the physics of two-dimensional (2D) systems. This approach has been used to study Wigner crystallization of electrons on the surface of liquid helium, and most recently, the insulating and metallic states of semiconductor-based two-dimensional systems. In this paper, we perform calculations of the screening effect of one 2D system on another and show that a 2D system is at least as effective as a metal in screening Coulomb interactions. We also show that the recent observation of the reduced effect of the ground-plane when the 2D system is in the metallic regime is due to intralayer screening.Comment: 14 pages, 7 figures Accepted in PR

Probing Ion-Ion and Electron-Ion Correlations in Liquid Metals within the Quantum Hypernetted Chain Approximation

We use the Quantum Hypernetted Chain Approximation (QHNC) to calculate the ion-ion and electron-ion correlations for liquid metallic Li, Be, Na, Mg, Al, K, Ca, and Ga. We discuss trends in electron-ion structure factors and radial distribution functions, and also calculate the free-atom and metallic-atom form-factors, focusing on how bonding effects affect the interpretation of X-ray scattering experiments, especially experimental measurements of the ion-ion structure factor in the liquid metallic phase.Comment: RevTeX, 19 pages, 7 figure

Fractional-Period Excitations in Continuum Periodic Systems

We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that when the potential is turned on non-adiabatically, the system explores a number of transient states whose periodicity is a fraction of that of the lattice. We illustrate the origin of fractional-period states analytically by treating them as resonant states of a parametrically forced Duffing oscillator and discuss their transient nature and potential observability.Comment: 10 pages, 6 figures (some with multiple parts); revised version: minor clarifications of a couple points, to appear in Physical Review