Open-boundary Ehrenfest molecular dynamics: towards a model of current unduced heating in nanowires

We present a time-dependent method based on the single-particle electron density matrix that allows the electronic and ionic degrees of freedom to be modelled within the Ehrenfest approximation in the presence of open boundaries. We describe a practical implementation using tight binding, and use it to investigate steady-state conduction through a single-atom device and to perform molecular dynamics. We find that in the Ehrenfest approximation an electric current allows both ionic heating and cooling to take place, depending on the bias

Interaction between electronic structure and strain in Bi nanolines on Si(001)

Heteroepitaxial strain can be a controlling factor in the lateral dimensions of 1-D nanostructures. Bi nanolines on Si(001) have an atomic structure which involves a large sub-surface reconstruction, resulting in a strong elastic coupling to the surrounding silicon. We present variable-bias STM and first principles electronic structure calculations of the Bi nanolines, which investigates this interaction. We show that the strain associated with the nanolines affects the atomic and electronic structure of at least two neighbouring Si dimers, and identify the mechanism behind this. We also present partial charge densities (projected by energy) for the nanoline with clean and hydrogenated surroundings and contrast it to the clean Si(001) surface.Comment: 10 pages, 3 figures, submitted to Surface Scienc

A first principles study of sub-monolayer Ge on Si(001)

Experimental observations of heteroepitaxial growth of Ge on Si(001) show a (2xn) reconstruction for sub-monolayer coverages, with dimer rows crossed by missing-dimer trenches. We present first-principles density-functional calculations designed to elucidate the energetics and relaxed geometries associated with this reconstruction. We also address the problem of how the formation energies of reconstructions having different stoichiometries should be compared. The calculations reveal a strong dependence of the formation energy of the missing-dimer trenches on spacing n, and demonstrate that this dependence stems almost entirely from elastic relaxation. The results provide a natural explanation for the experimentally observed spacings in the region of n \~ 8.Comment: 13 pages, 4 figures, submitted to Surface Scienc

Expansion algorithm for the density matrix

A purification algorithm for expanding the single-particle density matrix in terms of the Hamiltonian operator is proposed. The scheme works with a predefined occupation and requires less than half the number of matrix-matrix multiplications compared to existing methods at low (90%) occupancy. The expansion can be used with a fixed chemical potential in which case it is an asymmetric generalization of and a substantial improvement over grand canonical McWeeny purification. It is shown that the computational complexity, measured as number of matrix multiplications, essentially is independent of system size even for metallic materials with a vanishing band gap.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Efficient Recursion Method for Inverting Overlap Matrix

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations with the the non-orthogonal localized basis set. This efficient inverting method can be incorporated in several O(N) methods for diagonalization of a generalized secular equation. By studying convergence properties of the 1-norm of an error matrix for diamond and fcc Al, this method is compared to three other O(N) methods (the divide method, Taylor expansion method, and Hotelling's method) with regard to computational accuracy and efficiency within the density functional theory. The test calculations show that the new method is about one-hundred times faster than the divide method in computational time to achieve the same convergence for both diamond and fcc Al, while the Taylor expansion method and Hotelling's method suffer from numerical instabilities in most cases.Comment: 17 pages and 4 figure

Block bond-order potential as a convergent moments-based method

The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi bonds by introducing block elements, which produces rapid convergence of the energies and forces within insulators, semiconductors, metals, and molecules. The method gives the first convergent results for vacancies in semiconductors using a moments-based method with a low number of moments. Our use of the Lanczos basis simplifies the calculations of the band energy and forces, which allows the application of the method to the molecular dynamics simulations of large systems. As an illustration of this convergent O(N) method we apply the block bond-order potential to the large scale simulation of the deformation of a carbon nanotube.Comment: revtex, 43 pages, 11 figures, submitted to Phys. Rev.

STM characterization of the Si-P heterodimer

We use scanning tunneling microscopy (STM) and Auger electron spectroscopy to study the behavior of adsorbed phosphine (PH$_{3}$) on Si(001), as a function of annealing temperature, paying particular attention to the formation of the Si-P heterodimer. Dosing the Si(001) surface with ${\sim}$0.002 Langmuirs of PH$_{3}$ results in the adsorption of PH$_{x}$ (x=2,3) onto the surface and some etching of Si to form individual Si ad-dimers. Annealing to 350$^{\circ}$C results in the incorporation of P into the surface layer to form Si-P heterodimers and the formation of short 1-dimensional Si dimer chains and monohydrides. In filled state STM images, isolated Si-P heterodimers appear as zig-zag features on the surface due to the static dimer buckling induced by the heterodimer. In the presence of a moderate coverage of monohydrides this static buckling is lifted, rending the Si-P heterodimers invisible in filled state images. However, we find that we can image the heterodimer at all H coverages using empty state imaging. The ability to identify single P atoms incorporated into Si(001) will be invaluable in the development of nanoscale electronic devices based on controlled atomic-scale doping of Si.Comment: 6 pages, 4 figures (only 72dpi

Vibrational properties of amorphous silicon from tight-binding O(N) calculation

We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the short-range nature of the density matrix to calculate the vibrational density of states which is then compared with the same obtained from a standard O($N^4$) algorithm. For the purpose of illustration, an 1000-atom model is studied to calculate the localization properties of the vibrational eigenstates using the participation numbers calculation.Comment: 5 pages including 5 ps figures; added a figure and a few references; accepted in Phys. Rev.

Model Hessian for accelerating first-principles structure optimizations

We present two methods to accelerate first-principles structural relaxations, both based on the dynamical matrix obtained from a universal model of springs for bond stretching and bending. Despite its simplicity, the normal modes of this model Hessian represent excellent internal coordinates for molecules and solids irrespective of coordination, capturing not only the long-wavelength acoustic modes of large systems, but also the short-wavelength low-frequency modes that appear in complex systems. In the first method, the model Hessian is used to precondition a conjugate gradients minimization, thereby drastically reducing the effective spectral width and thus obtaining a substantial improvement of convergence. The same Hessian is used in the second method as a starting point of a quasi-Newton algorithm (Broyden's method and modifications thereof), reducing the number of steps needed to find the correct Hessian. Results for both methods are presented for geometry optimizations of clusters, slabs, and biomolecules, with speed-up factors between 2 and 8.Comment: 5 pages, 3 figures submites to Phys. Rev.

Gauge Theories on a 2+2 Anisotropic Lattice

The implementation of gauge theories on a four-dimensional anisotropic lattice with two distinct lattice spacings is discussed, with special attention to the case where two axes are finely and two axes are coarsely discretized. Feynman rules for the Wilson gauge action are derived and the renormalizability of the theory and the recovery of the continuum limit are analyzed. The calculation of the gluon propagator and the restoration of Lorentz invariance in on-shell states is presented to one-loop order in lattice perturbation theory for $SU(N_c)$ on both 2+2 and 3+1 lattices.Comment: 27 pages, uses feynmf. Font compatibility adjuste