Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on request), submitted to J. Phys. (A): Math. Ge

Spin Filtering via Resonant Reflection of Relativistic Surface States

A microscopic approach is developed to scattering of surface states from a non-magnetic linear defect at a surface with strong spin-orbit interaction. Spin-selective reflection resonances in scattering of Rashba-split surface states by an atomic stripe are theoretically discovered in a proof-of-principle calculation for a model crystal potential. Spin-filtering properties of such linear defects are analyzed within an envelope-function formalism for a perturbed surface based on the Rashba Hamiltonian. The continuous Rashba model is found to be in full accord with the microscopic theory, which reveals the essential physics behind the scattering resonance. The spin-dependent reflection suggests a novel mechanism to manipulate spins on the nanoscale.Comment: 6 pages, 4 figures, 1 tabl

The quasiparticle band gap in the topological insulator Bi2Te3

We present a theoretical study of dispersion of states which form the bulk band-gap edges in the three-dimensional topological insulator Bi2Te3. Within density functional theory, we analyze the effect of atomic positions varying within the error range of the available experimental data and approximation chosen for the exchange-correlation functional on the bulk band gap and k-space location of valence- and conduction-band extrema. For each set of the positions with different exchange-correlation functionals, we show how many-body corrections calculated within a one-shot GW approach affect the mentioned characteristics of electronic structure of Bi2Te3. We thus also illustrate to what degree the one-shot GW results are sensitive to the reference one-particle band structure in the case of bismuth telluride. We found that for this topological insulator the GW corrections enlarge the fundamental band gap and for certain atomic positions and reference band structure bring its value in close agreement with experiment.Comment: 12 pages, 6 figures, 5 table