Ordering of atomic mono-layers on a (001) cubic crystal surface

The self-organization of a chemi-sorbed mono-layer is studied as a two dimensional ordering process in presence of surface stress. As proved previously for a single phase separation, a steady surface state is yielded from the competition between the domain boundary energy and the surface stress elastic energy. In the present letter, the resulting patterns are shown to depend on the interplay between the symmetries of both the internal layer order and the underlying crystal. For experimental relevance, our study is focussed on a (001) copper surface and we believe to enhance a route to stabilize novel surface nanostructures.Comment: 5 pages, 2 figures. submitted to P

Small Bipolarons in the 2-dimensional Holstein-Hubbard Model. II Quantum Bipolarons

We study the effective mass of the bipolarons and essentially the possibility to get both light and strongly bound bipolarons in the Holstein-Hubbard model and some variations in the vicinity of the adiabatic limit. Several approaches to investigate the quantum mobility of polarons and bipolarons are proposed for this model. It is found that the bipolaron mass generally remains very large except in the vicinity of the triple point of the phase diagram, where the bipolarons have several degenerate configurations at the adiabatic limit (single site (S0), two sites (S1) and quadrisinglet (QS)), while the polarons are much lighter. This degeneracy reduces the bipolaron mass significantly. The triple point of the phase diagram is washed out by the lattice quantum fluctuations which thus suppress the light bipolarons. We show that some model variations, for example a phonon dispersion may increase the stability of the (QS) bipolaron against the quantum lattice fluctuations. The triple point of the phase diagram may be stable to quantum lattice fluctuations and a very sharp mass reduction may occur, leading to bipolaron masses of the order of 100 bare electronic mass for realistic parameters. Thus such very light bipolarons could condense as a superconducting state at relatively high temperature when their interactions are not too large, that is, their density is small enough. This effect might be relevant for understanding the origin of the high Tc superconductivity of doped cuprates far enough from half filling.Comment: accepted Eur. Phys. J. B (january 2000) Ref. B960

Many-polaron states in the Holstein-Hubbard model

A variational approach is proposed to determine some properties of the adiabatic Holstein-Hubbard model which describes the interactions between a static atomic lattice and an assembly of fermionic charge carriers. The sum of the electronic energy and the lattice elastic energy is proved to have minima with a polaron structure in a certain domain of the phase diagram. Our analytical work consists in the expansion of these energy minima from the zero electronic transfer limit which remarkably holds for a finite amplitude of the onsite Hubbard repulsion and for an unbounded lattice size.Comment: submitted to Journal of Statistical Physic

Small Bipolarons in the 2-dimensional Holstein-Hubbard Model. I The Adiabatic Limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction $\upsilon \geq 0$, which tends to break them, generates many different ground-states. There are four domains in the $g,\upsilon$ phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small $\upsilon$, large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large $\upsilon$, large g); or 3) be a "quadrisinglet state" which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron

Pseudogap in the optical phonon spectra

The energy spectrum of the quantum Klein-Gordon lattice is computed numerically for different nonlinear contributions to the Hamiltonian. In agreement with the studies on the effective Hubbard Hamiltonian for boson quasi-particles (see for instance Refs.\onlinecite{AGRANOVICH,Eilbeck}) a pairing of the phonon states is found when the nonlinearity of the lattice is significant. On the opposite, when the nonlinear contribution is weak or moderate, which is common in materials the effective Hamiltonian is not appropriate because it neglects all the energy terms that do not conserve the boson number. Then for a realistic modelling of the hybridization between the free phonon and the phonon bound pairs, the Klein-Gordon Hamiltonian is required since it is derived from the potential energy of the atoms and thus it does not involve any arbitrary quanta conservation. Actually, when the nonlinearity is weak we prove that the binding energy of the phonon bound pairs vanishes at the center of the lattice Brillouin zone whereas at the edge, it may be comparable to the phonon band width.Consequently, the signature of a weak nonlinearity is found to be a pseudogap that opens in the spectrum region of the two phonon energy, at the edge of the lattice Brillouin zone. Our results are shown to be valid for all the lattice dimensions and for some model parameters that are relevant for the optical phonon spectra.Comment: Brief communication on the quantum nonlinear Klein-Gordon Hamiltonia

Hydrogen and vacancy clustering in zirconium

The effect of solute hydrogen on the stability of vacancy clusters in hexagonal closed packed zirconium is investigated with an ab initio approach, including contributions of H vibrations. Atomistic simulations within the density functional theory evidence a strong binding of H to small vacancy clusters. The hydrogen effect on large vacancy loops is modeled through its interaction with the stacking faults. A thermodynamic modeling of H segregation on the various faults, relying on ab initio binding energies, shows that these faults are enriched in H, leading to a decrease of the stacking fault energies. This is consistent with the trapping of H by vacancy loops observed experimentally. The stronger trapping, and thus the stronger stabilization, is obtained for vacancy loops lying in the basal planes, i.e. the loops responsible for the breakaway growth observed under high irradiation dose.Comment: submitte

Dislocations pinning by substitutional impurities in an atomic-scale model for the Al(Mg) solid solutions

International audienceWe report our atomic-scale computations for the static depinning threshold of dislocations in the Al(Mg) solid solutions. The interaction between the dislocations and the isolated obstacles is studied for different types of obstacle, i.e., the single solute atoms situated at different positions and the solute dimers with different bond directions. A part of this work is used to apply different standard analytical theories for solid solution hardening, the predictions of which are finally compared with our direct atomic-scale simulations (AS) for the dislocation depinning in the random Al(Mg) solid solutions. According to our comparisons, the dislocation statistics in our AS is qualitatively well described by the Mott-Nabarro-Labusch theory. In agreement with earlier results about a different system, namely Ni(Al), the depinning thresholds are similar for the edge and for the screw dislocations