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

Atomic-scale avalanche along a dislocation in a random alloy

International audienceThe propagation of dislocations in random crystals is evidenced to be governed by atomic-scale avalanches whose the extension in space and the time intermittency characterizingly diverge at the critical threshold. Our work is the very first atomic-scale evidence that the paradigm of second order phase transitions applies to the depinning of elastic interfaces in random media

Bipolarons in the Extended Holstein Hubbard Model

We numerically and analytically calculate the properties of the bipolaron in an extended Hubbard Holstein model, which has a longer range electron-phonon coupling like the Fr\" ohlich model. In the strong coupling regime, the effective mass of the bipolaron in the extended model is much smaller than the Holstein bipolaron mass. In contrast to the Holstein bipolaron, the bipolaron in the extended model has a lower binding energy and remains bound with substantial binding energy even in the large-U limit. In comparison with the Holstein model where only a singlet bipolaron is bound, in the extended Holstein model a triplet bipolaron can also form a bound state. We discuss the possibility of phase separation in the case of finite electron doping.Comment: 5 pages, 3 figure

Mobile Bipolarons in the Adiabatic Holstein-Hubbard Model in 1 and 2 dimensions

The bound states of two electrons in the adiabatic Holstein-Hubbard model are studied numerically in one and two dimensions from the anticontinuous limit. This model involves a competition between a local electron-phonon coupling (with a classical lattice) which tends to form pairs of electrons and the repulsive Hubbard interaction $U \geq 0$ which tends to break them. In 1D, the ground-state always consists in a pair of localized polarons in a singlet state. They are located at the same site for U=0. Increasing U, there is a first order transition at which the bipolaron becomes a spin singlet pair of two polarons bounded by a magnetic interaction. The pinning mode of the bipolaron soften in the vicinity of this transition leading to a higher mobility of the bipolaron which is tested numerically. In 2D, and for any $U$, the electron-phonon coupling needs to be large enough in order to form small polarons or bipolarons instead of extended electrons. We calculate the phase diagram of the bipolaron involving first order transitions lines with a triple point. A pair of polarons can form three types of bipolarons: a) on a single site at small $U$, b) a spin singlet state on two nearest neighbor sites for larger $U$ as in 1D and c) a new intermediate state obtained as the resonant combination of four 2-sites singlet states sharing a central site, called quadrisinglet. The breathing and pinning internal modes of bipolarons in 2D generally only weakly soften and thus, they are practically not mobile. On the opposite, in the vicinity of the triple point involving the quadrisinglet, both modes exhibit a significant softening. However, it was not sufficient for allowing the existence of a classical mobile bipolaron (at least in that model)

Biphonons in the Klein-Gordon lattice

A numerical approach is proposed for studying the quantum optical modes in the Klein-Gordon lattices where the energy contribution of the atomic displacements is non-quadratic. The features of the biphonon excitations are investigated in detail for different non-quadratic contributions to the Hamiltonian. The results are extended to multi-phonon bound states.Comment: Comments and suggestions are welcom

Numerical study of the E⊗eE\otimes e Jahn-Teller polaron and bipolaron

The properties of the polaron and bipolaron are explored in the 1D Jahn-Teller model with dynamical quantum phonons. The ground-state properties of the polaron and bipolaron are computed using a recently developed variational method. Dynamical properties of the ground state of a polaron are investigated by calculating the optical conductivity $\sigma(\omega)$. Our numerical results suggest that the Jahn-Teller and Holstein polarons are similar. However, in the strong-coupling regime qualitative differences in $\sigma(\omega)$ between the two models are found and discussed. The influence of the electron-phonon coupling and the electrostatic repulsion on the bipolaron binding energy, bipolaron masses, and correlation functions is investigated.Comment: 9 pages including 11 figures. To appear in PR

Kink pair production and dislocation motion

The motion of extended defects called dislocations controls the mechanical properties of crystalline materials such as strength and ductility. Under moderate applied loads, this motion proceeds via the thermal nucleation of kink pairs. The nucleation rate is known to be a highly nonlinear function of the applied load, and its calculation has long been a theoretical challenge. In this article, a stochastic path integral approach is used to derive a simple, general, and exact formula for the rate. The predictions are in excellent agreement with experimental and computational investigations, and unambiguously explain the origin of the observed extreme nonlinearity. The results can also be applied to other systems modelled by an elastic string interacting with a periodic potential, such as Josephson junctions in superconductors

Atomistic mechanisms for the ordered growth of Co nano-dots on Au(788): comparison of VT-STM experiments and multi-scaled calculations

Hetero-epitaxial growth on a strain-relief vicinal patterned substrate has revealed unprecedented 2D long range ordered growth of uniform cobalt nanostructures. The morphology of a Co sub-monolayer deposit on a Au(111) reconstructed vicinal surface is analyzed by Variable Temperature Scanning Tunneling Microscopy (VT-STM) experiments. A rectangular array of nano-dots (3.8 nm x 7.2 nm) is found for a particularly large deposit temperature range lying from 60 K to 300 K. Although the nanodot lattice is stable at room temperature, this paper focus on the early stage of ordered nucleation and growth at temperatures between 35 K and 480 K. The atomistic mechanisms leading to the nanodots array are elucidated by comparing statistical analysis of VT-STM images with multi-scaled numerical calculations combining both Molecular Dynamics for the quantitative determination of the activation energies for the atomic motion and the Kinetic Monte Carlo method for the simulations of the mesoscopic time and scale evolution of the Co submonolayer