Magdalena A. Załuska-Kotur

Double step structure and meandering due to the many body interaction at GaN(0001) surface in N-rich conditions

Growth of gallium nitride on GaN(0001) surface is modeled by Monte Carlo method. Simulated growth is conducted in N-rich conditions, hence it is controlled by Ga atoms surface diffusion. It is shown that dominating four-body interactions of Ga atoms can cause step flow anisotropy. Kinetic Monte Carlo simulations show that parallel steps with periodic boundary conditions form double terrace structures, whereas initially V-shaped parallel step train initially bends and then every second step moves forward, building regular, stationary ordering as observed during metal organic vapor phase epitaxy or hydride vapor phase epitaxy growth of GaN layers. These two phenomena recover surface meandered pair step pattern observed, since 1953, on many semiconductor surfaces, such as SiC, Si, or GaN. Change in terrace width or step orientation particle diffusion jump barriers leads either to step meandering or surface roughening. Additionally it is shown that step behavior changes with the Schwoebel barrier height. Furt...

Spreading of step-like density profiles in interacting lattice gas on a hexagonal lattice

Abstract Diffusion in a single-layer adsorbate on a crystalline surface with a hexagonal lattice site symmetry is studied by Monte Carlo simulations. A step-like density profile of the adsorbate is allowed to spread. From the evolution of this density profile the diffusion coefficient is obtained by use of standard Boltzmann–Matano analysis. Results are compared with those obtained from the harmonic profile evolution studies undertaken by us previously. Agreement between both approaches is found at high and low temperatures. We show results for systems with two different activated state energies. For the first model the diffusion coefficient increases smoothly with the density, and for the second one the diffusion coefficient reaches a maximum for a half-occupied lattice. For this density the step profile forms a long flat terrace. No increase of the diffusion constant for densities where perfect ordering happens was observed.

Collective diffusion on hexagonal lattices – repulsive interactions

DiVusion of interacting particle on a hexagonal lattice is studied by use of Monte Carlo simulations for a range of densities and temperatures including ordered and disordered phases. The decay of the initially prepared density perturbation is analyzed. Fast, local ordering happens at the beginning of system relaxation and clearly separates as a function of time the much slower global diVusion process. Locally equilibrated density perturbation decays according to the macroscopic diVusion equation, which allows a collective diVusion coeYcient to be calculated. The density dependence of the collective diVusion coeYcient is shown for several temperatures above and below the critical temperature.

Step bunching process induced by the flow of steps at the sublimated crystal surface

Stepped GaN(0001) surface is studied by the kinetic Monte Carlo method and compared with the model based on Burton-Cabrera-Frank equations. Successive stages of surface pattern evolution during high temperature sublimation process are discussed. At low sublimation rates, clear, well defined step bunches form. The process happens in the absence or for very low Schwoebel barriers. Bunches of several steps are well separated, move slowly and stay straight. Character of the process changes for more rapid sublimation process where double step formations become dominant and together with meanders and local bunches assemble into the less ordered surface pattern. Solution of the analytic equations written for one dimensional system confirms that step bunching is induced by the particle advection caused by step movement. Relative particle flow towards moving steps becomes important when due to the low Schwoebel barrier both sides of the step are symmetric. Simulations show that in the opposite limit of very high S...

Dipole Interactions with Random Anisotropy: a Local-Mean-Field Study

Dipolar systems with randomly directed anisotropy axes are analysed within a local-mean-field approach and in the Ising limit. The properties of the system are shown to be essentially identical to those characterizing Ising spin glasses. Accounting for some departures from the spin glass behaviour that have been found in experiments on frozen ferrofluids requires more involved modelling.

Single-shot imaging of trapped Fermi gas

Recently developed techniques allow for simultaneous measurements of the positions of all ultra cold atoms in a trap with high resolution. Each such single shot experiment detects one element of the quantum ensemble formed by the cloud of atoms. Repeated single shot measurements can be used to determine all correlations between particle positions as opposed to standard measurements that determine particle density or two-particle correlations only. In this paper we discuss the possible outcomes of such single shot measurements in case of cloud of ultra-cold non-interacting Fermi atoms. We show that the Pauli exclusion principle alone leads to correlations between particle positions that originate from unexpected spatial structures formed by the atoms.

Diffusion of Cu adatoms and dimers on Cu(111) and Ag(111) surfaces

Abstract Diffusion of Cu adatoms and dimers on Cu(111) and Ag(111) surfaces is analyzed based on ab initio surface potentials. Single adatom diffusion is compared with dimer diffusion on both surfaces. Surface geometry makes the adatoms jump alternately between two states in the same way in both systems, whereas dimers undergo more complex diffusion process that combines translational and rotational motion. Small difference in the surface lattice constant between Cu and Ag crystals results in a completely different energy landscape for dimer jumps. As an effect the character of diffusion process changes. Homogeneous Cu dimer diffusion is more difficult and dimers rather rotate within single surface cell, whereas diffusion over Ag surface is faster and happens more smoothly. The temperature dependence of diffusion coefficient and its parameters: energy barrier and prefactor is calculated and compared for both surfaces.

Coupling of orthogonal diffusion modes in two-dimensional nonhomogeneous systems

Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. In our model particles reside and jump randomly between adsorption sites modeled as potential wells with different depths. Site blocking is the only allowed particle-particle interaction mechanism. It is shown that the value of the diffusion coefficient in one lattice direction depends nontrivially on the rate and the character of the particle jumps in other directions. The collective diffusion coefficient increases, eventually approaching values predicted within the mean-field approximation when the jump rate increases in the direction perpendicular to that in which the diffusion coefficient is measured. Analytical predictions of our model are supported by the Monte Carlo simulation performed for selected systems.

Destruction of a Bose-Einstein condensate by strong interactions

We study an exactly solvable system of trapped bosonic particles interacting by model harmonic forces. The model allows for a detailed examination of the order parameter (condensate wavefunction) as well as a concept of the off-diagonal and diagonal order. We analyse the effect of interactions on the condensate and show that sufficiently strong interactions (attractive or repulsive) lead to the destruction of the condensate. In the thermodynamic limit this destruction has a critical character. It is shown that the existence of the coherent state of bosons is related to the existence of two length scales determined by one- and two-particle reduced density matrices. The condensate can exist only if the two length scales are of the same order. Interactions, both repulsive and attractive, change their relative size which may lead to destruction of coherence in the system and depletion of the condensate. We suggest that this scenario is model independent.

The kinetic Potts model in the description of surface dynamics

Abstract A new model for the description of adsorption and desorption processes at the surface is proposed. The lattice gas version of the model is compared with other existing models. The lattice gas and the Potts model approaches to the surface kinetics are examined. Mean-field analysis of the kinetic Potts model is used to study the rates of isothermal and flash desorption processes. The change in the character of desorption with the phase transitions in the adatom layer is shown.