We provide a pedagogical calculation of the first two spacing distribution for a spin-1/2 XX chain in the presence of an external magnetic field. The results obtained from analytical expressions are compared with those from extensive quantum Monte Carlo simulations. The results obtained for the spacing distributions are used to describe the magnetic behavior of the system and contrasted with the standard analysis based on quantities such as the average energy, magnetization, and susceptibility. Finally, the equivalence between the analytical expressions for the spacing distributions provided by the second quantization formalism and those from the inter-particle distribution method is illustrated. As shown, the spacing distributions can be used as pedagogical examples of the use of the second quantization formalism in introductory courses of quantum statistical mechanics. Additionally, these distributions can be calculated easily from quantum Monte Carlo simulation and, therefore, can be used to illustrate this numerical method.

We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of the monomers to the occupied sites of the lattice. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction. We describe the time evolution of the system in terms of the monomer and island densities, N_{1} and N. We also calculate the gap length, the capture zone and the island distributions. For all the sets of barriers considered, the results given by the proposed analytical model are compared with those from kinetic Monte Carlo simulations. We found that the behavior of the system depends on the ratio of the nucleation barrier to the aggregation barrier. The two-step growth protocol allows more control and understanding on the island formation mechanism because it intrinsically separates the nucleation and aggregation processes in different time regimes.

First-principles calculations are used to probe the effects of mechanical strain on the magnetic and optical properties of monolayer (ML) 2H-TaSe$_2$. A complex dependence of these physical properties on strain results in unexpected behavior, such as ferromagnetism under uniaxial, in-plane, tensile strain and a lifting of the Raman-active E' phonon degeneracy. While ferromagnetism is observed under compression along x-axis and expansion along y-axis, no magnetic order occurs when interchanging the strain direction. The calculations show that the magnetic behavior of the system depends on the exchange within the 5d orbitals of the Ta atoms. The magnetic moment per Ta atom persists even when an additional compressive strain along the z-axis is added to a biaxially-strained ML, which suggests stability of the magnetic order. Exploring the effects of this mechanical strain on the Raman-active phonon modes, we find that the E$^"$ and E' modes are red-shifted due to Ta-Se bond elongation, and that strain lifts the E' mode degeneracy, except for the symmetrical biaxial tensile case. Our results demonstrate the possibility of tuning the properties of 2D-materials for nanoelectronic applications through strain.

Relationships between concentration of unintentionally doped carbon in GaN and its metalorganic vapor phase epitaxy conditions were investigated theoretically. A kinetic-thermodynamic model which considers kinetic behavior of adsorbed atoms on vicinal surface was proposed. Thermodynamic properties of gas species and adsorption energies obtained by first-principles calculation were used in the model. The predicted carbon concentration range, 10(15) similar to 10(17) cm(3), agreed with that of experimental results quantitatively. The calculation results also reproduced experimental tendency: Carbon concentration decreases with increase of NH3 partial pressure and total pressure and/or decrease of trimethylgallium partial pressure.

This paper modestly expands an invited talk at ISSS-8 with the same title. After reviewing the relevant interactions between adsorbates on substrates with metallic surface states [especially Cu(111)], it focuses on organic adsorbates. Of particular interest are those which form honeycomb lattices with pores of various sizes. The nature of the confined states derived from the surface-state electrons is discussed as their effect on admolecules inside the pores.

A scanning tunneling microscopy study of anthraquinone (AQ) on the Au(111) surface shows that the molecules self-assemble into several structures depending on the local surface coverage. At high coverages, a close-packed saturated monolayer is observed, while at low coverages, mobile surface molecules coexist with stable chiral hexamer clusters. At intermediate coverages, a disordered 2D porous network interlinking close-packed islands is observed in contrast to the giant honeycomb networks observed for the same molecule on Cu(111). This difference verifies the predicted extreme sensitivity [J. Wyrick et al., Nano Lett. 11, 2944 (2011)] of the pore network to small changes in the surface electronic structure. Quantitative analysis of the 2D pore network reveals that the areas of the vacancy islands are distributed log-normally. Log-normal distributions are typically associated with the product of random variables (multiplicative noise), and we propose that the distribution of pore sizes for AQ on Au(111) originates from random linear rate constants for molecules to either desorb from the surface or detach from the region of a nucleated pore.

We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length l_{a}. For l_{a}=0 the islands behave as perfect sinks while for l_{a}→∞ they behave as reflecting boundaries. For intermediate values of l_{a}, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and l_{a}. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and l_{a}). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of l_{a} and i=1, 2, and 3.

In this paper we explore the meandering instability of vicinal steps with a kinetic Monte Carlo simulations (kMC) model including the attractive next-nearest-neighbor (NNN) interactions. kMC simulations show that increase of the NNN interaction strength leads to considerable reduction of the meandering wavelength and to weaker dependence of the wavelength on the deposition rate F. The dependences of the meandering wavelength on the temperature and the deposition rate obtained with simulations are in good quantitative agreement with the experimental result on the meandering instability of Cu(0 2 24) [T. Maroutian et al., Phys. Rev. B 64, 165401 (2001)]. The effective step stiffness is found to depend not only on the strength of NNN interactions and the Ehrlich-Schwoebel barrier, but also on F. We argue that attractive NNN interactions intensify the incorporation of adatoms at step edges and enhance step roughening. Competition between NNN and nearest-neighbor interactions results in an alternative form of meandering instability which we call "roughening-limited" growth, rather than attachment-detachment-limited growth that governs the Bales-Zangwill instability. The computed effective wavelength and the effective stiffness behave as lambda(eff) similar to F-q and (beta) over tilde (eff) similar to F-p, respectively, with q approximate to p/2.

We present a kinetic Monte Carlo study of the relaxation dynamics and steady state configurations of 〈110〉 steps on a vicinal (001) simple cubic surface. This system is interesting because 〈110〉 (fully kinked) steps have different elementary excitation energetics and favor step diffusion more than 〈100〉 (nominally straight) steps. In this study we show how this leads to different relaxation dynamics as well as to different steady state configurations, including that 2-bond breaking processes are rate determining for 〈110〉 steps in contrast to 3-bond breaking processes for 〈100〉−steps found in previous work [Surface Sci. 602, 3569 (2008)]. The analysis of the terrace-width distribution (TWD) shows a significant role of kink-generation-annihilation processes during the relaxation of steps: the kinetic of relaxation, toward the steady state, is much faster in the case of 〈110〉−zigzag steps, with a higher standard deviation of the TWD, in agreement with a decrease of step stiffness due to orientation. We conclude that smaller step stiffness leads inexorably to faster step dynamics towards the steady state. The step-edge anisotropy slows the relaxation of steps and increases the strength of step-step effective interactions.

This chapter discusses the equilibrium crystal shape (ECS) from a physical perspective, beginning with a historical introduction to the Wulff theorem. It takes advantage of excellent prior reviews, particularly in the late 1980's, recapping highlights from them. It contains many ideas and experiments subsequent to those reviews. Alternatives to Wulff constructions are presented. Controversies about the critical behavior near smooth edges on the ECS are recounted, including the eventual resolution. Particular attention is devoted to the origin of sharp edges on the ECS, to the impact of reconstructed or adsorbed surface phases coexisting with unadorned phases, and to the role and nature of possible attractive step-step interactions.

We present a method of analyzing the results of density functional modeling of molecular adsorption in terms of an analogue of molecular orbitals. This approach permits intuitive chemical insight into the adsorption process. Applied to a set of anthracene derivates (anthracene, 9,10-anthraquinone, 9,10-dithioanthracene, and 9,10-diselenonanthracene), we follow the electronic states of the molecules that are involved in the bonding process and correlate them to both the molecular adsorption geometry and the species' diffusive behavior. We additionally provide computational code to easily repeat this analysis on any system.