Towards electron transport measurements in chemically modified graphene: The effect of a solvent

Chemical functionalization of graphene modifies the local electron density of the carbon atoms and hence electron transport. Measuring these changes allows for a closer understanding of the chemical interaction and the influence of functionalization on the graphene lattice. However, not only chemistry, in this case diazonium chemistry, has an effect on the electron transport. Latter is also influenced by defects and dopants resulting from different processing steps. Here, we show that solvents used in the chemical reaction process change the transport properties. In more detail, the investigated combination of isopropanol and heating treatment reduces the doping concentration and significantly increases the mobility of graphene. Furthermore, the isopropanol treatment alone increases the concentration of dopants and introduces an asymmetry between electron and hole transport which might be difficult to distinguish from the effect of functionalization. The results shown in this work demand a closer look on the influence of solvents used for chemical modification in order to understand their influence

Rate theory for correlated processes: Double-jumps in adatom diffusion

We study the rate of activated motion over multiple barriers, in particular the correlated double-jump of an adatom diffusing on a missing-row reconstructed Platinum (110) surface. We develop a Transition Path Theory, showing that the activation energy is given by the minimum-energy trajectory which succeeds in the double-jump. We explicitly calculate this trajectory within an effective-medium molecular dynamics simulation. A cusp in the acceptance region leads to a sqrt{T} prefactor for the activated rate of double-jumps. Theory and numerical results agree

Selfduality for coupled Potts models on the triangular lattice

We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points

Avalanche Size Scaling in Sheared Three-Dimensional Amorphous Solid

We have studied the statistics of plastic rearrangement events in a simulated amorphous solid at T=0. Events are characterized by the energy release and the ``slip volume'', the product of plastic strain and system volume. Their distributions for a given system size $L$ appear to be exponential, but a characteristic event size cannot be inferred, because the mean values of these quantities increase as $L^{\alpha}$ with $\alpha \sim 3/2$. In contrast to results obtained in 2D models, we do not see simply connected avalanches. The exponent suggests a fractal shape of the avalanches, which is also evidenced by the mean fractal dimension and participation ratio.Comment: Accepted for publication in Physical Review Letter

Simulations of energetic beam deposition: from picoseconds to seconds

We present a new method for simulating crystal growth by energetic beam deposition. The method combines a Kinetic Monte-Carlo simulation for the thermal surface diffusion with a small scale molecular dynamics simulation of every single deposition event. We have implemented the method using the effective medium theory as a model potential for the atomic interactions, and present simulations for Ag/Ag(111) and Pt/Pt(111) for incoming energies up to 35 eV. The method is capable of following the growth of several monolayers at realistic growth rates of 1 monolayer per second, correctly accounting for both energy-induced atomic mobility and thermal surface diffusion. We find that the energy influences island and step densities and can induce layer-by-layer growth. We find an optimal energy for layer-by-layer growth (25 eV for Ag), which correlates with where the net impact-induced downward interlayer transport is at a maximum. A high step density is needed for energy induced layer-by-layer growth, hence the effect dies away at increased temperatures, where thermal surface diffusion reduces the step density. As part of the development of the method, we present molecular dynamics simulations of single atom-surface collisions on flat parts of the surface and near straight steps, we identify microscopic mechanisms by which the energy influences the growth, and we discuss the nature of the energy-induced atomic mobility

Variational QMC study of a Hydrogen atom in jellium with comparison to LSDA and LSDA-SIC solutions

A Hydrogen atom immersed in a finite jellium sphere is solved using variational quantum Monte Carlo (VQMC). The same system is also solved using density functional theory (DFT), in both the local spin density (LSDA) and self-interaction correction (SIC) approximations. The immersion energies calculated using these methods, as functions of the background density of the jellium, are found to lie within 1eV of each other with minima in approximately the same positions. The DFT results show overbinding relative to the VQMC result. The immersion energies also suggest an improved performance of the SIC over the LSDA relative to the VQMC results. The atom-induced density is also calculated and shows a difference between the methods, with a more extended Friedel oscillation in the case of the VQMC result.Comment: 16 pages, 9 Postscript figure

Monte Carlo Study of Short-Range Order and Displacement Effects in Disordered CuAu

The correlation between local chemical environment and atomic displacements in disordered CuAu alloy has been studied using Monte Carlo simulations based on the effective medium theory (EMT) of metallic cohesion. These simulations correctly reproduce the chemically-specific nearest-neighbor distances in the random alloy across the entire Cu\$_x\$Au\$_{1-x}\$ concentration range. In the random equiatomic CuAu alloy, the chemically specific pair distances depend strongly on the local atomic environment (i.e. fraction of like/unlike nearest neighbors). In CuAu alloy with short-range order, the relationship between local environment and displacements remains qualitatively similar. However the increase in short-range order causes the average Cu-Au distance to decrease below the average Cu-Cu distance, as it does in the ordered CuAuI phase. Many of these trends can be understood qualitatively from the different neutral sphere radii and compressibilities of the Cu and Au atoms.Comment: 9 pages, 5 figures, 2 table

A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N=100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the exponential running time ~ exp(0.245 N) provided by the hitherto best known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded. Version 3 shows that the worst-case running time is sub-exponential in the number of vertice

Logarithmic observables in critical percolation

Although it has long been known that the proper quantum field theory description of critical percolation involves a logarithmic conformal field theory (LCFT), no direct consequence of this has been observed so far. Representing critical bond percolation as the Q = 1 limit of the Q-state Potts model, and analyzing the underlying S_Q symmetry of the Potts spins, we identify a class of simple observables whose two-point functions scale logarithmically for Q = 1. The logarithm originates from the mixing of the energy operator with a logarithmic partner that we identify as the field that creates two propagating clusters. In d=2 dimensions this agrees with general LCFT results, and in particular the universal prefactor of the logarithm can be computed exactly. We confirm its numerical value by extensive Monte-Carlo simulations.Comment: 11 pages, 2 figures. V2: as publishe