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T. L. Einstein

Publications and source records attributed to T. L. Einstein.

At least 19 recordsLinked to original sources
arXiv2018

Strain Controlled Magnetic and Optical Properties of Monolayer 2H-TaSe$_2$

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.

cond-mat.mtrl-sci↗
arXiv2015

From atoms to steps: The microscopic origins of crystal evolution

The BCF theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect to a facet plane; thus, the BCF theory views such systems as composed of staircase-like structures of steps separating terraces. Adsorbed atoms (adatoms), which are represented by a continuous density, diffuse on terraces, and steps move by absorbing or emitting these adatoms. Here we shed light on the microscopic origins of the BCF theory by deriving a simple, one-dimensional (1D) version of the theory from an atomistic, kinetic restricted solid-on- solid (KRSOS) model without external material deposition. We define the time-dependent adatom density and step position as appropriate ensemble averages in the KRSOS model, thereby exposing the non-equilibrium statistical mechanics origins of the BCF theory. Our analysis reveals that the BCF theory is valid in a low adatom-density regime, much in the same way that an ideal gas approximation applies to dilute gasses. We find conditions under which the surface remains in a low-density regime and discuss the microscopic origin of corrections to the BCF model.

cond-mat.mes-hall↗
arXiv2014

How "hot precursors" modify island nucleation: A rate-equations model

We propose a novel island nucleation and growth model explicitly including transient (ballistic) mobility of the monomers deposited at rate $F$, assumed to be in a hot precursor state before thermalizing. In limiting regimes, corresponding to fast (diffusive) and slow (ballistic) thermalization, the island density $N$ obeys scaling $N \propto F^α$. In between is found a rich, complex behavior, with various distinctive scaling regimes, characterized by effective exponents $α_{\rm eff}$ and activation energies that we compute exactly. Application to $N(F,T)$ of recent organic-molecule deposition experiments yields an excellent fit.

cond-mat.mes-hall↗
arXiv2013

Dynamical Scaling Implications of Ferrari, Prähofer, and Spohn's Remarkable Spatial Scaling Results for Facet-Edge Fluctuations

Spurred by theoretical predictions from Spohn and coworkers [Phys. Rev. E {\bf 69}, 035102(R) (2004)], we rederived and extended their result heuristically as well as investigated the scaling properties of the associated Langevin equation in curved geometry with an asymmetric potential. With experimental colleagues we used STM line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces. The correlation functions was shown to go as $t^{0.15(3)}$ decidedly different from the $t^{0.26(2)}$ behavior for fluctuations of isolated steps. From the exponents, we were able to categorize the universality, confirming the prediction that the non-linear term of the KPZ equation, long known to play a central role in non-equilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy. We also considered, with modest Monte Carlo simulations, a toy model to show that confinement of a step by another nearby step can modify as predicted the scaling exponents of the step's fluctuations. This paper is an expansion of a celebratory talk at the 95$^{\rm th}$ Rutgers Statistical Mechanics Conference, May 2006.

cond-mat.stat-mech↗
arXiv2013

Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications

We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) $P(s)=a s^β\exp(-b s^2)$, where $s$ is the CZ area divided by its average value. This approach offers arguably the best method to find the critical nucleus size $i$, since $β\approx i + 2$. Various analytical and numerical investigations, which we discuss, show that the simple GWD expression is inadequate in the tails of the distribution, it does account well for the central regime $0.5 < s < 2$, where the data is sufficiently large to be reliably accessible experimentally. We summarize and catalog the many experiments in which this method has been applied.

cond-mat.mes-hall↗
arXiv2013

Interacting Steps With Finite-Range Interactions: Analytical Approximation and Numerical Results

We calculate an analytical expression for the terrace-width distribution $P(s)$ for an interacting step system with nearest and next nearest neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent 1D system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions $q$ on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

cond-mat.stat-mech↗
arXiv2012

Princess and the Pea at the nanoscale: Wrinkling and delamination of graphene on nanoparticles

Thin membranes exhibit complex responses to external forces or geometrical constraints. A familiar example is the wrinkling, exhibited by human skin, plant leaves, and fabrics, resulting from the relative ease of bending versus stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest known membrane, deposited on a silica substrate decorated with silica nanoparticles. At small nanoparticle density monolayer graphene adheres to the substrate, detached only in small regions around the nanoparticles. With increasing nanoparticle density, we observe the formation of wrinkles which connect nanoparticles. Above a critical nanoparticle density, the wrinkles form a percolating network through the sample. As the graphene membrane is made thicker, global delamination from the substrate is observed. The observations can be well understood within a continuum elastic model and have important implications for strain-engineering the electronic properties of graphene.

cond-mat.mes-hall↗
arXiv2011

Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)

The response of the Cu(111) Shockley surface state to an external electrical field is characterized by combining a density-functional theory calculation for a slab geometry with an analysis of the Kohn-Sham wavefunctions. Our analysis is facilitated by a decoupling of the Kohn-Sham states via a rotation in Hilbert space. We find that the surface state displays isotropic dispersion, quadratic until the Fermi wave vector but with a significant quartic contribution beyond. We calculate the shift in energetic position and effective mass of the surface state for an electrical field perpendicular to the Cu(111) surface; the response is linear over a broad range of field strengths. We find that charge transfer occurs beyond the outermost copper atoms and that accumulation of electrons is responsible for a quarter of the screening of the electrical field. This allows us to provide well-converged determinations of the field-induced changes in the surface state for a moderate number of layers in the slab geometry.

cond-mat.mtrl-sci↗
arXiv2011

Voronoi Cell Patterns: theoretical model and applications

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We use our model to describe the Voronoi cell patterns of several systems. Specifically, we study the island nucleation with irreversible attachment, the 1D car parking problem, the formation of second-level administrative divisions, and the pattern formed by the Paris Métro stations.

cond-mat.stat-mech↗
arXiv2011

Mean-Field Approximation for Spacing Distribution Functions in Classical Systems

We propose a mean-field method to calculate approximately the spacing distribution functions $p^{(n)}(s)$ in 1D classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation (IIA) and the extended Wigner surmise (EWS). In our mean-field approach, $p^{(n)}(s)$ is calculated from a set Langevin equations which are decoupled by using a mean-field approximation. We found that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples in which the three methods mentioned previously give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

cond-mat.stat-mech↗
arXiv2011

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density $p^{XY}_{n}(x,y)$, which represents the probability density to have nucleation at position $x$ within a gap of size $y$. Our proposed functional form for $p^{XY}_{n}(x,y)$ describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

cond-mat.stat-mech↗
arXiv2009

Rings sliding on a honeycomb network: Adsorption contours, interactions, and assembly of benzene on Cu(111)

Using a van der Waals density functional (vdW-DF) [Phys. Rev. Lett. 92, 246401 (2004)], we perform ab initio calculations for the adsorption energy of benzene (Bz) on Cu(111) as a function of lateral position and height. We find that the vdW-DF inclusion of nonlocal correlations (responsible for dispersive interactions) changes the relative stability of eight binding-position options and increases the binding energy by over an order of magnitude, achieving good agreement with experiment. The admolecules can move almost freely along a honeycomb web of "corridors" passing between fcc and hcp hollow sites via bridge sites. Our diffusion barriers (for dilute and two condensed adsorbate phases) are consistent with experimental observations. Further vdW-DF calculations suggest that the more compact (hexagonal) Bz-overlayer phase, with lattice constant a = 6.74 Å, is due to direct Bz-Bz vdW attraction, which extends to ~8 Å. We attribute the second, sparser hexagonal Bz phase, with a = 10.24 Å, to indirect electronic interactions mediated by the metallic surface state on Cu(111). To support this claim, we use a formal Harris-functional approach to evaluate nonperturbationally the asymptotic form of this indirect interaction. Thus, we can account well for benzene self-organization on Cu(111).

cond-mat.mes-hall↗
arXiv2008

Effect of impurities on pentacene island nucleation

Pentacenequinone (PnQ) impurities have been introduced into a pentacene source material in a controlled manner to quantify the relative effects of the impurity content on grain boundary structure and thin film nucleation. Atomic force microscopy (AFM) has been employed to directly characterize films grown using 0.0-7.5% PnQ by weight in the source material. Analysis of the distribution of capture zones areas of submonolayer islands as a function of impurity content shows that for large PnQ content the critical nucleus size for forming a Pn island is smaller than for low PnQ content. This result indicates a favorable energy for formation of Pn-PnQ complexes, which in turn suggests that the primary effect of PnQ on Pn mobility may arise from homogeneous distribution of PnQ defects.

cond-mat.mtrl-sci↗
arXiv2008

Relaxation of Terrace-width Distributions: Physical Information from Fokker-Planck Time

Recently some of us have constructed a Fokker-Planck formalism to describe the equilibration of the terrace-width distribution of a vicinal surface from an arbitrary initial configuration. However, the meaning of the associated relaxation time, related to the strength of the random noise in the underlying Langevin equation, was rather unclear. Here we present a set of careful kinetic Monte Carlo simulations that demonstrate convincingly that the time constant shows activated behavior with a barrier that has a physically plausible dependence on the energies of the governing microscopic model. Furthermore, the Fokker-Planck time at least semiquantitatively tracks the actual physical time.

cond-mat.mtrl-sci↗
arXiv2007

Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior

In studies of island nucleation and growth, the distribution of capture zones, essentially proximity cells, can give more insight than island-size distributions. In contrast to the complicated expressions, ad hoc or derived from rate equations, usually used, we find the capture-zone distribution can be described by a simple expression generalizing the Wigner surmise from random matrix theory that accounts for the distribution of spacings in a host of fluctuation phenomena. Furthermore, its single adjustable parameter can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory sheds light on the result.

cond-mat.stat-mech↗
arXiv2006

Analytic Formulas for the Orientation Dependence of Step Stiffness and Line Tension: Key Ingredients for Numerical Modeling

We present explicit analytic, twice-differentiable expressions for the temperature-dependent anisotropic step line tension and step stiffness for the two principal surfaces of face-centered-cubic crystals, the square {001} and the hexagonal {111}. These expressions improve on simple expressions that are valid only for low temperatures and away from singular orientations. They are well suited for implementation into numerical methods such as finite-element simulation of step evolution.

cond-mat.stat-mech↗
arXiv2006

Correlations in nano-scale step fluctuations: comparison of simulation and experiments

We analyze correlations in step-edge fluctuations using the Bortz-Kalos-Lebowitz kinetic Monte Carlo algorithm, with a 2-parameter expression for energy barriers, and compare with our VT-STM line-scan experiments on spiral steps on Pb(111). The scaling of the correlation times gives a dynamic exponent confirming the expected step-edge-diffusion rate-limiting kinetics both in the MC and in the experiments. We both calculate and measure the temperature dependence of (mass) transport properties via the characteristic hopping times and deduce therefrom the notoriously-elusive effective energy barrier for the edge fluctuations. With a careful analysis we point out the necessity of a more complex model to mimic the kinetics of a Pb(111) surface for certain parameter ranges.

cond-mat.stat-mech↗