Function Of Chemical Potential Research Articles

Dynamical mean-field theory for bosons

We discuss the recently developed bosonic dynamical mean-field theory (B-DMFT) framework, which maps a bosonic lattice model onto the self-consistent solution of a bosonic impurity model with coupling to a reservoir of normal and condensed bosons. The effective impurity action is derived in several ways: (i) as an approximation to the kinetic energy functional of the lattice problem, (ii) using a cavity approach and (iii) using an effective medium approach based on adding a one-loop correction to the self-consistently defined condensate. To solve the impurity problem, we use a continuous-time Monte Carlo algorithm based on the sampling of a perturbation expansion in the hybridization functions and the condensate wave function. As applications of the formalism, we present finite-temperature B-DMFT phase diagrams for the bosonic Hubbard model on a three-dimensional (3D) cubic and a 2D square lattice, the condensate order parameter as a function of chemical potential, critical exponents for the condensate, the approach to the weakly interacting Bose gas regime for weak repulsions and the kinetic energy as a function of temperature.

Properties on the edge: graphene edge energies, edge stresses, edge warping, and the Wulff shape of graphene flakes

It has been shown that the broken bonds of an unreconstructed graphene edge generate compressive edge stresses leading to edge warping. Here, we investigate edge energies and edge stresses of graphene nanoribbons with arbitrary orientations from armchair to zigzag, considering both flat and warped edge shapes in the presence and absence of hydrogen. We use the second generation reactive empirical bond order potential to calculate the edge energies and stresses for clean and hydrogenated edges. Using these energies, we perform a Wulff construction to determine the equilibrium shapes of flat graphene flakes as a function of hydrogen chemical potential. While edge stresses for clean, flat edges are compressive, they become tensile if allowed to warp. Conversely, we find that edge energies change little (∼1%) with edge warping. Hydrogenation of the edges virtually eliminates both the edge energy and edge stresses. For warped edges an approximately linear relationship is found between amplitudes and wavelengths. The equilibrium shape of a graphene flake is determined by the value of the hydrogen chemical potential. For very small (and large) values of it the flakes have a nearly hexagonal (dodecagon) shape with zigzag oriented edges, while for intermediate values graphene flakes are found with complex shapes.

Chlorination of the Cu(110) Surface and Copper Nanoparticles: A Density Functional Theory Study

The interaction of atomic chlorine with the Cu(110) surface is studied using density functional theory and ab initio atomistic thermodynamics. The calculated surface free energies of different Cl/Cu(110) structures as a function of chlorine chemical potential show that under ultrahigh-vacuum conditions, the c(2 × 2)-Cl structure is the most stable for coverages up to and including 1/2 ML, whereas the (2 × 3)-Cl and (1 × 4)-Cl configurations are the most stable at 2/3 and 3/4 ML coverages, respectively. It is also shown that although there are thermodynamically stable geometries for high (1 ML) coverage of Cl, these structures are only kinetically accessible. The morphology of a copper nanostructure terminated by low-index Cu surfaces in a chlorine environment has been predicted using a Wulff construction. It is found that the (111) facets dominate at low chlorine concentration, but as the chlorine concentration is increased, the (100) planes become predominant, resulting in a cubical crystal shape.

QCD Phase Diagram According to the Center Group

We study an effective theory for QCD at finite temperature and density which contains the leading center symmetric and center symmetry breaking terms. The effective theory is studied in a flux representation where the complex phase problem is absent and the model becomes accessible to Monte Carlo techniques also at finite chemical potential. We simulate the system by using a generalized Prokof'ev-Svistunov worm algorithm and compare the results to a low temperature expansion. The phase diagram is determined as a function of temperature, chemical potential, and quark mass. The shape and quark mass dependence of the phase boundaries are as expected for QCD. The transition into the deconfined phase is smooth throughout, without any discontinuities or critical points.

Towards a holographic model of color superconductivity

In this paper, we discuss the basic elements that should appear in a gravitational system that is dual to a confining gauge theory displaying color superconductivity at large baryon density. We consider a simple system with these minimal elements and show that for a range of parameters, the phase structure of this model as a function of temperature and baryon chemical potential exhibits phases that can be identified with confined, deconfined and color superconducting phases in the dual field theory. We find that the critical temperature at which the superconducting phase disappears is remarkably small (relative to the chemical potential). This small number arises from the dynamics and is unrelated to any small parameter in the model that we study. We discuss similar models that exhibit flavor superconductivity.

Thermodynamics of the 3D Hubbard Model on Approaching the Néel Transition

We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the Néel temperature by using cluster dynamical mean-field theory. In particular, we calculate the energy, entropy, density, double occupancy, and nearest-neighbor spin correlations as a function of chemical potential, temperature, and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle S/N ≈ 0.65(6) at U/t = 8 is sufficient to achieve a Néel state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.

De Haas–van Alphen effect in 2D systems: application to mono- and bilayer graphene

A generalization of the Shoenberg theory of de Haas–van Alphen magnetic oscillations in 2D metals to the case of electrons with arbitrary spectral dispersion is used to propose a method for determining the nature of charge carriers in the 2D conducting systems mono- and bilayer graphene. We analyze an analytical expression for the oscillating susceptibility as a function of chemical potential and determine its behavior for carriers with normal parabolic and Dirac-like linear spectra, which can be detected experimentally.

A nanoscale mechanism of hydrogen embrittlement in metals

The embrittlement of metallic systems by hydrogen is a widespread phenomenon but the precise role of hydrogen in this process is not well understood and predictive mechanisms are not available. Here, a new model is proposed wherein hydrogen accumulation around a microcrack tip prevents crack-tip dislocation emission or absorption, and thus suppresses crack-tip blunting and ductile fracture while promoting cleavage fracture. The conceptual model is demonstrated via atomistic simulations of the evolution of equilibrium hydrogen distributions around a crack tip in Ni under increasing applied load, followed by measurement of dislocation emission and/or cleavage. These analyses are performed in single crystal Ni and for several tilt grain boundaries and several initial crack notch radii, using molecular statics and embedded-atom-method interatomic potentials. A kinetic analysis is used to calculate the size of the “nanohydride” formed at the crack tip as a function of hydrogen chemical potential, temperature, H diffusion rate, load level, and loading rate. Combining the kinetic analysis with the deformation/fracture analysis generates a mechanism map that predicts a ductile-to-brittle transition as a function of material and loading parameters. The mechanism map is applied to predict H embrittlement of unnotched tensile specimens of Ni, and the predictions and experiments match well for material parameter values expected to be pertinent in these materials. The mechanism proposed and validated here directly identifies the role of H in driving a change in fracture mode and toughness as a function of material and loading parameters.

Stability of graphene oxide phases from first-principles calculations

We determine the energy diagram of graphene oxides (GOs) as a function of oxygen and hydrogen chemical potentials by systematic first-principles calculations. The diagram reveals that thermodynamically stable GOs can exist only in stringent growth conditions in the form of hydroxyl, epoxy, or mixed hydroxyl/epoxy phases. There is no mixed phase with $s{p}^{2}$ carbon because of substrate relaxation, which is unique to two-dimensional system with little coupling in the third direction such as graphene. The mixed phase observed experimentally is interpreted instead, in terms of a kinetic stability of nonequilibrium grown GOs against phase separation.

Hyperfine interaction in graphene: The relevance for spintronics

AbstractWe study the nuclear magnetic resonance (NMR) properties of graphene. The interaction between nuclear spins and the orbital motion of Dirac electrons is strongly modified by the linear electronic dispersion with respect to its canonical form. The NMR shift and spin‐lattice relaxation time are calculated as function of temperature, chemical potential, and magnetic field for clean and impure graphene, and three distinct regimes are identified: Fermi‐, Dirac‐gas, and extreme quantum limit (EQL) behaviors. A critical spectrometer assessment shows that NMR is within reach for fully 13C enriched graphene of reasonable size.

Unidirectional hopping transport of interacting particles on a finite chain

Particle transport through an open, discrete one-dimensional channel against a mechanical or chemical bias is analyzed within a master equation approach. The channel, externally driven by time-dependent site energies, allows multiple occupation due to the coupling to reservoirs. Performance criteria and optimization of active transport in a two-site channel are discussed as a function of reservoir chemical potentials, the load potential, interparticle interaction strength, driving mode, and driving period. Our results, derived from exact rate equations, are used in addition to test a previously developed time-dependent density functional theory, suggesting a wider applicability of that method in investigations of many particle systems far from equilibrium.

Influence of some foreign metal ions on crystal growth kinetics of brushite (CaHPO 4·2H 2O)

Brushite, CaHPO 4·2H 2O, has been precipitated at 25 °C in the presence of Mg 2+, Ba 2+ or Cu 2+ at concentrations up to 0.5 mM. When initial pH is sufficiently low to exclude nanocrystalline apatite as the initial solid phase, overall crystal growth rate may be determined from simple mass crystallization by recording pH as function of time. A combination of surface nucleation (birth-and-spread) and spiral (BCF) growth was found. Edge free energy was determined from the former contribution and was found to be a linear function of chemical potential of the additive, indicating constant adsorption over a wide range of additive concentrations. Average distances between adsorbed additive ions as calculated from slopes of plots are compatible with lattice parameters of brushite: 0.54 nm for Mg 2+, 0.43 nm for Ba 2+ and 0.86 nm for Cu 2+. With the latter a sharp decrease in growth rate occurred early in the crystallization process, followed by an equally sharp increase to the previous level. When interpreted in terms of the Cabrera–Vermilyea theory of crystal growth inhibition, the results are consistent with an average distance between Cu ions of 0.88 nm, in perfect agreement with the above value.

Inhomogeneous structures in holographic superfluids. II. Vortices

We study vortex solutions in a holographic model of Herzog, Hartnoll, and Horowitz, with a vanishing external magnetic field on the boundary, as is appropriate for vortices in a superfluid. We study relevant length scales related to the vortices and how the charge density inside the core of the vortex behaves as a function of temperature or chemical potential. We extract the critical superfluid velocity from the vortex solutions, study how it behaves as a function of the temperature, and compare it to earlier studies and to the Landau criterion. We also comment on the possibility of a Berezinskii-Kosterlitz-Thouless vortex confinement-deconfinement transition.

Modeling the thermopower of ballistic graphene ribbons

We investigate the thermopower of ballistic graphene ribbons using linear response theory and the Landauer formalism. The dependence of thermopower on temperature and chemical potential is investigated and the obtained results are qualitatively in agreement with many features recently observed in thermoelectric measurements on high mobility graphene ribbons. Fabry–Perot oscillations in the thermopower of short nannoribbons as a function of chemical potential, at finite temperatures, are revealed. The validity of generalized Mott's relation between thermopower and temperature dependent conductivity, is investigated in a wide range of temperatures.

Nuclear Physics from Lattice QCD at Strong Coupling

We study numerically the strong coupling limit of lattice QCD with one flavor of massless staggered quarks. We determine the complete phase diagram as a function of temperature and chemical potential, including a tricritical point. We clarify the nature of the low temperature dense phase, which is strongly bound "nuclear" matter. This strong binding is explained by the nuclear potential, which we measure. Finally, we determine, from this first-principles limiting case of QCD, the masses of "atomic nuclei" up to A=12 "carbon".

Statistical model of defects in Al-H system

Vacancy and hydrogen concentrations in Al were determined by first-principles calculations and statistical-mechanics modeling, as functions of temperature and hydrogen chemical potential ${\ensuremath{\mu}}_{\text{H}}$. Formation energies of Al vacancies, H interstitials, and H-Al vacancy complexes were obtained from first-principles calculations. The statistical-mechanics model incorporated these energies and included configurational entropy contributions through the grand canonical ensemble. We found that the hydrogen chemical potential under different chemical environments plays an important role in determining the relative equilibrium defect concentrations in the Al-H system. Estimates of the hydrogen chemical potential during hydrogen charging were obtained experimentally. At comparable the calculated concentrations are consistent with these values, along with previously reported measurements of hydrogen concentration.

First-Principles and Quantum Transport Studies of Metal-Graphene End Contacts

AbstractMetal-graphene contact is of critical significance in graphene-based nanoelectronics. There are two possible metal-graphene contact geometries: side-contact and end-contact. In this paper, we apply first-principles calculations to study metal-graphene end-contact for these three commonly used electrode metals (Ni, Pd and Ti) and find that they have distinctive stable end-contact geometries with graphene. Transport properties of these metal-graphene-metal (M-G-M) end-contact structures are investigated by density functional theory non-equilibrium Green’s function (DFT-NEGF) algorithm. The Transmission as a function of chemical potential (E-EF) shows asymmetric curves relative to the Fermi level. Transmission curves of Ni-G-Ni and Ti-G-Ti contact structures indicate that bulk graphene sheet is n-doped by Ni and Ti electrodes, but that of Pd-G-Pd shows p-doping of graphene by Pd electrode. The contact behaviors of these electrodes are consistent with experimental observations.

The sign problem across the QCD phase transition

The average phase factor of the QCD fermion determinant signals the strength of the QCD sign problem. We compute the average phase factor as a function of temperature and baryon chemical potential using a two-flavor NJL model. This allows us to study the strength of the sign problem at and above the chiral transition. It is discussed how the $U_A(1)$ anomaly affects the sign problem. Finally, we study the interplay between the sign problem and the endpoint of the chiral transition.

The influence of micelle formation on the stability of colloid surfactant mixtures

The stability of colloidal dispersions can be severely affected by the presence of surfactants. Because surfactants can adsorb at colloidal surfaces as well as form micelles, one can expect an interplay between both phenomena. Using grand-canonical coarse-grained Monte Carlo simulations on surfactant solutions confined between two surfaces, we investigate how adsorption and micelle formation affects the effective interaction between two colloidal particles, and hence, the stability of the colloidal dispersion. For solvophilic colloidal surfaces, we observe a short-ranged oscillatory solvation pressure that is hardly affected by the presence of surfactants in the system. The effective surface-surface interaction, however, reveals a decrease in solvophilic stabilization as a function of surfactant chemical potential. For solvophobic surfaces, we find that the capillary evaporation observed in a confined pure solvent, is counteracted by the addition of surfactants. Around the critical micelle concentration (CMC), the surface-surface interaction even becomes repulsive, enhancing stabilization of the colloidal dispersion. In contrast, the formation of micelles at concentrations above the CMC causes an additional depletion effect, resulting in an effective attraction, which in turn can destabilize a colloidal dispersion.

Formation and migration of charged native point defects inMgH2: First-principles calculations

Using first-principles calculations we have investigated the possible native point defects in bulk ${\text{MgH}}_{2}$. Due to the interest in this material for hydrogen storage, we have paid particular attention to hydrogen-related defects that are likely to be involved in the absorption and release kinetics of hydrogen. We have considered neutral and charged defects and calculated formation energies as a function of Fermi-level position and hydrogen chemical potential. In the absence of impurities, we find that under extreme H-poor conditions the lowest-energy defects are positively and negatively charged hydrogen vacancies (${V}_{\text{H}}^{+}$ and ${V}_{\text{H}}^{\ensuremath{-}}$). Under extreme H-rich conditions, the lowest-energy defects are ${V}_{\text{H}}^{+}$, negatively charged hydrogen interstitials $({\text{H}}_{i}^{\ensuremath{-}})$, and negatively charged Mg vacancies ${V}_{\text{Mg}}^{2\ensuremath{-}}$. The defects are characterized by unusually large local structural rearrangements. The hydrogen-related defects are also highly mobile, with a lowest migration barrier of less than 0.10 eV for ${\text{H}}_{i}^{\ensuremath{-}}$ and ${\text{H}}_{2i}$, and a highest barrier of 0.63 eV for ${V}_{\text{H}}^{\ensuremath{-}}$. By combining the calculated formation energies with migration barriers, we find that the lowest activation energy for self-diffusion is about 1.48 eV under H-poor conditions. The consequences of these results for the hydrogenation and dehydrogenation kinetics are discussed.