Genuine converging solution of self-consistent field equations for extended many-electron systems

Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set of equations, one believes in the iterative method for the solution that should consist in consecutive improvement of the potential and the electron density until the self-consistency is attained. Though this approach exists for a long time there are two grave problems accompanying its implementation to infinitely extended systems. The first of them is related with the Poisson equation and lies in possible incompatibility of the boundary conditions for the potential with the electron density distribution. The analysis of this difficulty and suggested resolution are presented for both infinite conducting systems in jellium approximation and periodic solids. It provides the existence of self-consistent solution for the potential at every iteration step due to realization of a screening effect. The second problem results from the existence of continuous spectrum of Hamiltonian eigenvalues for unbounded systems. It needs to have a definition of Hilbert space basis with eigenfunctions of continuous spectrum as elements, which would be convenient in numerical applications. The definition of scalar product specifying the Hilbert space is proposed that incorporates a limiting transition. It provides self-adjointness of Hamiltonian and, respectively, the orthogonality of eigenfunctions corresponding to the different eigenvalues. In addition, it allows to normalize them effectively to delta-function and to prove in the general case the orthogonality of the 'right' and 'left' eigenfunctions belonging to twofold degenerate eigenvalues.Comment: 12 pages. Reported on Interdisciplinary Workshop "Nonequilibrium Green's Functions III", August 22 - 26, 2005, University Kiel, Germany. To be published in Journal of Physics: Conference Series, 2006; Typos in Eqs. (37), (53) and (54) are corrected. The content of the footnote is changed. Published version available free online at http://www.iop.org/EJ/abstract/1742-6596/35/1/01

The Nature of Electronic States in Atomically Thin MoS2 Field-Effect Transistors

We present low temperature electrical transport experiments in five field effect transistor devices consisting of monolayer, bilayer and trilayer MoS2 films, mechanically exfoliated onto Si/SiO2 substrate. Our experiments reveal that the electronic states in all films are localized well up to the room temperature over the experimentally accessible range of gate voltage. This manifests in two dimensional (2D) variable range hopping (VRH) at high temperatures, while below \sim 30 K the conductivity displays oscillatory structures in gate voltage arising from resonant tunneling at the localized sites. From the correlation energy (T0) of VRH and gate voltage dependence of conductivity, we suggest that Coulomb potential from trapped charges in the substrate are the dominant source of disorder in MoS2 field effect devices, which leads to carrier localization as well.Comment: 10 pages, 5 figures; ACS Nano (2011

Mechanistic insights into the reversible lithium storage in an open porous carbon via metal cluster formation in all solid-state batteries

Porous carbons are promising anode materials for next generation lithium batteries due to their large lithium storage capacities. However, their high voltage slope during lithiation and delithiation as well as capacity fading due to intense formation of solid electrolyte interphase (SEI) limit their gravimetric and volumetric energy densities. Herein we compare a microporous carbide-derived carbon material (MPC) as promising future anode for all solid-state batteries with a commercial high-performance hard carbon anode. The MPC obtains high and reversible lithiation capacities of 1000 mAh g−1carbon in half-cells exhibiting an extended plateau region near 0 V vs. Li/Li+ preferable for full-cell application. The well-defined micro porosity of the MPC with a specific surface area of >1500 m2 g−1 combines well with the argyrodite-type electrolyte (Li6PS5Cl) suppressing extensive SEI formation to deliver high coulombic efficiencies. Preliminary full-cell measurements vs. nickel-rich NMC-cathodes (LiNi0.9Co0.05Mn0.05O2) provide a considerably improved average potential of 3.76 V leading to a projected energy density as high as 449 Wh kg−1 and reversible cycling for more than 60 cycles. 7Li Nuclear Magnetic Resonance spectroscopy was combined with ex-situ Small Angle X-ray Scattering to elucidate the storage mechanism of lithium inside the carbon matrix. The formation of extended quasi-metallic lithium clusters after electrochemical lithiation was revealed

Fully sp²‐carbon‐linked crystalline two‐dimensional conjugated polymers: insight into 2D poly(phenylenecyanovinylene) formation and their optoelectronic properties

Cyano‐substituted polyphenylene vinylenes (PPVs) have been in the focus of research for several decades due to their interesting optoelectronic properties and potential applications in organic electronics. With the advent of organic two‐dimensional (2D) crystals, the question arose how the chemical and optoelectronic advantages of PPVs evolve in 2D compared to their linear counterparts. In this work, we present the efficent synthesis of two novel 2D fully sp²‐carbon‐linked crystalline PPVs and investigate the essentiality of inorganic bases for their catalytic formation. Notably, among all bases screened, cesium carbonate (Cs₂CO₃) plays a crucial role and enables reversibility in the first step with subsequent structure locking by formation of a C=C double bond to maintain crystallinity, which is supported by density functional theory (DFT) calculation. We propose a quantifiable energy diagram of a “quasi‐reversible reaction” which allows to identify further suitable C‐C bond formation reactions for 2D polymerizations. Moreover, we delineate the narrowing of the HOMO‐LUMO gap by expanding conjugation into two dimensions. To enable environmentally benign processing, we further perform the post‐modification of 2D PPVs, which renders stable dispersions in the aqueous phase

Self-consistent solution of Kohn-Sham equations for infinitely extended systems with inhomogeneous electron gas

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves iterations with alternate solving of the Poisson and Schr\"{o}dinger equations. One of problems of such an approach is that the charge distribution renewed by means of the Schr\"{o}dinger equation solution does not conform to boundary conditions of Poisson equation for Coulomb potential. The resulting instability or even divergence of iterations manifests itself most appreciably in the case of infinitely extended systems. The published attempts to deal with this problem are reduced in fact to abandoning the original iterative method and replacing it with some approximate calculation scheme, which is usually semi-empirical and does not permit to evaluate the extent of deviation from the exact solution. In this work, we realize the iterative scheme of solving the Kohn-Sham equations for extended systems with inhomogeneous electron gas, which is based on eliminating the long-range character of Coulomb interaction as the cause of tight coupling between charge distribution and boundary conditions. The suggested algorithm is employed to calculate energy spectrum, self-consistent potential, and electrostatic capacitance of the semi-infinite degenerate electron gas bounded by infinitely high barrier, as well as the work function and surface energy of simple metals in the jellium model. The difference between self-consistent Hartree solutions and those taking into account the exchange-correlation interaction is analyzed. The case study of the metal-semiconductor tunnel contact shows this method being applied to an infinitely extended system where the steady-state current can flow.Comment: 38 pages, 9 figures, to be published in ZhETF (J. Exp. Theor. Phys.

Transport properties of copper phthalocyanine based organic electronic devices

Ambipolar charge carrier transport in Copper phthalocyanine (CuPc) is studied experimentally in field-effect transistors and metal-insulator-semiconductor diodes at various temperatures. The electronic structure and the transport properties of CuPc attached to leads are calculated using density functional theory and scattering theory at the non-equilibrium Green's function level. We discuss, in particular, the electronic structure of CuPc molecules attached to gold chains in different geometries to mimic the different experimental setups. The combined experimental and theoretical analysis explains the dependence of the mobilityand the transmission coefficient on the charge carrier type (electrons or holes) and on the contact geometry. We demonstrate the correspondence between our experimental results on thick films and our theoretical studies of single molecule contacts. Preliminary results for fluorinated CuPc are discussed.Comment: 18 pages, 16 figures; to be published in Eur. Phys. J. Special Topic

New mechanism to cross the phantom divide

Recently, type Ia supernovae data appear to support a dark energy whose equation of state $w$ crosses -1, which is a much more amazing problem than the acceleration of the universe. We show that it is possible for the equation of state to cross the phantom divide by a scalar field in the gravity with an additional inverse power-law term of Ricci scalar in the Lagrangian. The necessary and sufficient condition for a universe in which the dark energy can cross the phantom divide is obtained. Some analytical solutions with $w<-1$ or $w>-1$ are obtained. A minimal coupled scalar with different potentials, including quadratic, cubic, quantic, exponential and logarithmic potentials are investigated via numerical methods, respectively. All these potentials lead to the crossing behavior. We show that it is a robust result which is hardly dependent on the concrete form of the potential of the scalar.Comment: 11 pages, 5 figs, v3: several references added, to match the published versio

Structural Mechanism of Laforin Function in Glycogen Dephosphorylation and Lafora Disease

Glycogen is the major mammalian glucose storage cache and is critical for energy homeostasis. Glycogen synthesis in neurons must be tightly controlled due to neuronal sensitivity to perturbations in glycogen metabolism. Lafora disease (LD) is a fatal, congenital, neurodegenerative epilepsy. Mutations in the gene encoding the glycogen phosphatase laforin result in hyperphosphorylated glycogen that forms water-insoluble inclusions called Lafora bodies (LBs). LBs induce neuronal apoptosis and are the causative agent of LD. The mechanism of glycogen dephosphorylation by laforin and dysfunction in LD is unknown. We report the crystal structure of laforin bound to phosphoglucan product, revealing its unique integrated tertiary and quaternary structure. Structure-guided mutagenesis combined with biophysical and biochemical analyses reveal the basis for normal function of laforin in glycogen metabolism. Analyses of LD patient mutations define the mechanism by which subsets of mutations disrupt laforin function. These data provide fundamental insights connecting glycogen metabolism to neurodegenerative disease

Towards analytical typologies of plot systems: quantitative profile of five European cities

The importance of the plot (also referred to as ‘property’) as one of the fundamental elements of urban form is well recognized within the field of urban morphology. Despite the fact that it is often described as the basic element in the pattern of land divisions, which are essential as organizational frameworks for urban form, studies offering comprehensive descriptions and classifications of plot systems are quite scant. The aim of the paper is to introduce a classification of plot systems into typologies based on five European cities, in order to distinguish particular spatial differences and similarities in terms of their plot structure. The proposed typologies are developed using unsupervised k-means cluster analysis based on numeric attributes derived from central theories in urban morphology. The introduced typologies are essentially configurational, allowing collective systematic properties of plot systems to be captured. Numeric attributes include plot differentiation (or plot size), plot frontage and compactness ratio, corresponding to essential qualities of plot systems such as the capacity to carry differences in space, the ability to operate as interface between street and building and providing a framework for evolution of built form over time. All three attributes are translated into configurational measures in order to capture the context of the plot system, rather than the parameters of individual plots. The combination of these deductively defined variables with algorithmically defined classification methods results in seven plot types that can be used to scale up traditional urban morphological analysis to whole city regions and conduct substantial comparison of patterns within, but also between these regions. Further, it also makes it possible to describe commonly recognized plot patterns and discover new ones