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Kohn-Sham Exchange Potential for a Metallic Surface

The behavior of the surface barrier that forms at the metal-vacuum interface is important for several fields of surface science. Within the Density Functional Theory framework, this surface barrier has two non-trivial components: exchange and correlation. Exact results are provided for the exchange component, for a jellium metal-vacuum interface, in a slab geometry. The Kohn-Sham exact-exchange potential $V_{x}(z)$ has been generated by using the Optimized Effective Potential method, through an accurate numerical solution, imposing the correct boundary condition. It has been proved analytically, and confirmed numerically, that $V_{x}(z\to \infty)\to - e^{2}/z$; this conclusion is not affected by the inclusion of correlation effects. Also, the exact-exchange potential develops a shoulder-like structure close to the interface, on the vacuum side. The issue of the classical image potential is discussed.Comment: Phys. Rev. Lett. (to appear

The quenching of compressible edge states around antidots

We provide a systematic quantitative description of the edge state structure around a quantum antidot in the integer quantum Hall regime. The calculations for spinless electrons within the Hartree approximation reveal that the widely used Chklovskii et al. electrostatic description greatly overestimates the widths of the compressible strips; the difference between these approaches diminishes as the size of the antidot increases. By including spin effects within density functional theory in the local spin-density approximation, we demonstrate that the exchange interaction can suppress the formation of compressible strips and lead to a spatial separation between the spin-up and spin-down states. As the magnetic field increases, the outermost compressible strip, related to spin-down states starts to form. However, in striking contrast to quantum wires, the innermost compressible strip (due to spin-up states) never develops for antidots.Comment: submitted to Phys. Rev. Let

Magnetosubband and edge state structure in cleaved-edge overgrown quantum wires

We provide a systematic quantitative description of the structure of edge states and magnetosubband evolution in hard wall quantum wires in the integer quantum Hall regime. Our calculations are based on the self-consistent Green's function technique where the electron- and spin interactions are included within the density functional theory in the local spin density approximation. We analyze the evolution of the magnetosubband structure as magnetic field varies and show that it exhibits different features as compared to the case of a smooth confinement. In particularly, in the hard-wall wire a deep and narrow triangular potential well (of the width of magnetic length $l_B$) is formed in the vicinity of the wire boundary. The wave functions are strongly localized in this well which leads to the increase of the electron density near the edges. Because of the presence of this well, the subbands start to depopulate from the central region of the wire and remain pinned in the well region until they are eventually pushed up by increasing magnetic field. We also demonstrate that the spin polarization of electron density as a function of magnetic field shows a pronounced double-loop pattern that can be related to the successive depopulation of the magnetosubbands. In contrast to the case of a smooth confinement, in hard-wall wires the compressible strips do not form in the vicinity of wire boundaries and spatial spin separation between spin-up and spin-down states near edges is absent.Comment: 9 pages, submitted to Phys. Rev.

Conceptualising 'the relationship' in intensive key worker support as a therapeutic medium

Across various welfare and justice systems, intensive key worker support is a model of working considered effective for individuals and families identified as having multiple and complex needs. The high profile 'troubled families' programme in England is the most recent prominent example of such a model. The key worker role is to assess an individual’s needs, carry out support planning, provide and/or co-ordinate the delivery of supportive interventions and complete care plan reviews. This requires the key worker to work on a one-to-one basis with individuals which, in turn, demands the ability to form effective relationships. In this paper and using evidence from a number of studies, I look at how the key worker-client relationship is developed and maintained. I examine the skills, processes and communication strategies that allow key workers to engage clients, build relationships and drive change. I also explore the notion that the key worker-service user relationship is itself a ‘therapeutic’ medium and is therefore a productive practice in its own right. The paper suggests that while key workers might not be trained therapists or counsellors, they might be equipped to address some emotional challenges that individuals with complex needs face and build therapeutic relationships with them

National and Regional Impacts of U.S. Agricultural Exports

International Trade, Output, Employment, Exports, International Relations/Trade, Q10, Q11, Q13, Q17,

Novel properties of the Kohn-Sham exchange potential for open systems: application to the two-dimensional electron gas

The properties of the Kohn-Sham (KS) exchange potential for open systems in thermodynamical equilibrium, where the number of particles is non-conserved, are analyzed with the Optimized Effective Potential (OEP) method of Density Functional Theory (DFT) at zero temperature. The quasi two-dimensional electron gas (2DEG) is used as an illustrative example. The main findings are that the KS exchange potential builds a significant barrier-like structure under slight population of the second subband, and that both the asymptotic value of the KS exchange potential and the inter-subband energy jump discontinuously at the one-subband (1S) -> two-subband (2S) transition. The results obtained in this system offer new insights on open problems of semiconductors, such as the band-gap underestimation and the band-gap renormalization by photo-excited carriers.Comment: 7 pages, 3 figures, uses epl.cls(included), accepted for publication in Europhysics Letter

Electron Transport Through Molecules: Self-consistent and Non-self-consistent Approaches

A self-consistent method for calculating electron transport through a molecular device is proposed. It is based on density functional theory electronic structure calculations under periodic boundary conditions and implemented in the framework of the nonequilibrium Green function approach. To avoid the substantial computational cost in finding the I-V characteristic of large systems, we also develop an approximate but much more efficient non-self-consistent method. Here the change in effective potential in the device region caused by a bias is approximated by the main features of the voltage drop. As applications, the I-V curves of a carbon chain and an aluminum chain sandwiched between two aluminum electrodes are calculated -- two systems in which the voltage drops very differently. By comparing to the self-consistent results, we show that this non-self-consistent approach works well and can give quantitatively good results.Comment: 11 pages, 10 figure