Signatures of Discontinuity in the Exchange-Correlation Energy Functional Derived from the Subband Electronic Structure of Semiconductor Quantum Wells

The discontinuous character of the exact exchange-correlation $(xc)$ energy functional of Density Functional Theory is shown to arise naturally in the subband spectra of semiconductor quantum wells. Using an \emph{ab-initio} $xc$ functional, including exchange exactly and correlation in an exact partial way, a discontinuity appears in the $xc$ potential, each time a subband becomes slightly occupied. Exchange and correlation give opposite contributions to the discontinuity, with correlation overcoming exchange. The jump in the intersubband energy is in excellent agreement with experimental data.Comment: 5 pages, 3 figure

Pseudospin anisotropy of trilayer semiconductor quantum Hall ferromagnets

When two Landau levels are brought to a close coincidence between them and with the chemical potential in the Integer Quantum Hall regime, the two Landau levels can just cross or collapse while the external or pseudospin field that induces the alignment changes. In this work, all possible crossings are analyzed theoretically for the particular case of semiconductor trilayer systems, using a variational Hartree-Fock approximation. The model includes tunneling between neighboring layers, bias, intra-layer and inter-layer Coulomb interaction among the electrons. We have found that the general pseudospin anisotropy classification scheme used in bilayers applies also to the trilayer situation, with the simple crossing corresponding to an easy-axis ferromagnetic anisotropy analogy, and the collapse case corresponding to an easy-plane ferromagnetic analogy. An isotropic case is also possible, with the levels just crossing or collapsing depending on the filling factor and the quantum numbers of the two nearby levels. While our results are valid for any integer filling factor $\nu$ (=1,2,3,...), we have analyzed in detail the crossings at $\nu=3$ and $4$, and we have given clear predictions that will help in their experimental search. In particular, the present calculations suggest that by increasing the bias, the trilayer system at these two filling factors can be driven from an easy-plane anisotropy regime to an easy-axis regime, and then can be driven back to the easy-plane regime. This kind of reentrant behavior is an unique feature of the trilayers, compared with the bilayers

Single-Stage, Venturi-Driven Desalination System

Water demand is increasing at a rapid pace due to population increase, industrial expansion, and agricultural development. The use of desalination technology to meet the high water demands has increased global online desalination capacity from 47 million m^3/d in 2007 to 92.5 million m^3/d as of June 2017 [49]. Membrane and thermal processes are the two mainstream desalination categories used worldwide for desalination plants. Reverse Osmosis (RO) is the most widely used membrane process and it has become the dominant technology for building desalination plants over recent decades. Thermal distillation, however, has become less and less competitive due to its high production costs, mainly due to a reliance on increasing fuel prices and large thermal energy requirements. Although heat recuperation is commonly used, it adds investment cost and increases complexity of the system. The concept of Single-Stage Venturi-driven (SSV) Desalination, a single-stage, thermal desalination system, using a Multifunctional Venturi Water Ejector (Venturi system), is proposed, analyzed, and demonstrated. The system requires only low-grade solar heat (\u3c 60 °C) mainly to supplement the heat loss during operation. As compared to the conventional methods of solar desalination, the proposed system has the following intellectual novelties: First, the novel multifunctional water ejector integrates a vacuum pump for steam production, a compressor for condensation, and a starter for heat recuperation. Second, only residential-grade solar water heating is needed for the heat demand which greatly reduces the production cost of solar desalination, as compared to those systems using concentrated solar power (CSP). Third, the proposed system is operated standalone based solely on solar energy. The main objective of this research is to accurately analyze and model the SSV system, and achieve an estimated levelized cost of water (LCOW) close to the DOE target of $0.50/m3 (DE-FOA-0001778) [55]. Additionally, prototypes, operating at about 0.1 bar, were built to prove the concept that very low-grade heat sources can be utilized with the system. While similar to other thermal methods, such as MSF (multi-stage flash desalination), MED (multi-effect desalination), and VC (vapor compression desalination), the SSV system utilizes a unique water ejector to reduce vapor pressure in a “boiler” and operate at lower temperatures, thereby increasing the heat regeneration efficiency and decreasing the heat input temperature requirements. The concept, as well as the scalability, of the system is proven in the results. The performance of the Venturi System was simulated using Comsol Multiphysics. The simulation results were compared to both the theoretical and experimental results. The lowest experimental vacuum pressure achieved during operation was 0.07 bar, equating to a boiling point of 40 ℃. High-performance, customized Venturi water ejector designs are projected to further lower vacuum pressures. In this study, a thermo-economic analysis was performed as a theoretical baseline for the performance of the novel technology. In the future, the baseline results should be compared to experimental results of a pilot or operational SSV desalination plant. The resulting energy requirements of the system are calculated as 40.6 kWh/m3 for thermal and 0.23 kWh/m3 for electrical energy requirements. The performance ratio and exergy efficiency are calculated as 15.4 and 39$0.67/m3, achieving a lower price point than most commercialized solar desalination technologies

Coulomb and tunneling coupled trilayer systems at zero magnetic field

The ground-state electronic configuration of three coupled bidimensional electron gases has been determined using a variational Hartree-Fock approach, at zero magnetic field. The layers are Coulomb coupled, and tunneling is present between neighboring layers. In the limit of small separation between layers, the tunneling becomes the dominant energy contribution, while for large distance between layers the physics is driven by the Hartree electrostatic energy. Transition from tunneling to hartree dominated physics is shifted towards larger layer separation values as the total bidimensional density of the trilayers decreases. The inter-layer exchange helps in stabilize a "balanced" configuration, where the three layers are approximately equally occupied; most of the experiments are performed in the vicinity of this balanced configuration. Several ground-state configurations are consequence of a delicate interplay between tunneling and inter-subband exchange

Position-dependent exact-exchange energy for slabs and semi-infinite jellium

The position-dependent exact-exchange energy per particle $\varepsilon_x(z)$ (defined as the interaction between a given electron at $z$ and its exact-exchange hole) at metal surfaces is investigated, by using either jellium slabs or the semi-infinite (SI) jellium model. For jellium slabs, we prove analytically and numerically that in the vacuum region far away from the surface $\varepsilon_{x}^{\text{Slab}}(z \to \infty) \to - e^{2}/2z$, {\it independent} of the bulk electron density, which is exactly half the corresponding exact-exchange potential $V_{x}(z \to \infty) \to - e^2/z$ [Phys. Rev. Lett. {\bf 97}, 026802 (2006)] of density-functional theory, as occurs in the case of finite systems. The fitting of $\varepsilon_{x}^{\text{Slab}}(z)$ to a physically motivated image-like expression is feasible, but the resulting location of the image plane shows strong finite-size oscillations every time a slab discrete energy level becomes occupied. For a semi-infinite jellium, the asymptotic behavior of $\varepsilon_{x}^{\text{SI}}(z)$ is somehow different. As in the case of jellium slabs $\varepsilon_{x}^{\text{SI}}(z \to \infty)$ has an image-like behavior of the form $\propto - e^2/z$, but now with a density-dependent coefficient that in general differs from the slab universal coefficient 1/2. Our numerical estimates for this coefficient agree with two previous analytical estimates for the same. For an arbitrary finite thickness of a jellium slab, we find that the asymptotic limits of $\varepsilon_{x}^{\text{Slab}}(z)$ and $\varepsilon_{x}^{\text{SI}}(z)$ only coincide in the low-density limit ($r_s \to \infty$), where the density-dependent coefficient of the semi-infinite jellium approaches the slab {\it universal} coefficient 1/2.Comment: 26 pages, 7 figures, to appear in Phys. Rev.