The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Self-interaction correction to density-functional approximations for many-electron systems

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

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Electronic excitations: density-functional versus many-body Green's-function approaches

http://nano-bio.ehu.es/files/articles/Gonze_CPC_2009_590.pdf

ABINIT: First-principles approach to material and nanosystem properties

Two-dimensional (2D) materials, such as molybdenum disulfide (MoS2), have been shown to exhibit excellent electrical and optical properties. The semiconducting nature of MoS2 allows it to overcome the shortcomings of zero-bandgap graphene, while still sharing many of graphene’s advantages for electronic and optoelectronic applications. Discrete electronic and optoelectronic components, such as field-effect transistors, sensors, and photodetectors made from few-layer MoS2 show promising performance as potential substitute of Si in conventional electronics and of organic and amorphous Si semiconductors in ubiquitous systems and display applications. An important next step is the fabrication of fully integrated multistage circuits and logic building blocks on MoS2 to demonstrate its capability for complex digital logic and high-frequency ac applications. This paper demonstrates an inverter, a NAND gate, a static random access memory, and a five-stage ring oscillator based on a direct-coupled transistor logic...

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Integrated Circuits Based on Bilayer MoS2 Transistors

Please format your submission as a single PDF file according to the instructions in the syllabus and submit it on UBlearns before 11:59 pm on Sunday, April 6. 1. (17 points) A variational calculation of the ground state energy of the Hydrogen atom is discussed in Thijssen Section 3.2.2. Review this section and the lecture notes to understand the method. Write a code, or use the hydrogen codes, to do the Programming Exercise on page 36: Check 1 Fortunately, we again have an exact answer for the ground state energy: this should be equal to −0.5 hartree = 13.6058 eV, and, if your program contains no errors, you should find −0.499278 hartree, which is amazingly good if you realize that only four functions have been taken into account. Check 2 The soution of the eigenvalue problem not only yields the eigenvalues (energies) but also the eigenvectors. Use these to draw the variational ground state wave function and compare with the exact form ψ(r) = 2 a 3/2 0 e −r/a0. 2. (17 points) The Kronig-Penney model of a periodic potential in one dimension is discussed in Thijssen Problem 6.2 on pages 164-165. Write a code, or use the kronig-penney codes, also studied in PHY 410-505 last semester, to compute a plot a band structure diagram for the model.

Electronic structure of

Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems.

An exactly soluble model is used to study magnetization and persistent currents of electrons confined in two-dimensional mesoscopic rings and dots. The model allows the calculation of magnetization and persistent currents for a range of device geometries containing a large number of electrons $(g{10}^{3})$ with little computational requirement. It is shown that in the weak-magnetic-field limit, the persistent current is simply proportional to the magnetization, presenting Aharonov-Bohm (AB) type oscillations. Such oscillations are aperiodic due to the penetration of magnetic field into the conducting region. In the strong-magnetic-field regime, however, the persistent currents and the magnetization have very different behaviors. While the persistent currents still show a rapid AB-type oscillation, the magnetization is dominated by de Haas--van Alphen (dHvA) type oscillations with the much weaker AB-type oscillations superimposed on them. The effect of device geometry on the persistent current is also very different from that on magnetization. Both the oscillation amplitude and the period of the persistent current are very sensitive to the device geometry, while the magnetization in different devices shows very similar dHvA-type oscillations. Our calculated typical value of weak-magnetic-field persistent current in a semiconductor ring, 4.95 nA, is in very good agreement with the experimental result of Mailly, Chapelier, and Benoit [Phys. Rev. Lett. 70, 2020 (1993)]: $4\ifmmode\pm\else\textpm\fi{}2$ nA.

Magnetization, persistent currents, and their relation in quantum rings and dots

An exactly soluble model for a two-dimensional ring is proposed. Using this model, we have obtained analytically the energy spectrum and wavefunctions for a ring in the presence of a uniform magnetic field and a thin magnetic flux. The model can also describe quantum dots, anti-dots, one-dimensional rings and straight two-dimensional wires, which provides an integrated picture for the electron states and their magnetic field response in these geometries. The simplicity and the flexibility of the model make it an ideal tool for the modelling of the Aharonov - Bohm effects and the persistent currents in quantum rings.

https://iopscience.iop.org/article/10.1088/0268-1242/11/11/001/pdf

Electron states in a two-dimensional ring : an exactly soluble model

A surface dielectric function of a semi-infinite plane-bounded metal is defined in the spirit of the plasmon-pole dielectric function of the bulk. It is modeled in such a way that the surface-plasmon dispersion relation is recovered for small momentum transfer. This function is employed to compute the image potential at all distances outside the surface. Interaction with bulk modes is neglected for simplicity and clarity. The interaction of a massive point charge with a metal surface is also considered in the context of a boson model for surface-plasmon excitation. We present a new definition of the image potential for this case.

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J C Inkson

Papers

Electronic structure of

Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems.

Magnetization, persistent currents, and their relation in quantum rings and dots

Electron states in a two-dimensional ring : an exactly soluble model

Semiclassical image potential at a solid surface