Band Theory, Valence Bond, and Tight‐Binding Calculations

1962 ◽  
Vol 33 (1) ◽  
pp. 251-280 ◽  
Author(s):  
Per‐Olov Löwdin
Keyword(s):  
Tight Binding ◽  
Valence Bond ◽  
Band Theory

Symmetry Violations in Partially Oxidized One-Dimensional (1D)Transition Metal Polymers. Metal-Ligand-Metal(M-L-M) Bridged Systems

1984 ◽  
Vol 39 (9) ◽  
pp. 807-829
Author(s):  
Michael C. Böhm
Keyword(s):  
Transition Metal ◽  
Density Wave ◽  
Tight Binding ◽  
Mean Field ◽  
Valence Bond ◽  
Hole State ◽  
One Dimensional ◽  
Metal Derivatives ◽  
A Charge ◽  
Metal Ligand

The band structure of the metal-ligand-metal (M-L-M) bridged quasi one-dimensional (1D) cyclopentadienylmanganese polymer, MnCp 1, has been studied in the unoxidized state and in a partly oxidized modification with one electron removed from each second MnCp fragment. The tight-binding approach is based on a semiempirical self-consistent-field (SCF) Hartree-Fock (HF) crystal orbital (CO) model of the INDO-type (intermediate neglect of differential overlap) combined with a statistical averaging procedure which has its origin in the grand canonical ensemble. The latter approximation allows for an efficient investigation of violations of the translation symmetries in the oxidized 1D material. The oxidation process in 1 is both ligand- and metal-centered (Mn 3d-2 states). The mean-field minimum corresponds to a charge density wave (CDW) solution with inequivalent Mn sites within the employed repeat-units. The symmetry adapted solution with electronically identical 3d centers is a maximum in the variational space. The coupling of this electronic instability to geometrical deformations is also analyzed. The ligand amplitudes encountered in the hole-state wave function prevent extremely large charge separations between the 3d centers which are found in ID systems without bridging moieties (e.g. Ni(CN)2-5 chain). The symmetry reduction in oxidized 1 is compared with violations of spatial symmetries in finite transition metal derivatives and simple solids. The stabilization of the valence bond-type (VB) solution is physically rationalized (i.e. left-right correlations between the 3d centers). The computational results derived for 1 are generalized to oxidized transition metal chains with band occupancies that are simple fractions of the number of stacking units and to 1D systems that deviate from this relation. The entropy-influence for temperatures T ≠ 0 is shortly discussed (stabilization of domain or cluster structures).

scholarly journals Dodecagonal bilayer graphene quasicrystal and its approximants

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Guodong Yu ◽  
Zewen Wu ◽  
Zhen Zhan ◽  
Mikhail I. Katsnelson ◽  
Shengjun Yuan
Keyword(s):  
Large Scale ◽  
Lattice Mismatch ◽  
Tight Binding ◽  
Bilayer Graphene ◽  
Dominant Factor ◽  
Honeycomb Lattice ◽  
Fermi Velocity ◽  
Band Theory ◽  
Incommensurate Structures ◽  
Unfolding Method

AbstractDodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scale tight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduce accurately the properties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallest approximant with only 2702 atoms, the effective band structure of graphene quasicrystal is derived. The features, such as the emergence of new Dirac points (especially the mirrored ones), the band gap at $$M$$M point and the Fermi velocity are all in agreement with recent experiments. The properties of quasicrystal states are identified in the Landau level spectrum and optical excitations. Importantly, our results show that the lattice mismatch is the dominant factor determining the accuracy of layered approximants. The proposed approximants can be used directly for other layered materials in honeycomb lattice, and the design principles can be applied for any quasi-periodic incommensurate structures.

Topological Insulators: Electronic Structure, Material Systems and Applications

2017 ◽  
Vol 26 (03) ◽  
pp. 1740018
Author(s):  
Parijat Sengupta
Keyword(s):  
Quantum Wells ◽  
Topological Insulator ◽  
Topological Insulators ◽  
Tight Binding ◽  
Surface States ◽  
Internal Electric Field ◽  
Linear Dispersion ◽  
Band Theory ◽  
Magnetic Perturbations ◽  
Polarized Surface

Topological insulators are a new class of materials characterized by fully spin-polarized surface states, a linear dispersion, imperviousness to external non-magnetic perturbations, and a helical character arising out of the perpendicular spin-momentum locking. This article answers in a pedagogical way the distinction between a topological and normal insulator, the role of topology in band theory of solids, and the origin of these surface states. Numerical techniques including diagonalization of the TI Hamiltonians are described to quantitatively evaluate the behaviour of topological insulator states. The Hamiltonians based on continuum and tight binding approaches are contrasted. The application of TIs as components of a fast switching environment or channel material for transistors is examined through I-V curves. The potential pitfall of such devices is presented along with techniques that could potentially circumvent the problem. Additionally, it is demonstrated that a strong internal electric field can also induce topological insulator behaviour with wurtzite nitride quantum wells as representative materials.

scholarly journals A Unified View of Topological Phase Transition in Band Theory

Research ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Huaqing Huang ◽  
Feng Liu
Keyword(s):  
Intermediate Phase ◽  
Tight Binding ◽  
Structural Disorder ◽  
Crystalline Solid ◽  
Linear Scaling ◽  
Topological Order ◽  
Topological Phase ◽  
Binding Model ◽  
Band Theory ◽  
Unified View

We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Reevaluating the band evolution from an “atomic crystal” (a normal insulator (NI)) to a solid crystal, such as a semiconductor, we demonstrate that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory. The validity of the scaling relation is verified in various two-dimensional (2D) lattices regardless of lattice symmetry, periodicity, and form of electron hoppings, based on a generic tight-binding model. Significantly, this linear scaling is shown to set an upper bound for the degree of structural disorder to destroy the topological order in a crystalline solid, as exemplified by formation of vacancies and thermal disorder. Our work formulates a simple framework for understanding the physical nature of TPTs with significant implications in practical applications of topological materials.

Bonding at theCaF2/Si(111) interface from tight-binding cluster and band theory

1988 ◽  
Vol 38 (12) ◽  
pp. 8264-8268 ◽  
Author(s):  
K. Nath ◽  
Alfred B. Anderson
Keyword(s):  
Tight Binding ◽  
Band Theory

Atom-superposition and electron-delocalization tight-binding band theory

1990 ◽  
Vol 41 (9) ◽  
pp. 5652-5660 ◽  
Author(s):  
K. Nath ◽  
Alfred B. Anderson
Keyword(s):  
Tight Binding ◽  
Electron Delocalization ◽  
Band Theory

scholarly journals Non-Bloch band theory and bulk–edge correspondence in non-Hermitian systems

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Kazuki Yokomizo ◽  
Shuichi Murakami
Keyword(s):  
Brillouin Zone ◽  
Tight Binding ◽  
Topological Invariant ◽  
Edge States ◽  
Energy Bands ◽  
Open Chain ◽  
Band Theory ◽  
Continuum Energy ◽  
Bloch Band ◽  
Simple Models

Abstract In this paper, we review our non-Bloch band theory in 1D non-Hermitian tight-binding systems. In our theory, it is shown that in non-Hermitian systems, the Brillouin zone is determined so as to reproduce continuum energy bands in a large open chain. By using simple models, we explain the concept of the non-Bloch band theory and the method to calculate the Brillouin zone. In particular, for the non-Hermitian Su–Schrieffer–Heeger model, the bulk–edge correspondence can be established between the topological invariant defined from our theory and existence of the topological edge states.

Basic concepts

2018 ◽  
Author(s):  
Jean-Pierre Launay ◽  
Michel Verdaguer
Keyword(s):  
Electronic Structure ◽  
Molecular Orbital ◽  
Density Functional ◽  
Valence Bond ◽  
Molecular Solids ◽  
Orbital Theory ◽  
Band Theory ◽  
Quantum Tunnelling ◽  
Hartree Fock ◽  
Self Consistent Field

The electronic structure of molecules is described, starting from qualitative Molecular Orbital (MO) theory. After the case of simple atoms and molecules, one treats molecular solids and develops the relation between Molecular Orbital theory and band theory. In both cases, one shows that the electronic structure can influence the geometrical structure, through Jahn–Teller effects or Peierls distortion. The effect of interelectronic repulsion, the central problem of Quantum Chemistry, is put in perspective by a synthetic presentation of different approaches: Hartree–Fock Self-Consistent Field with treatment of electron correlation, Valence Bond models, and finally Density Functional Theory methods (DFT). The last section is devoted to quantum tunnelling and its dynamical aspects.

scholarly journals Charge and Spin Currents in Ferromagnet-Insulator-Superconductor Tunneling Junctions Using Hg-1223 High-Tc Superconductor

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Michihide Kitamura ◽  
Yoshitaka Uchiumi ◽  
Akinobu Irie
Keyword(s):  
Magnetic Circular Dichroism ◽  
Atomic Orbital ◽  
Tight Binding ◽  
Spin Current ◽  
Differential Conductance ◽  
Tunneling Junction ◽  
Band Theory ◽  
Insulating Layer ◽  
Spin Currents ◽  
Tunneling Junctions

Charge and spin currents along the c-axis in ferromagnet-insulator-superconductor (F/I/S) tunneling junctions have been studied within the framework of the tunneling Hamiltonian model. As a superconductor S, HgBa2Ca2Cu3O8+δ (Hg-1223) with δ=0.4 copper-oxide high-Tc superconductor has been selected, and as a ferromagnet F, Fe metal with bcc structure has been selected for simplicity. The electronic structures of above materials have been calculated on the basis of the band theory using the spin-polarized self-consistent-field data for the atomic orbital energies and the universal tight-binding parameters (UTBP) for the interactions. For the η↑ and η↓(=1-η↑) defined in the present paper, which are tunneling probabilities of the majority and the minority spin electrons, it is shown that the condition η↑=η↓ means the standard F/I/S tunneling junction with a nonmagnetic insulating layer, and the condition η↑≠η↓means the F/I/S tunneling junction with a magnetic insulating layer showing a detectable magnetization. We have found that the charge current and the differential conductance nearly remain the same as the change of η↑, but the spin current is largely changed due to the change of η↑. As an experimental method to detect the change of the spin current, the validity of an X-ray magnetic circular dichroism (XMCD) has been pointed out.

Interpretation of Electron Channeling by the Dynamical Theory of Electron Diffraction

1974 ◽  
Vol 29 (7) ◽  
pp. 1034-1044 ◽  
Author(s):  
K. Kambe ◽  
G. Lehmpfuhl ◽  
F. Fujimoto
Keyword(s):  
Electron Diffraction ◽  
Tight Binding ◽  
Diffraction Theory ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Two Dimensions ◽  
Band Theory ◽  
Bloch Waves ◽  
Electron Channeling ◽  
The Many

The connection between electron channeling and electron diffraction is discussed on the basis of the dynamical theory. Results of the many-beam calculations for 50 keV to 2 MeV electrons incident almost parallel to a [110] axis of a MgO crystal are used as examples. Bloch waves with a marked concentration of electron density at rows of atoms are obtained, and interpreted as states of electrons bound to the rows of atoms, corresponding to the classical picture of channeling. This can be shown properly by applying the tight-binding method of band theory in the two dimensions perpendicular to the axis. In this picture the "rosette motions"' in the classical theory are interpreted as p-tvpe, d-type, etc. Bloch waves, and the "weavons" as loosely-bound s-type Bloch waves. They are connected to the pictures of the Borrmann effect and the Bloch-wave channeling in the diffraction theory.

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