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.

scholarly journals Non-Hermitian Bulk-Boundary Correspondence and Singular Behaviors of Generalized Brillouin Zone

2021 ◽  
Author(s):  
Gang-Feng Guo ◽  
Xi-Xi Bao ◽  
Lei Tan
Keyword(s):  
Brillouin Zone ◽  
Closed Loop ◽  
Boundary Energy ◽  
Topological Invariant ◽  
Open Boundary ◽  
Band Theory ◽  
Boundary Correspondence ◽  
Bloch Band ◽  
Definition Of ◽  
The Continuum

Abstract The bulk boundary correspondence, which connects the topological invariant, the continuum band and energies under different boundary conditions, is the core concept in the non-Bloch band theory, in which the generalized Brillouin zone (GBZ), appearing as a closed loop generally, is a fundamental tool to rebuild it. In this work, it can be shown that the recovery of the open boundary energy spectrum by the continuum band remains unchanged even if the GBZ itself shrinks into a point. Contrastively, if the bizarreness of the GBZ occurs, the winding number will become illness. Namely, we find that the bulk boundary correspondence can still be established whereas the GBZ has singularities from the perspective of the energy, but not from the topological invariant. Meanwhile, regardless of the fact that the GBZ comes out with the closed loop, the bulk boundary correspondence can not be well characterized yet because of the ill-definition of the topological number. Here, the results obtained may be useful for improving the existing non-Bloch band theory.

scholarly journals Topological Atomic Chains on 2D Hybrid Structure

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3289
Author(s):  
Tomasz Kwapiński ◽  
Marcin Kurzyna
Keyword(s):  
Tight Binding ◽  
Wide Band ◽  
Hybrid Structure ◽  
Spectral Density Function ◽  
Hybrid Structures ◽  
Function Technique ◽  
Edge States ◽  
Surface Singularities ◽  
Atomic Chains ◽  
Topological States

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

scholarly journals Non-Bloch band theory in bosonic Bogoliubov–de Gennes systems

2021 ◽  
Vol 103 (16) ◽  
Author(s):  
Kazuki Yokomizo ◽  
Shuichi Murakami
Keyword(s):  
Band Theory ◽  
Bloch Band

Zero Valley Splitting at Zero Magnetic Field for Strained Si/SiGe Quantum Wells

2007 ◽  
Vol 1017 ◽  
Author(s):  
Seungwon Lee ◽  
Paul von Allmen
Keyword(s):  
Quantum Well ◽  
Quantum Wells ◽  
Conduction Band ◽  
Brillouin Zone ◽  
Tilt Angle ◽  
Tight Binding ◽  
Direct Consequence ◽  
Zero Magnetic Field ◽  
Strained Si ◽  
Valley Splitting

AbstractThe electronic structure for a strained silicon quantum well grown on a tilted SiGe substrate is calculated using an empirical tight-binding method. For a zero substrate tilt angle the two lowest minima of the conduction band define a non-zero valley splitting at the center of the Brillouin zone. A finite tilt angle for the substrate results in displacing the two lowest conduction band minima to finite k0 and -k0 in the Brillouin zone with equal energy. The vanishing of the valley splitting for quantum wells grown on tilted substrates is found to be a direct consequence of the periodicity of the steps at the interfaces between the quantum well and the buffer materials.

Transfer Integrals and Band Structures in (Et)2X Salts

1989 ◽  
Vol 173 ◽  
Author(s):  
Oliver H. Leblanc ◽  
Margaret L. Blohm ◽  
Richard P. Messmer
Keyword(s):  
Low Temperature ◽  
Nearest Neighbor ◽  
Spherical Wave ◽  
Tight Binding ◽  
Ab Initio Method ◽  
Energy Bands ◽  
Hubbard Hamiltonian ◽  
Transfer Integrals ◽  
Semi Empirical ◽  
Very Low Temperature

ABSTRACTTransfer integrals (tij) between pairs of nearest neighbor ET molecules were calculated by an ab initio method. Tight-binding one-electron energy bands constructed from the tij are similar to those previously calculated by Mori and by Whangbo and their coworkers by semi-empirical, extended Hückel methods, but quite different from those found by Kübler et al. in β-(ET)2I3 using the augmented spherical wave (ASW) method. However, all these band models are suspect. The Hubbard on-site repulsion parameter U is estimated to be about twice the band widths, indicating that a full treatment of the Hubbard hamiltonian is needed. Also, polaron effects appear to control transport except at very low temperature.

Band Theory: Origin of Energy Bands

2021 ◽  
Author(s):  
Mathieu Hautefeuille ◽  
Juan Hernández-Cordero
Keyword(s):  
Energy Bands ◽  
Band Theory

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.

Photoelectron Spectra and Molecular Properties, XLVIII Carbonates and Thiocarbonates

1975 ◽  
Vol 30 (11-12) ◽  
pp. 862-874 ◽  
Author(s):  
K. Wittel ◽  
E. E. Astrup ◽  
H. Bock ◽  
G. Graeffe ◽  
H. Juslén
Keyword(s):  
Ionization Potential ◽  
Substituent Effects ◽  
Lone Pair ◽  
Emission Spectra ◽  
Low Energy ◽  
Photoelectron Spectra ◽  
Energy Bands ◽  
Open Chain ◽  
First Ionization Potential ◽  
Cndo Calculations

Photoelectron (PE) spectra of ethylene and vinylene carbonates and thiocarbonates as well as of methylene trithiocarbonate and some open-chain derivatives are reported.The low energy bands, well separated in the unsaturated compounds, are assigned to lone pair and π type ionizations. The assignment is based on comparison of PE spectra, modified CNDO calculations, and sulfur Κβ emission spectra. The pronounced substituent effects due to which the first ionization potential varies from 8.4 eV to 11.1 eV are discussed.

THEORETICAL APPROACH USING EXTENDED HUCKEL TIGHT-BINDING METHOD OF THE ELECTRONIC STRUCTURE OF CeOs4Sb12 FILLED SKUTTERUDITE

2006 ◽  
Vol 20 (08) ◽  
pp. 1005-1014
Author(s):  
DONALD H. GALVAN ◽  
J. C. SAMANIEGO
Keyword(s):  
Heavy Fermion ◽  
Energy Gap ◽  
Population Analysis ◽  
Tight Binding ◽  
Energy Bands ◽  
Mulliken Population ◽  
Semiconductor Behavior ◽  
Tight Binding Method ◽  
Strong Hybridization ◽  
Heavy Fermion Behavior

Based on band structure, total and projected density of states and Mulliken Population Analysis, the electronic properties of CeOs 4 Sb 12 were investigated. The calculated energy bands depict a semiconductor behavior with an energy gap (direct gap at H ) of the order of 0.45 eV. On the other hand, a strong hybridization occurs between Ce f-orbitals with Os d-, p-, and Sb p-orbitals, which convince us to believe that this hybridization, added to the existence of a mini gap, are responsible for the heavy Fermion behavior, as well as the possibility to consider it a candidate for thermoelectric applications.

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