Modified tight-binding equations for wave functions of semi-infinite crystals and interfaces

We investigate the effects of vacancies, disorder and sublattice polarization on the electronic properties of a monolayer graphene in the quantum Hall regime. Energy spectra as a function of magnetic field and the localization properties of the states within the graphene Landau levels (LLs) are calculated through a tight-binding model. We first discuss our results considering vacancies in the lattice, where we show that vacancies introduce extra levels (or well-defined bands) between consecutive LLs. An striking consequence here is that extra Hall resistance plateaus are expected to emerge when an organized vacancy superlattice is considered. Secondly, we discuss the anomalous localization properties we have found for the lowest LL, where an increasing disorder is shown to enhance the wave functions delocalization (instead of inducing localization). This unexpected effect is shown to be directly related to the way disorder increasingly destroys the sublattice (valley) polarization of the states in the lowest LL. The reason why this anomalous disorder effect occurs only for the zero-energy LL is that, in absence of disorder, only for this level all the states are sublattice polarized, i.e., their wave functions have amplitudes in only one of the sublattices.

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Filling-enforced quantum band insulators in spin-orbit coupled crystals

Science Advances ◽

10.1126/sciadv.1501782 ◽

2016 ◽

Vol 2 (4) ◽

pp. e1501782 ◽

Cited By ~ 25

Author(s):

Hoi Chun Po ◽

Haruki Watanabe ◽

Michael P. Zaletel ◽

Ashvin Vishwanath

Keyword(s):

Tight Binding ◽

Surface States ◽

Wave Functions ◽

Spin Orbit Coupling ◽

Spin Orbit ◽

Body Centered Cubic ◽

Cubic Crystals ◽

Atomic Orbitals ◽

Theoretical Discovery ◽

Classical Picture

An early triumph of quantum mechanics was the explanation of metallic and insulating behavior based on the filling of electronic bands. A complementary, classical picture of insulators depicts electrons as occupying localized and symmetric Wannier orbitals that resemble atomic orbitals. We report the theoretical discovery of band insulators for which electron filling forbids such an atomic description. We refer to them as filling-enforced quantum band insulators (feQBIs) because their wave functions are associated with an essential degree of quantum entanglement. Like topological insulators, which also do not admit an atomic description, feQBIs need spin-orbit coupling for their realization. However, they do not necessarily support gapless surface states. Instead, the band topology is reflected in the insulating behavior at an unconventional filling. We present tight binding models of feQBIs and show that they only occur in certain nonsymmorphic, body-centered cubic crystals.

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Tight-Binding Initialization for Generating High-Quality Initial Wave Functions: Application to Defects and Impurities in GaN

MRS Proceedings ◽

10.1557/proc-408-43 ◽

1995 ◽

Vol 408 ◽

Cited By ~ 5

Author(s):

Jörg Neugebauer ◽

Chris G. Van De Walle

Keyword(s):

Plane Wave ◽

Total Energy ◽

Tight Binding ◽

Wave Functions ◽

Basis Set ◽

Energy Methods ◽

High Quality ◽

Initial Wave ◽

Efficient Construction ◽

Energy Convergence

AbstractWe describe a new method that allows an efficient construction of high-quality initial wavefunctions which are required as input for iterative total-energy methods. The key element of the method is the reduction of the parameter space (number of wavefunctions) by about two orders of magnitude by projecting the plane-wave basis onto an atomic basis. We show that the wave functions constructed within this basis set are very close to the exact plane-wave wavefunctions, resulting in a rapid total-energy convergence.

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Surface-state energies and wave functions in layered organic conductors

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0223 ◽

2020 ◽

Vol 75 (11) ◽

pp. 987-998

Author(s):

Danica Krstovska ◽

Aleksandar Skeparovski

Keyword(s):

Magnetic Field ◽

Surface State ◽

Tight Binding ◽

Surface States ◽

Organic Conductors ◽

Wave Functions ◽

Energy Dispersion ◽

Quantization Rule ◽

Tight Binding Approximation ◽

Dispersion Law

AbstractWe have calculated and analyzed the surface-state energies and wave functions in quasi-two dimensional (Q2D) organic conductors in a magnetic field parallel to the surface. Two different forms for the electron energy spectrum are used in order to obtain more information on the elementary properties of surface states in these conductors. In addition, two mathematical approaches are implemented that include the eigenvalue and eigenstate problem as well as the quantization rule. We find significant differences in calculations of the surface-state energies arising from the specific form of the energy dispersion law. This is correlated with the different conditions needed to calculate the surface-state energies, magnetic field resonant values and the surface wave functions. The calculations reveal that the value of the coordinate of the electron orbit must be different for each state in order to numerically calculate the surface energies for one energy dispersion law, but it has the same value for each state for the other energy dispersion law. This allows to determine more accurately the geometric characteristics of the electron skipping trajectories in Q2D organic conductors. The possible reasons for differences associated with implementation of two distinct energy spectra are discussed. By comparing and analyzing the results we find that, when the energy dispersion law obtained within the tight-binding approximation is used the results are more relevant and reflect the Q2D nature of the organic conductors. This might be very important for studying the unique properties of these conductors and their wider application in organic electronics.

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VARIATIONAL STUDY OF THE PAIR HOPPING MODEL

International Journal of Modern Physics B ◽

10.1142/s0217979289001135 ◽

1989 ◽

Vol 03 (12) ◽

pp. 1765-1781 ◽

Cited By ~ 3

Author(s):

P. Fazekas

Keyword(s):

Tight Binding ◽

Wave Functions ◽

Nearest Neighbour ◽

Electron Pairs ◽

Gutzwiller Approximation ◽

Variational Treatment ◽

Variational Study ◽

Hopping Model ◽

Pair Hopping ◽

Paired State

We study the ground state of a Hamiltonian introduced by Kolb and Penson for modelling situations in which small electron pairs are formed. The Hamiltonian consists of a tight binding band term, and a term describing the nearest neighbour hopping of electron pairs. We give a Gutzwiller-type variational treatment, first with a single-parameter Ansatz treated in the single site Gutzwiller approximation, and then with more complicated trial wave functions, and an improved Gutzwiller approximation. The calculation yields a transition from a partially paired normal state, in which the spin susceptibility has a diminished value, into a fully paired state.

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Multifractal properties of the wave functions of the square-lattice tight-binding model with next-nearest-neighbor hopping in a magnetic field

Physical Review B ◽

10.1103/physrevb.55.12971 ◽

1997 ◽

Vol 55 (19) ◽

pp. 12971-12975 ◽

Cited By ~ 8

Author(s):

I. Chang ◽

K. Ikezawa ◽

M. Kohmoto

Keyword(s):

Magnetic Field ◽

Nearest Neighbor ◽

Tight Binding ◽

Wave Functions ◽

Square Lattice ◽

Tight Binding Model ◽

Binding Model

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Efficient Electronic Energy Functionals for Tight-Binding

MRS Proceedings ◽

10.1557/proc-491-35 ◽

1997 ◽

Vol 491 ◽

Author(s):

Roger Haydock

Keyword(s):

Ground State ◽

State Energy ◽

Correlation Energy ◽

Tight Binding ◽

Electronic Energy ◽

Wave Functions ◽

Electronic Charge ◽

Energy Functionals ◽

Exchange Correlation ◽

Band Structure Energy

ABSTRACTGeneralized functionals are constructed from the exchange-correlation energy by a Legendre transformation which makes the new functionals stationary at the electronic charge density, potential, and wave functions for the ground-state. Using generalized functionals, the density, potential, and wave functions can be independently parameterized and varied to determine the ground-state energy-surface for a system of atoms. This eliminates the computationally awkward steps of constructing densities from wave functions or potentials from densities, and is particularly well suited to parameterizations using tight-binding orbitale together with atomic-like densities and potentials. For each choice of parameters, the only quantities which must be computed are the electron-electron energy for the density, the integral of the potential over the density, and the band structure energy for the wave functions. To second order in the density, potential, and wave functions, the energy for a configuration of atoms is given by the generalized functional evaluated at a superposition of atomic densities, a potential made by stitching together the atomic potentials where they are equal, and atomic wave functions. For more accurate stationary energies the densities, potentials, and wave functions can be improved by one or more conjugate gradient steps.

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