Effects of Landau Level Coupling on the Magnetic Band Structure for Electrons in a Two-Dimensional Hexagonal Lattice

1994 ◽  
Vol 358 ◽  
Author(s):  
O. Kühn ◽  
V. Fessatidis ◽  
H.L. Cui ◽  
N.J.M. Horing
Keyword(s):  
Landau Level ◽  
Uniform Magnetic Field ◽  
Periodic Potential ◽  
Hexagonal Lattice ◽  
Particle Energy ◽  
Landau Levels ◽  
Two Dimensional ◽  
Single Particle Energy ◽  
Hexagonal Symmetry ◽  
Cyclotron Energy

ABSTRACTThe single-particle energy spectrum of two-dimensional electrons in a lateral surface superlattice of hexagonal symmetry, subject to a normal uniform magnetic field is investigated. Special attention is focused on the coupling of different Landau levels due to the periodic potential. It is shown that the inclusion of this coupling causes strong modifications of the spectrum compared with the limit of no coupling investigated previously. It is found that the importance of Landau level coupling is mainly determined by the relation between the potential amplitude and the cyclotron energy, as well as the Landau level index.

scholarly journals LANDAU LEVELS AND QUANTUM GROUP

1994 ◽  
Vol 09 (05) ◽  
pp. 451-458 ◽  
Author(s):  
HARU-TADA SATO
Keyword(s):  
Quantum Group ◽  
Uniform Magnetic Field ◽  
Periodic Potential ◽  
Group Structure ◽  
Quantum Algebra ◽  
Wave Functions ◽  
Landau Levels ◽  
Group Symmetry ◽  
Factor V ◽  
Level Degeneracy

We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wave functions of the system. The quantum group symmetry commutes with the Hamiltonian and is relevant to the Landau level degeneracy. The deformation parameter q of the quantum algebra turns out to be given by the fractional filling factor v=1/m (m odd integer).

Stability of Anomalous States of a Local Potential in Graphene

2015 ◽  
Vol 15 (10) ◽  
pp. 8263-8266
Author(s):  
S. C. Kim ◽  
Y. H. Jeong ◽  
S.-R. Eric Yang
Keyword(s):  
Probability Density ◽  
Landau Level ◽  
Landau Levels ◽  
Scaling Analysis ◽  
Two Dimensional ◽  
Zero Energy ◽  
Magnetic Length ◽  
Simple Scaling ◽  
Integer Quantum ◽  
Anomalous State

Graphene Landau levels have discrete energies consisting zero energy chiral states and non-zero energy states with mixed chirality. Each Landau level splits into discrete energies when a localized potential is present. A simple scaling analysis suggests that a localized potential can act as a strong perturbation, and that it can be even more singular in graphene than in ordinary two-dimensional systems of massful electrons. Parabolic, Coulomb, and Gaussian potentials in graphene may have anomalous boundstates whose probability density has a sharp peak inside the potential and a broad peak of size magnetic length l outside the potential. The n = 0 Landau level with zero energy has only one anomalous state while the n = ±1 Landau levels with non-zero energy have two (integer quantum number n is related to the quantized Landau level energies). These anomalous states can provide a new magnetospectroscopic feature in impurity cyclotron resonances of graphene. In the present work we investigate quantitatively the conditions under which the anomalous states can exist. These results may provide a guide in searching for anomalous states experimentally.

LANDAU LEVEL SPECTRUM FOR CHARGED PARTICLE IN A CLASS OF NON-UNIFORM MAGNETIC FIELDS

1993 ◽  
Vol 08 (06) ◽  
pp. 523-529 ◽  
Author(s):  
AVINASH KHARE ◽  
C. NAGARAJA KUMAR
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Landau Level ◽  
Wide Class ◽  
Uniform Magnetic Field ◽  
Landau Levels ◽  
Level Spectrum

The spectrum of a charged particle in uniform magnetic field consists of equally spaced Landau levels which are infinitely degenerate. We consider isospectral deformations of this problem and show that the spectrum is again equispaced but nondegenerate for a wide class of non-uniform magnetic fields.

scholarly journals Landau levels in QCD in an external magnetic field

2018 ◽  
Vol 175 ◽  
pp. 07014 ◽  
Author(s):  
Falk Bruckmann ◽  
Gergely Endrődi ◽  
Matteo Giordano ◽  
Sándor D. Katz ◽  
Tamás G. Kovács ◽  
...  
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Landau Level ◽  
Low Energy ◽  
Landau Levels ◽  
Dimensional Case ◽  
Strong Interactions ◽  
Two Dimensional ◽  
Energy Models ◽  
Lowest Landau Level

We will discuss the issue of Landau levels of quarks in lattice QCD in an external magnetic field. We will show that in the two-dimensional case the lowest Landau level can be identified unambiguously even if the strong interactions are turned on. Starting from this observation, we will then show how one can define a “plowest Landau level” in the four-dimensional case, and discuss how much of the observed effects of a magnetic field can be explained in terms of it. Our results can be used to test the validity of low-energy models of QCD that make use of the lowest-Landau-level approximation.

Microdiffraction analysis of precipitate crystallography and morphology in Al alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 954-955
Author(s):  
B.C. Muddle ◽  
G.R. Hugo
Keyword(s):  
Point Group ◽  
Hexagonal Lattice ◽  
Intersection Point ◽  
Saed Pattern ◽  
Point Symmetry ◽  
Hexagonal Symmetry ◽  
Precipitate Crystal ◽  
The Matrix ◽  
The Subject ◽  
Electron Microdiffraction

Electron microdiffraction has been used to determine the crystallography of precipitation in Al-Cu-Mg-Ag and Al-Ge alloys for individual precipitates with dimensions down to 10 nm. The crystallography has been related to the morphology of the precipitates using an analysis based on the intersection point symmetry. This analysis requires that the precipitate form be consistent with the intersection point group, defined as those point symmetry elements common to precipitate and matrix crystals when the precipitate crystal is in its observed orientation relationship with the matrix.In Al-Cu-Mg-Ag alloys with high Cu:Mg ratios and containing trace amounts of silver, a phase designated Ω readily precipitates as thin, hexagonal-shaped plates on matrix {111}α planes. Examples of these precipitates are shown in Fig. 1. The structure of this phase has been the subject of some controversy. An SAED pattern, Fig. 2, recorded from matrix and precipitates parallel to a <11l>α axis is suggestive of hexagonal symmetry and a hexagonal lattice has been proposed on the basis of such patterns.

scholarly journals Two-dimensional iodine-monofluoride epitaxy on WSe2

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Yung-Chang Lin ◽  
Sungwoo Lee ◽  
Yueh-Chiang Yang ◽  
Po-Wen Chiu ◽  
Gun-Do Lee ◽  
...  
Keyword(s):  
Density Functional ◽  
Surface Passivation ◽  
Hexagonal Lattice ◽  
Chemical Vapor ◽  
Growth Promoter ◽  
Two Dimensional ◽  
Epitaxial Relationship ◽  
Chemical Vapor Deposition Growth ◽  
Scanning Transmission ◽  
Great Possibility

AbstractInterhalogen compounds (IHCs) are extremely reactive molecules used for halogenation, catalyst, selective etchant, and surface modification. Most of the IHCs are unstable at room temperature especially for the iodine-monofluoride (IF) whose structure is still unknown. Here we demonstrate an unambiguous observation of two-dimensional (2D) IF bilayer grown on the surface of WSe2 by using scanning transmission electron microscopy and electron energy loss spectroscopy. The bilayer IF shows a clear hexagonal lattice and robust epitaxial relationship with the WSe2 substrate. Despite the IF is known to sublimate at −14 °C and has never found as a solid form in the ambient condition, but surprisingly it is found stabilized on a suitable substrate and the stabilized structure is supported by a density functional theory. This 2D form of IHC is actually a byproduct during a chemical vapor deposition growth of WSe2 in the presence of alkali metal halides as a growth promoter and requires immediate surface passivation to sustain. This work points out a great possibility to produce 2D structures that are unexpected to be crystallized or cannot be obtained by a simple exfoliation but can be grown only on a certain substrate.

scholarly journals EDGE ASYMPTOTICS OF PLANAR ELECTRON DENSITIES

1994 ◽  
Vol 08 (11n12) ◽  
pp. 1625-1638 ◽  
Author(s):  
GERALD V. DUNNE
Keyword(s):  
Asymptotic Expansion ◽  
Magnetic Flux ◽  
Landau Level ◽  
Particle Number ◽  
Landau Levels ◽  
Electron Densities ◽  
Boundary Location ◽  
Boundary Characteristics ◽  
Planar Electron

The N→∞ limit of the edges of finite planar electron densities is discussed for higher Landau levels. For full filling, the particle number is correlated with the magnetic flux, and hence with the boundary location, making the N→∞ limit more subtle at the edges than in the bulk. In the nth Landau level, the density exhibits n distinct steps at the edge, in both circular and rectangular samples. The boundary characteristics for individual Landau levels, and for successively filled Landau levels, are computed in an asymptotic expansion.

Molecular Dynamics Simulations of Shock-Defect Interactions in Two-Dimensional Nonreactive Crystals

1992 ◽  
Vol 296 ◽  
Author(s):  
Robert S. Sinkovits ◽  
Lee Phillips ◽  
Elaine S. Oran ◽  
Jay P. Boris
Keyword(s):  
Molecular Dynamics ◽  
Hexagonal Lattice ◽  
Square Lattice ◽  
Two Dimensional ◽  
Connection Machine ◽  
Defect Sites ◽  
Principal Axes ◽  
Shock Motion ◽  
Defect Interactions ◽  
Dynamics Simulations

AbstractThe interactions of shocks with defects in two-dimensional square and hexagonal lattices of particles interacting through Lennard-Jones potentials are studied using molecular dynamics. In perfect lattices at zero temperature, shocks directed along one of the principal axes propagate through the crystal causing no permanent disruption. Vacancies, interstitials, and to a lesser degree, massive defects are all effective at converting directed shock motion into thermalized two-dimensional motion. Measures of lattice disruption quantitatively describe the effects of the different defects. The square lattice is unstable at nonzero temperatures, as shown by its tendency upon impact to reorganize into the lower-energy hexagonal state. This transition also occurs in the disordered region associated with the shock-defect interaction. The hexagonal lattice can be made arbitrarily stable even for shock-vacancy interactions through appropriate choice of potential parameters. In reactive crystals, these defect sites may be responsible for the onset of detonation. All calculations are performed using a program optimized for the massively parallel Connection Machine.

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