Diamagnetic band structure up to second order in the crystal potential

Neumann, Heinz; Rauh, Alexander

doi:10.1002/pssb.2220960123

Cited by 10 publications

(2 citation statements)

References 19 publications

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“…The fractal nature of the Hofstadter butterfly had captivated researchers for many years [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The paper by Hofstadter [5] was for the energy spectrum of a periodic square lattice in the tight-binding approximation and subject to a perpendicular magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Revealing Hofstadter spectrum for graphene in a periodic potential

Gumbs

Iurov²,

Huang³

et al. 2014

Phys. Rev. B

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We calculate the energy bands for graphene monolayers when electrons move through a periodic electrostatic potential in the presence of a uniform perpendicular magnetic field. We clearly demonstrate the quantum fractal nature of the energy bands at reasonably low magnetic fields. We present results for the energy bands as functions of both wave number and magnetic flux through the unit cells of the resulting moiré superlattice. The effects due to pseudospin coupling and Landau orbit mixing by a strong scattering potential have been exhibited. At low magnetic fields when the Landau orbits are much larger than the period of the modulation, the Landau levels are only slightly broadened. This feature is also observed at extremely high magnetic fields. The density of states has been calculated and shows a remarkable self-similarity like the energy bands. We estimate that for modulation period of 10 nm the region where the Hofstadter butterfly is revealed is B 2 T.

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Section: Introductionmentioning

confidence: 99%

Revealing Hofstadter spectrum for graphene in a periodic potential

Gumbs

Iurov²,

Huang³

et al. 2014

Phys. Rev. B

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“…The tight-binding method, applicable in the limit of weak magnetic fields, is a semiclassical method, which starts from electron states localized in real space at different lattice sites and introduces a single-band effective Hamiltonian by the application of the Peierls's substitution [14][15][16][17]. The nearly-free-electron method, on the other hand, is a quantum mechanical approach that is suitable for strong magnetic fields [18][19][20][21][22][23]. It starts from plane waves localized in reciprocal space and uses free-electron Landau eigenstates as a basis and the periodic lattice potential as a perturbation.…”

Section: Introductionmentioning

confidence: 99%

Magnetic subband structure of Bloch electrons in a two-dimensional lattice under magnetic modulation

Fekete

Gumbs

1999

J. Phys.: Condens. Matter

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This paper presents an analytical and numerical investigation of the energy spectrum of two-dimensional Bloch electrons subject to a periodic potential of square and hexagonal symmetry and a perpendicular sine-modulated magnetic field, applying the tight-binding model. The energy spectrum is found using an effective Hamiltonian obtained by employing the Peierls substitution in the ground-state energy band function. The resulting Schrödinger equation is solved by applying a matrix method. The energy spectrum found exhibits recursive properties similar to those discussed by Hofstadter for the case of a uniform perpendicular magnetic field. It is the objective of this paper to show that this technique can be extended successfully in the presence of a modulated magnetic field of arbitrary strength. We successfully demonstrate a Hofstadter-type spectrum in the presence of both a uniform and a modulated magnetic field.

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Diamagnetic Band Structure Comparison of Second‐Order Perturbation with a First‐Principles Calculation

Rauh

Schellnhuber

1981

Physica Status Solidi (b)

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The comparison is restricted to the Landau region where the periodic potential can be treated as a perturbation. The first-principles calculation is done within a recently developed variational formalism. A two-dimensional model potential is supposed and rational magnetic fields. For all Landau levels considered a striking agreement is found between the two energy spectra which are obtained by the perturbative and the variational method, respectively. The second-order perturbation yields also the magnetic breakdown condition with high accuracy.Der Vergleich wird auf den Landaubereich beschrlnkt, wo das periodische Potential als Storung behandelt werden kann. Die ab initio Rechnung erfolgt im Rahmen eines kiirzlich entwickelten Variationsverfahrens. Es wird von einem zwei-dimensionalen Modellpotential und von rationalen Magnetfeldern ausgegangen. Fur alle betrachteten Landauniveaus finden wir eine auffallende tfbereinstimmung zwischen den beiden Energiespektren, die mit Storungsrechnung bzw. Variationsverfahren erhalten werden. Die Storungsrechnung zweiter Ordnung liefert die Bedingung fur den magnetischen Durchbruch mit groBer Genauigkeit.

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Diamagnetic band structure up to second order in the crystal potential

Cited by 10 publications

References 19 publications

Revealing Hofstadter spectrum for graphene in a periodic potential

Revealing Hofstadter spectrum for graphene in a periodic potential

Magnetic subband structure of Bloch electrons in a two-dimensional lattice under magnetic modulation

Diamagnetic Band Structure Comparison of Second‐Order Perturbation with a First‐Principles Calculation

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