The Thomas-Fermi and the Thomas-Fermi-Dirac Models in Two-Dimension- the Effect of Strong Quantizing Magnetic Field

Abstract

Using Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models, we have investigated the properties of electron gas inside two-dimensional (2D) Wigner-Seitz (WS) cells in presence of a strong orthogonal quantizing magnetic field. The electron-electron Coulomb exchange interaction in quasi-2D case is obtained. The exact form of exchange term in 2D is derived making the width of the system tending to zero. Further, using the exchange term, the Thomas-Fermi-Dirac equation in 2D is established. It has been observed that only the ionized WS cell can have finite radius in the Thomas-Fermi model, even in presence of a strong quantizing magnetic field. On the other hand, in the Thomas-Fermi-Dirac model a neutral WS cell can have finite radius.

9 pages LATEX file with two .eps figures (included), some version will appear in EPJ D 71:5 (2017), DOI: 10.1140/epjd/e2016-70295-1

References in corpus (9)

• The electronic properties of graphene
• Topological Insulators with Inversion Symmetry
• Graphane: a two-dimensional hydrocarbon
• Coexistence of the topological state and a two-dimensional electron gas on the surface of Bi2Se3
• Analysis of $Λ_b \rar Λ\ell^+ \ell^-$ transition in SM4 using form factors from Full QCD
• In-plane and transverse superconducting fluctuation diamagnetism in the presence of charge-density waves in 2H-NbSe2 single crystals
• On the Crustal Matter of Magnetars
• The Study of Relatively Low Density Stellar Matter in Presence of Strong Quantizing Magnetic Field
• A Theoretical Study of the Magnetically Deformed Inner Crust Matter of Magnetars