Eur. Phys. J. D (2017) 71: 5
https://doi.org/10.1140/epjd/e2016-70295-1

Regular Article

Thomas-Fermi and Thomas-Fermi-Dirac models in two-dimension – Effect of strong quantizing magnetic field

Department of Physics, Visva-Bharati, 741235 Santiniketan, India

^a e-mail: somenath.chakrabarty@visva-bharati.ac.in

Received: 29 April 2016
Received in final form: 15 November 2016
Published online: 10 January 2017

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.