Eur. Phys. J. Plus (2014) 129: 233
https://doi.org/10.1140/epjp/i2014-14233-9

Regular Article

Fractional quantum Hall effect within the relativistic formalism

¹ Physics Department, Shahrood University, P. O. Box 3619995161-316, Shahrood, Iran
² Department of Sciences, Islamic Azad University, Ahvaz Branch, Ahvaz, Iran
³ Department of Sciences, Islamic Azad University, Abadan Branch, Abadan, Iran

^* e-mail: s.rahmani120@gmail.com

Received: 28 June 2014
Revised: 27 August 2014
Accepted: 9 September 2014
Published online: 23 October 2014

Abstract

Applying Dirac equation with an external magnetic field we find the wave function of electrons in two dimensions. We study the fractional quantum Hall effect using the obtained wave function and we find the current, resistance and Hall’s voltage for the arbitrary n, λ quantum numbers. Furthermore, we have shown a magnetic field, in which Hall’s electric field can be minimum.