Eur. Phys. J. Plus (2022) 137: 655
https://doi.org/10.1140/epjp/s13360-022-02831-3

Regular Article

Room temperature quantum Hall effect in q-formalism

¹ Department of Physics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
² Department of Physics, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czechia

^b behzadlari1979@gmail.com

Received: 4 January 2022
Accepted: 15 May 2022
Published online: 3 June 2022

Abstract

We consider the quantum Hall effect (QHE) in $q$-formalism and obtain its spectrum in thermal non-equilibrium conditions (TNEQ). Moreover, we calculate the electrical potential for QHE using the density probability current in TNEQ. We find that the geometric region q < 1 can explain the Landau energy gap on graphene-based materials for the room temperature quantum Hall effect (RTQHE), while the geometric region q ≥ 1 describes the ordinary quantum Hall effect close to absolute zero temperature. To satisfy Tsallis conditions, we present two separate integral bounds for partition function to calculate the integrals in QHE and RTQHE cases. We geometrically prove that the magnitude of the Hall potentials depends on the $q$-region (i.e., $\left|V_H^{(q>1)}\right|>\left|V_H^{\left(q=1\right)}\right|>\left|V_H^{(q<1)}\right|$). Our method may be applied to analyze new electronic devices based on graphene in TNEQ.