The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios

TL;DR

This paper explores the noncommutative quantum Hall effect with anomalous magnetic moment across three relativistic scenarios, deriving bound-state solutions, energy levels, and analyzing parameter influences, thus generalizing previous results.

Contribution

It introduces a comprehensive analysis of NCQHE with AMM in inertial and noninertial curved spacetimes, considering non-zero angular momentum and position noncommutativity, extending existing literature.

Findings

Derived eigenfunctions and energy levels for all scenarios.

Identified parameter influences on relativistic Landau levels.

Generalized previous results to more complex spacetime and noncommutative settings.

Abstract

In the present paper, we investigate the bound-state solutions of the noncommutative quantum Hall effect (NCQHE) with anomalous magnetic moment (AMM) in three different relativistic scenarios, namely: the Minkowski spacetime (inertial flat case), the spinning cosmic string (CS) spacetime (inertial curved case), and the spinning CS spacetime with noninertial effects (noninertial curved case). In particular, in the first two scenarios, we have an inertial frame, while in the third, we have a rotating frame. With respect to bound-state solutions, we focus primarily on eigenfunctions (Dirac spinor and wave function) and on energy eigenvalues (Landau levels), where we use the flat and curved Dirac equation in polar coordinates to reach such solutions. However, unlike the literature, here we consider a CS with an angular momentum non-null and also the NC of the positions, and therefore, we seek a more general description for the QHE. Once the solutions are obtained, we discuss the influence of all parameters and physical quantities on relativistic energy levels. Finally, we analyze the nonrelativistic limit, and we also compared our problem with other works, where we verified that our results generalize some particular cases of the literature.