An analogy of the quantum hall conductivity in a Lorentz-symmetry violation setup

Abstract

We investigated some influences of unconventional physics, such as Lorentzsymmetry violation, for quantum mechanical systems. In this context, we calculated an important contribution for the standard model extension. In the non-relativistic limit, we obtained an analogy of the Landau levels and the quantum Hall conductivity related to this contribution for low energy systems.

A Landau-type quantization from a Lorentz symmetry violation background with crossed electric and magnetic fields

“…In the present work, we follow this line of research given in Refs. [2][3][4][5][6][7][8][9][10][11][12][13][14] and neglect any effect from rotation, therefore, the background field is invariant under particle transformations. However, in order to achieve a more realistic measure in a laboratory placed at the surface of the Earth, we should take into account the movement of the earth in relation to a nonrotating frame relative to Sun's center of mass.…”

Lorentz symmetry breaking effects on relativistic EPR correlations

“…[110], one can find the current limits on the coefficients of the Lorentz symmetry violation. In recent years, Lorentz symmetry breaking effects have been investigated in the hydrogen atom [111], on the Rashba coupling [112,113], in a quantum ring [114], in Weyl semi-metals [115], in tensor backgrounds [116,117], in the quantum Hall effect [118], and geometric quantum phases [119][120][121].…”

An analogue of the quantum Hall conductivity for a magnetic quadrupole moment

“…By following Refs. [14,25,28,29], the Landau quantization for neutral particles with permanent magnetic or electric dipole moments can be achieved by considering non-uniform electric or magnetic fields that interact with the dipole moments aligned in the z-direction, respectively. By analogy with the Landau quantization for neutral particles, let us first consider the magnetic quadrupole tensor to be defined as…”

“…At present days, the quantum Hall effect has been investigated in non-inertial systems [8][9][10][11], in the presence of topological defects [12,13], in Aharonov-Casher systems [14][15][16], anyons [17], graphene [18,19], superconducting arrays [20], noncommutative quantum mechanics [21][22][23][24] and in a background of the violation of the Lorentz symmetry [25]. In studies of the quantum Hall effect, the Landau quantization [26,27] is the simplest system that we can work with, then, with the purpose of extending to neutral particle systems, analogues of the Landau quantization have been proposed in recent years to neutral particles that possess permanent magnetic dipole moment [14], permanent electric dipole moment [28,29] and electric quadrupole moment [30].…”