Sagnac effect and quantum Hall effect in rotating GaAs/Ga1−xAlxAs systems

This study investigates the intricate interplay between inertial effects and the quantum Hall effect (QHE) in two-dimensional electron systems (2DEGs), specifically in a $GaAs/G{a}_{1-x}A{l}_{x}As$ system. We analyze how hydrostatic pressure, temperature, and aluminum concentration influence the effective electronic mass and consequently modify the energy levels of the system. A key aspect of our work is the distinction between effective mass and gravitational mass, which plays a crucial role in the behavior of electrons under inertial forces. The Hamiltonian incorporates the Sagnac effect, revealing distinct behaviors in the energy structure of a rotating 2DEG under a perpendicular magnetic field. Our results demonstrate that rotational motion breaks the degeneracy of Landau levels, resulting in a complex energy spectrum that significantly impacts Hall conductivity. We show that the Hall conductivity is enhanced by the rotational motion and is sensitive to variations in the effective mass due to changes in aluminum concentration and pressure. These findings provide crucial insights into the dynamics of 2DEGs in rotating frames and highlight the need to account for inertial effects in future theoretical and experimental studies of quantum systems.