Quantum magnetotransport properties of silicene: Influence of the acoustic phonon correction

We study the transport properties of silicene in a perpendicular magnetic field by evaluating the Hall and longitudinal conductivities and resistivities when the acoustic phonon correction to the Landau level (LL) energy is taken into account. The acoustic phonons are considered by three modes: the transverse (TA), longitudinal, and out-of-plane ones. Under the influence of the acoustic phonon correction, the quantum Hall effect plateaus occur at higher values of the magnetic field, where the TA phonon displays the strongest effect. The combined effects of the strong spin-orbit coupling in silicene, the external electric field, and the Zeeman field on the transport parameters are investigated. These combined effects lift the spin and valley degeneracy of the LLs, leading to the additional plateaus in the Hall conductivity with the sequence being found as ${\ensuremath{\sigma}}_yx=(4{e}²/h)(n/4+1/2)$. The temperature has a significant effect on the width of the Hall conductivity plateaus. We also appraise the longitudinal conductivity ${\ensuremath{\sigma}}_xx$ and the Hall, ${\ensuremath{\rho}}_xy$, and longitudinal, ${\ensuremath{\rho}}_xx$, resistivities and show the difference between the present results and those for graphene as well as for silicene without the Zeeman field effect. The combined effects of the electric and Zeeman fields lead to the quadrupled peaks of ${\ensuremath{\rho}}_xx$ and the sequence of $(h/{e}²)/(n+2)$ in the height of the plateaus in ${\ensuremath{\rho}}_xy$.