Quantum magneto-transport properties of monolayers MoSi$_2$N$_4$, WSi$_2$N$_4$, and MoSi$_2$As$_4$.

We study the transport properties of monolayers MoSi$_2$N$_4$, WSi$_2$N$_4$, and MoSi$_2$As$_4$ in a perpendicular magnetic field. The Landau level (LL) band structures including spin and exchange field effects are derived and discussed using a low-energy effective model. We show that the LLs band structures of these materials are similar to those of phosphorene and transition-metal dichalcogenides rather than graphene or silicene. The combination between strong spin-orbit coupling and exchange fields reduces the degradation of the LLs, leading to new plateaus in the Hall conductivity and Hall resistivity and new peaks in the longitudinal conductivity and longitudinal resistivity. The effect of the exchange field, carrier density, and LLs band structure on the conductivities and resistivities have been investigated. At high temperatures, the steps in Hall conductivity and resistivity plateaus disappear and reduce to their corresponding classical forms.