Magnetotransport properties of the α-T ₃ model

Using the well-known Kubo formula, we evaluate magnetotransport quantities, such as the collisional and Hall conductivities of the α-T ₃ model. The collisional conductivity exhibits a series of peaks at a strong magnetic field. Each of the conductivity peaks for [Formula: see text] (graphene) splits into two in the presence of a finite α. This splitting occurs due to a finite phase difference between the contributions coming from the two valleys. The density of states is also calculated to explore the origin of the splitting of conductivity peaks. As α approaches 1, the right split part of a conductivity peak comes closer to the left split part of the next conductivity peak. At [Formula: see text], they merge with each other to produce a new series of the conductivity peaks. On the other hand, the Hall conductivity undergoes a smooth transition from [Formula: see text] to [Formula: see text] with n  =  0,1,2,... as we tune α from 0-1. For intermediate α, we obtain the Hall plateaus at values 0,2,4,6,8,... in units of e ²/h.