Geometrical transport in pseudospin-1 fermions

Electronic transport in the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}₃$ model of pseudospin-1 fermions with a finite gap is studied within the semiclassical Boltzmann approximation. We show that coupling of the orbital magnetic moment to the external magnetic field, which is otherwise absent in the massless model, breaks valley symmetry, results in finite and measurable corrections to the longitudinal and Hall conductivity, and yields a geometrical contribution to the Hall conductivity due to the Berry curvature. We also show that, for a generic two-dimensional system, remarkably, magnetoresistance induced by the orbital magnetic moment can be either positive or negative; the sign depends on the amount of disorder and is different for both conventional and geometric contributions to the magnetoresistance.