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The Berry-phase mediated valley-selected skew scattering in alpha-T3 latticesis demonstrated. The interplay of Lorentz and Berry forces in position andmomentum spaces is revealed and analyzed. Many-body screening of theelectron-impurity interaction is taken into account to avoid overestimation ofback- and skew-scattering of electrons in the system. Triplet peak from skewinteractions at two valleys is found in near-vertical and near-horizontalforward- and backward-scattering directions for small Berry phases and lowmagnetic fields. Magnetic-field dependence in both non-equilibrium andthermal-equilibrium currents is also presented for valley-dependentlongitudinal and transverse transports mediated by a Berry phase.Mathematically, two Boltzmann moment equations are employed for computingscattering-angle distributions of non-equilibrium skew currents by usingmicroscopic inverse energy- and momentum-relaxation times. Meanwhile, avalley-dependent unbalanced thermal-equilibrium anomalous Hall current inducedby the Berry force in momentum space, due to different mobilities for twovalleys, is also computed for comparisons.

Interplay of Lorentz-Berry forces in position-momentum spaces for valley-dependent impurity scattering in alpha-T3 lattices