Effect of trigonal warping on the Berry curvature and valley/spin Hall effects in monolayer MoS2

Abstract

Recently, the nonlinear optical processes study on monolayer MoS2 has revealed the existence of a trigonal warping in the band structure which distorts the Fermi surface from a circle at low energies to a triangle at higher energies. Here we theoretically demonstrate that the trigonal warping induce important modifications on the Berry curvature, orbital magnetic moment, and valley Hall conductance in monolayer MoS2. The analytical results show that both Berry curvature and orbital magnetic moment are trigonally warped in contrast to the isotropic case without warping, which is consistent with the numerical calculations. The valley Hall conductance is reduced by the trigonal warping due to the warped Berry curvatures, whereas the spin Hall conductance remains nearly intact. Our findings are useful in explaining the valley and spin Hall data on monolayer MoS2 and other transition metal dichalcogenides.