Nonlinear Hall effect in kagome and Lieb lattices with staggered hopping

Recently, significant theoretical and experimental progress on the nonlinear Hall effect has been achieved in graphene. However, the nonlinear Hall effect in other prototypical two-dimensional lattices, e.g., the kagome and Lieb lattices, remains unexplored. In this work, we investigate the nonlinear Hall effect in both the kagome and Lieb lattices with the staggered hopping and intrinsic spin-orbit coupling. In both systems, the staggered hopping breaks the inversion symmetry and gives rise to the nonlinear Hall effect characterized by the Berry curvature dipole. Interestingly, our findings reveal a distinct pattern of the nonlinear Hall effect in the kagome lattice, where the Berry curvature dipole remains stable when the strength of the staggered hopping varies. This scenario is different from that in the Lieb lattice, where the Berry curvature dipole is prominent only within a narrow window close to the phase transitions induced by the staggered hopping. Our discovery is helpful for future studies on the nonlinear Hall effect.