Two-dimensional (2D) Dirac states and Dirac points with linear dispersion are the hallmark of graphene, topological insulators, semimetals, and superconductors. Lowering a symmetry by the ferroelectric polarization opens the gap in Dirac points and introduces finite Berry curvature. Combining this with Dirac points detached from high symmetry points of the Brillouin zone offers additional ways to tailor topological properties. We explore this concept by studying topological phenomena emerging in 2D materials with movable Dirac points and broken out-of-plane mirror reflection. The resulting topological kink states and Berry curvature dipoles are changed by movable 2D Dirac points with experimental signatures in electrical conductance and second-harmonic nonlinear Hall conductivity. We identify materials platforms where our predictions can be realized and support that with the first-principles results for ${\mathrm{Cl}}_2{\mathrm{Rh}}_2{\mathrm{S}}_2$-GeS junction.

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• Ferroelectric domains
• Second order nonlinear optical processes
• Symmetry protected topological states
• Topological materials
• Valley degrees of freedom
• 2-dimensional systems
• Dirac semimetal
• Ferroelectrics