Movable Dirac Points with Ferroelectrics: Kink States and Berry Curvature Dipoles

Two-dimensional (2D) Dirac states and Dirac points with linear dispersion are the hallmark of graphene, topological insulators, semimetals, and superconductors. Unlike in the 3D case, the protection of these gapless points in two dimensions is not robust [1,2]: In the absence of the protection, the gap opening favors topological effects by realizing sub-band-gap edge states and equips Dirac states with finite Berry curvature. Combining this with Dirac points detached from high symmetry points of the Brillouin zone offers additional ways to tailor topological properties. In our work [3], we study topological phenomena emerging in 2D materials with movable Dirac points that can be further controlled by ferroelectrics (FEs). We focus on transforming topology-enforced kink electronic states at structural domain walls (DWs) separating opposite FE polarizations. Movable Dirac points control the measured conductance from kink states sensitive to the crystallographic orientation of DWs, and they also modify the dipole character of the Berry curvature, which is responsible for switching between the zero and nonzero second-harmonic nonlinear Hall conductivity. We develop a minimal tight-binding model for movable gapped Dirac points, identify materials platforms where our predictions can be realized and support that with the first-principles results for Cl2Rh2S2-GeS junction.

References

[1] S. M. Young and C. L. Kane, Phys. Rev. Lett. 115, 126803 (2015).

[2] F. Liu, F. Qu, I. Žutić, and M. Malard, Sci. Rep. 12, 14981 (2022).

[3] K. S. Denisov, Y. Liu and I. Žutić, Phys. Rev. Lett. 134, 246602 (2025).