Berry curvature dipole senses topological transition in twisted double bilayer graphene

The topological phase of quantum materials can be characterized by the band-specific topological invariant Chern number. Often, systems undergo a transition between topological phases, and these transitions are hard to detect. Moiré systems host flat Chern bands. However, time-reversal symmetry dictates the Chern numbers from two valleys, namely, K and K', to be opposite, making the total Chern number C_K + C_K' = 0. In such cases, Berry curvature dipole (BCD) can be used as an indicator of the underlying topological transition of the valley Chern type, that is, a change in Z₂=(C_K – C_K')/2. Unlike the quantum Hall effect or anomalous Hall effect, the approach based on the BCD does not require explicitly breaking the time-reversal symmetry. We reveal, using the nonlinear Hall (NLH) effect measurements in twisted double bilayer graphene (TDBG), that the BCD detects Z₂ transition and changes its sign. Furthermore, we find hysteresis of longitudinal and NLH responses with electric field that can be attributed to switching of electric polarization in moiré systems—this holds promise for next-generation Berry curvature-based memory devices. Probing topological transitions, as we show, can be emulated in other 3D topological systems.