Second-Order Conductivity Probes a Cascade of Singularities in a Moiré Superlattice

Systems lacking inversion symmetry inherently demonstrate a nonlinear electrical response (NLER) to an applied electric bias, emerging through extrinsic mechanisms. This response is highly sensitive to the electronic band structure, which can be precisely engineered in moiré superlattices formed from atomically thin quantum materials. Moiré superlattices host complex Fermi surface reconstructions near van Hove singularities (vHSs) in the electronic density of states. However, the role of these reconstructions in shaping the NLER remains insufficiently understood. In this work, we systematically explore NLER in moiré superlattices of twisted double bilayer graphene (tDBLG) by tuning the Fermi level across multiple moiré bands on both sides of the charge neutrality point. We observe sharp variations and sign reversals in the NLER appearing via extrinsic pathways near midband vHSs. The second-order conductivity near the vHSs demonstrates a value as high as ∼70 μm V^-1 Ω^-1 at zero vertical displacement field. Our results demonstrate that the NLER can serve as a sensitive probe of Fermi surface reconstructions and establish tDBLG as a versatile and highly efficient platform for generating and controlling the nonlinear electrical response.