Nonlinear nanoscale optics, a success story driven by ultra-short laser pulses of immense power, commonly invokes surface plasmons, highly sensitive to details of the tightly confined electric field. Intrinsically 2D materials like graphene or so-called TMDs additionally offer gate-tunability of their nonlinear response.
We develop the spectral representation of $n$th order response functions in general, then focus on the cubic longitudinal density response of charge carriers in semiconductor heterostructures. Depending on the perturbing signal, collective and single-particle modes give a rich spectrum displaying multifaceted frequency mixing. We further discuss spin-/valley-polarized systems, relevant in plasmonics, and give preliminary results for graphene.