  Collective plasmon modes, riding on top of drifting electrons, acquire a
fascinating nonreciprocal dispersion characterized by $\omega_p(\bm{q}) \neq
\omega_p(-\bm{q})$. The {\it classical} plasmonic Doppler shift arises from the
polarization of the Fermi surface due to the applied DC bias voltage. Going
beyond this paradigm, we predict a {\it quantum} plasmonic Doppler shift
originating from the quantum metric of the Bloch wavefunction. We
systematically compare the classical and quantum Doppler shifts by
investigating the drift-induced nonreciprocal plasmon dispersion in generic
quantum systems. We demonstrate quantum nonreciprocal plasmons in graphene and
twisted bilayer graphene. We show that the quantum plasmonic Doppler shift
dominates in \moire systems at large wavevectors, yielding plasmonic
nonreciprocity up to 20\% in twisted bilayer graphene. Our findings demonstrate
the supremacy of plasmonic quantum Doppler shift in \moire systems, motivating
the design of innovative nonreciprocal photonic devices with potential
technological implications.
