Plasmon Worldlines Reveal Quantum Geometrical Breakdown of Galilean Invariance in Graphene Bilayer

Galilean invariance asserts that physical laws remain unchanged under coordinate transformations that include both space and time translations. Plasmons, the quanta of charge density oscillations, are generally analyzed within a Galilean-invariant framework. In this work, we investigated plasmon wave packets residing in parabolic bands of Bernal bilayer graphene, a system that theoretically should exhibit Galilean invariance. However, the pseudospin texture, arising from the quantum geometry of the electronic wave function, disrupts Galilean invariance at the length scales of plasmon wavelengths and timescales of inverse plasmon frequency. By employing nano-terahertz spacetime metrology, we directly visualized plasmon worldlines in spacetime coordinates. Our experiments revealed a pronounced enhancement of the Drude weight as the carrier density approached the charge neutrality point. This renormalization of the plasmon dispersion deviates from classical plasmonic theory, resulting from the interplay between many-body correlations and the nontrivial quantum geometry of chiral fermions in Bernal bilayer graphene. These findings provide new insights into the influence of spacetime symmetry, electronic correlations, and quantum geometry on the macroscopic plasmonic response of quantum many-body systems.