  Correlated materials may exhibit unusually high resistivity increasing
linearly in temperature, breaking through the Mott-Ioffe-Regel bound, above
which coherent quasiparticles are destroyed. The fate of collective charge
excitations, or plasmons, in these systems is a subject of debate. Several
studies suggest plasmons are overdamped while others detect unrenormalized
plasmons. Here, we present direct optical images of low-loss hyperbolic plasmon
polaritons (HPPs) in the correlated van der Waals metal MoOCl2. HPPs are
plasmon-photon modes that waveguide through extremely anisotropic media and are
remarkably long-lived in MoOCl2. Many-body theory supported by photoemission
results reveals that MoOCl2 is in an orbital-selective and highly incoherent
Peierls phase. Different orbitals acquire markedly different
bonding-antibonding character, producing a highly-anisotropic, isolated Fermi
surface. The Fermi surface is further reconstructed and made partly incoherent
by electronic interactions, renormalizing the plasma frequency. HPPs remain
long-lived in spite of this, allowing us to uncover previously unseen imprints
of electronic correlations on plasmonic collective modes.
