  We report about the energy and momentum dependent charge response in
Ca$_{1.9}$Na$_{0.1}$CuO$_2$Cl$_2$ employing electron energy-loss spectroscopy.
Along the diagonal of the Brillouin zone (BZ) we find a plasmon
peak---indicating the presence of metallic states in this momentum
region---which emerges as a consequence of substantial spectral-weight transfer
from excitations across the charge-transfer (CT) gap and is the two-particle
manifestation of the small Fermi pocket or arc observed with photoemission in
this part of the BZ. In contrast, the spectrum along the [100]-direction is
almost entirely dominated by CT excitations, reminiscent of the insulating
parent compound. We argue that the observed polarization dependent shape of the
spectrum is suggestive of a breaking of the underlying tetragonal lattice
symmetry, possibly due to fluctuating nematic order in the charge channel. In
addition we find the plasmon bandwidth to be suppressed compared to optimally
doped cuprates.
