  We have used rotational anisotropic polarized Raman spectroscopy to study the
symmetries, the temperature and the doping dependence of the charge ordered
state in metallic $(Sr_{1-x}La_{x})_{3}Ir_{2}O_{7}$. Although the Raman probe
size is greater than the charge ordering length, we establish that the charge
ordering breaks the fourfold rotational symmetry of the underlying tetragonal
crystal lattice into twofold, as well as the translational symmetry, and forms
short-range domains with $90^{\circ}$ rotated charge order wave vectors, as
soon as the charge order sets in below $T_{CO} = \sim$ 200K and across the
doping-induced insulator metal transition. We observe that this charge order
mode frequency remains nearly constant over a wide temperature range and up to
the highest doping level. These above features are highly reminiscent of the
ubiquitous unidirectional charge order in underdoped high-$T_C$
copper-oxide-based superconductors (cuprates). We further resolve that the
charge order damping rate diverges when approaching $T_{CO}$ from below and
increases significantly as increasing the La doping level, which resembles the
behaviors for a disorder-interrupted ordered phase and has not been observed
for the charge order in cuprates.
