  Charge order is now accepted as an integral constituent of cuprate
high-temperature superconductors, one that is intimately related to other
instabilities in the phase diagram including antiferromagnetism and
superconductivity. Unlike nesting-induced Peierls-like density waves, the
charge correlations in the CuO2 planes have been predicted to display a rich
momentum space topology depending on the detailed fermiology of the system.
However, to date charge order has only been observed along the high-symmetry
Cu-O bond directions. Here, using resonant soft X-ray scattering, we
investigate the evolution of the full momentum space topology of charge
correlations in Ln2CuO4 (Ln=Nd, Pr) as a function of intrinsic electron doping.
We report that, upon electron doping the parent Mott insulator, charge
correlations first emerge in a hitherto-unobserved form, with full (Cinf)
rotational symmetry in momentum-space. At higher doping levels, the orientation
of charge correlations is sharply locked to the Cu-O bond high-symmetry
directions, restoring a more conventional bidirectional charge order with
enhanced correlation lengths. Through charge susceptibility calculations, we
closely reproduce the drastic evolution in the topology of charge correlations
across an antiferromagnetic quantum phase transition, highlighting the
interplay between spin and charge degrees of freedom in electron-doped
cuprates. Finally, using the established link between charge correlations and
the underlying fermiology, we propose a revised phase diagram of Ln2CuO4 with a
superconducting region extending toward the Mott limit.
