Electronic phase separation and dramatic inverse band renormalisation in the mixed valence cuprate LiCu$_2$O$_2$

We measured by ARPES the electronic structure of LiCu$_2$O$_2$, a mixed valence cuprate where planes of formally Cu(I) ($3d^{10}$) ions are sandwiched between layers containing one-dimensional edge-sharing Cu(II) ($3d^{9}$) chains. We find that the Cu(I)- and Cu(II)-derived electronic states form separate electronic subsystems, in spite of being coupled by bridging O ions. The valence band, of Cu(I) character, disperses within the charge-transfer gap of the strongly correlated Cu(II) states. This anomalous electronic structure produces an unexpected and unprecedented 250\% $broadening$ of the valence band with respect to the predictions of density functional theory. Our observation is at odds with two widely accepted tenets of many-body theory, namely that correlation effects are weak in filled bands, and that they generally yield narrower bands and larger electron masses.