  Excess charge on polar surfaces of ionic compounds is commonly described by
the two-dimensional electron gas (2DEG) model, a homogeneous distribution of
charge, spatially-confined in a few atomic layers. Here, by combining scanning
probe microscopy with density functional theory calculations, we show that
excess charge on the polar TaO$_2$ termination of KTaO$_3$(001) forms more
complex electronic states with different degrees of spatial and electronic
localization: charge density waves (CDW) coexist with strongly-localized
electron polarons and bipolarons. These surface electronic reconstructions,
originating from the combined action of electron-lattice interaction and
electronic correlation, are energetically more favorable than the 2DEG
solution. They exhibit distinct spectroscopy signals and impact on the surface
properties, as manifested by a local suppression of ferroelectric distortions.
Controlling the degree of charge ordering and the transition from ferroelectric
to paraelectric states could be of great benefit for the generation and
transport of carriers in electronic applications.
