A model for liquid-striped liquid phase separation in liquids of anisotropic polarons

The phase separation between a striped polaron liquid at the particular density and a high density polaron liquid is described by a modified Van der Waals scheme. The striped polaron liquid represents the pseudo gap matter or Wigner-like polaron phase at 1/8 doping in cuprate superconductors. The model includes the tendency of pseudo- Jahn-Teller polarons to form anisotropic directional bonds at a preferential volume with the formation of different liquid phases. The model gives the coexistence of a first low density polaron striped liquid and a second high density liquid that appears in cuprate superconductors for doping larger than 1/8. We discuss how the strength of anisotropic bonds controls the variation the phase separation scenarios for complex systems in the presence of a quantum critical point where the phase separation vanishes.