What is the most important for a nanoscale structure formations in HTSC?, spin, phonon or third way in Coulomb interaction and correlations?

We show that nanoscale superstructures observed in STM experiments in high temperature superconductor (HTSC) such as cuprates in superconducting state [1] are well described by a model of two-dimensional charged boson gas(2DBG). The bosons are located on top of a uniform, structureless, jellium neutralizing background. This model is the most fundamental and clean quantum system where different properties of the formation of the superconducting and insulating states mcan be studied by changing only one parameter -the boson density n ₀. At high densities the ground state is always superconducting, that is associated with the Bose-Einstein condensation of the charged bosons which form a superfluid state. Whereas at very low densities bosons localize into a Wigner crystal. Here we show that a dilute amount of impurities with opposite charge to bosons alter dramatically the properties of the system. Any charged impurity induces density oscillations, similar to Friedel oscillations in Fermi liquids. When the density decreases the amplitude of these charge density wave(CDW) oscillations increases. At some critical density there arises the CDW instability. As the result around each impurity a Coulomb bubble(CB) is formed. At such a CB there arises an orthogonality catastrophe associated with the formation of localized states inside CB orthogonal to the fluid of free bosons. The creation of localized states may be accompanied by a formation of local lattice distortions. The phenomenon is very similar to the conventional self-trapping or a formation of electronic strings[2]. The CDW instability arises due to over-screening of the Coulomb interaction. The phenomenon of CB formation is very general. They can be created and become localized around any potential induced by phonons or by individual impurities or both. As the result the quantum system separates into two phases: localized CBs distributed randomly and superfluid bosons forming a homogeneous state. When the density decreases after the formation of CBs the area covered by them increases while the superfluid area decreases. Also with decreasing density the number of Coulomb bubbles grows in a step-like manner. At each such step more remote impurities outside the superconducting plane take part in trapping of CBs and reduce significantly the superfluid density. The insulating state emerges either via creation of an infinite percolating cluster of CBs or due to the Wigner crystallization of the bosonic phase.