Theory of High Temperature Superconductivity in Doped Polar Insulator
  In the last two decades there have been tremendous attempts to built an adequate theory of high-temperature superconductivity. Most studies (including our efforts) used some model Hamiltonians with input parameters not directly related to the material. The dielectric response function of electrons in strongly correlated high-temperature superconductors is apriori unknown. Hence one has to start with the generic Hamiltonian including unscreened Coulomb and Froehlich electron-phonon interactions operating on the same scale since any ad-hoc assumption on their range and relative magnitude might fail. Using such a generic Hamiltonian I have built the analytical theory of high-temperature superconductivity in doped polar insulators predicting the critical temperature in excess of a hundred Kelvin without any adjustable parameters. The many-particle electron system is described by an analytically solvable polaronic "t-Jp" Hamiltonian with reduced hopping integral, t, allowed double on-site occupancy, large phonon-induced antiferromagnetic exchange, Jp >> t, and a high-temperature superconducting state of small superlight bipolarons protected from clustering. 
A. S. Alexandrov
cond-mat.supr-con cond-mat.str-el quant-ph