The high temperature superconductivity in cuprates: physics of the pseudogap region

We discuss the physics of the high temperature superconductivity in hole doped copperoxide ceramics in the pseudogap region. Starting from an effective reduced Hamiltonianrelevant to the dynamics of holes injected into the copper oxide layers proposed in aprevious paper, we determine the superconductive condensate wavefunction. We show that thelow-lying elementary condensate excitations are analogous to the rotons in superfluid4He. We arguethat the rotons-like excitations account for the specific heat anomaly at the criticaltemperature. We discuss and compare with experimental observations the London penetrationlength, the Abrikosov vortices, the upper and lower critical magnetic fields, and thecritical current density. We give arguments to explain the origin of the Fermi arcs andFermi pockets. We investigate the nodal gap in the cuprate superconductors and discussboth the doping and temperature dependence of the nodal gap. We suggest that the nodal gapis responsible for the doping dependence of the so-called nodal Fermi velocity detected inangle resolved photoemission spectroscopy studies. We discuss the thermodynamics of thenodal quasielectron liquid and their role in the low temperature specific heat. We proposethat the ubiquitous presence of charge density wave in hole doped cuprate superconductorsin the pseudogap region originates from instabilities of the nodal quasielectrons drivenby the interaction with the planar CuO2 lattice. We investigate the doping dependence of thecharge density wave gap and the competition between charge order and superconductivity. Wediscuss the effects of external magnetic fields on the charge density wave gap andelucidate the interplay between charge density wave and Abrikosov vortices. Finally, weexamine the physics underlying quantum oscillations in the pseudogap region.