Coulomb pairing of like-charged particles with negative effective mass in high-temperature superconductors

Quasi-steady states of pairs of like-charged quasi-particles can be formed because the electronic structure of compounds exhibiting high-temperature superconductivity has various important characteristics: a quasi-two-dimensional electron spectrum, clearly defined nesting of constant-energy lines, and the presence of a logarithmic singularity of the density of states in the immediate vicinity of the Fermi level. Thus, a situation is achieved where, in an extensive region of the Brillouin zone adjacent to the Fermi level, the principal values of the tensor of the reciprocal effective masses have opposite signs and differ appreciably in absolute value. As a result, the nature of the Coulomb correlation interaction between charge carriers of the same sign (holes in p-cuprates) varies: effective attraction may predominate, leading to the formation of long-lived states of relative motion of quasi-particles which form a pair having a quasi-momentum approximately equal to twice the Fermi quasi-momentum typical of this direction (focused pairs). Assuming that the correlation interaction is short-range (screened Coulomb interaction attenuated by filling of states inside the Fermi contour), we determine the energies and envelope functions of the relative motion of a hole pair which correspond to the density-of-states maxima of the pairs attributable to these quasi-steady states. The dependence of these quantities on the polar angle in the plane of the conducting layer reflects the symmetry of the electronic structure of the compound in the normal state and is generally consistent with a mixture of states assigned to s and d types of orbital symmetry. The quasi-steady state as a function of the doping level of the system agrees qualitatively with the concentration dependence of the temperature for the appearance of a pseudogap observed in p-cuprates at below-optimum doping levels. An estimate of the pair concentration above which a gain in correlation energy occurs gives a value which corresponds to the onset of effective pair overlap (for which the characteristic spatial scale is a few or a few tens of interatomic distances).