Overlapping hot spots and charge modulation in cuprates

Particle-hole instabilities are studied within a two dimensional model of fermions interacting with antiferromagnetic spin fluctuations (spin-fermion model). In contrast to previous works, we assume that neighboring hot spots overlap due to a shallow dispersion of the electron spectrum in the antinodal region and include in the consideration effects of a remnant low energy and momentum Coulomb interaction. It turns out that this modification of the model drastically changes the behavior of the system. The leading particle-hole instability at not very weak fermion-fermion interaction is no longer a charge density wave with a modulation along the diagonals of the Brillouin zone predicted previously but a Pomeranchuk-type deformation of the Fermi surface breaking the C$_{4}$ symmetry of the system. This order does not prevent from further phase transitions at lower temperatures. We show that, depending on parameters of the interaction, either d-wave superconductivity or charge density wave with modulations along the bonds of the $CuO$ lattice is possible. The low momentum remnant Coulomb interaction enhances the d-form factor of the charge density wave. Comparison with experimental data allows us to conclude that in many cuprate compounds the conditions for the proposed scenario are indeed fulfilled. Our results may explain important features of the charge modulations observed recently.