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We study particle-hole instabilities in the framework of the spin-fermion(SF) model. In contrast to previous studies, we assume that adjacent hot spotscan overlap due to a shallow dispersion of the electron spectrum in theantinodal region. In addition, we take into account effects of a remnant lowenergy and momentum Coulomb interaction. We demonstrate that at sufficientlysmall values $|\varepsilon (\pi ,0)-E_{F}|\lesssim \Gamma $, where $E_{F}$ isthe Fermi energy, $\varepsilon \left( \pi ,0\right) $ is the energy in themiddle of the Brillouin zone edge, and $\Gamma $ is a characteristic energy ofthe fermion-fermion interaction due to the antiferromagnetic fluctuations, theleading particle-hole instability is a d-form factor Fermi surface deformation(Pomeranchuk instability) rather than the charge modulation along the Brillouinzone diagonals predicted within the standard SF model previously. At lowertemperatures, we find that the deformed Fermi surface is further unstable toformation of a d-form factor charge density wave (CDW) with a wave vector alongthe Cu-O-Cu bonds (axes of the Brillouin zone). We show that the remnantCoulomb interaction enhances the d-form factor symmetry of the CDW. Thesefindings can explain the robustness of this order in the cuprates. Theapproximations made in the paper are justified by a small parameter that allowsone an Eliashberg-like treatment. Comparison with experiments suggests that inmany cuprate compounds the prerequisites for the proposed scenario are indeedfulfilled and the results obtained may explain important features of the chargemodulations observed recently.

Spin-fermion model with overlapping hot spots and charge modulation in cuprates