Possible charge instabilities in two-dimensional doped Mott insulators

Abstract

Motivated by the growing evidence of the importance of charge fluctuations in the pseudogap phase in high-temperature cuprate superconductors, we apply a large-$N$ expansion formulated in a path integral representation of the two-dimensional $t$-$J$ model on a square lattice. We study all possible charge instabilities of the paramagnetic state in leading order of the $1/N$ expansion. While the $d$-wave charge density wave (flux phase) becomes the leading instability for various choices of model parameters, we find that a $d$-wave Pomeranchuk (electronic nematic phase) instability occurs as a next leading one. In particular, the nematic state has a strong tendency to become inhomogeneous. In the presence of a large second nearest-neighbor hopping integral, the flux phase is suppressed and the electronic nematic instability becomes leading in a high doping region. Besides these two major instabilities, bond-order phases occur as weaker instabilities close to half-filling. Phase separation is also detected in a finite temperature region near half-filling.