Description
Several well-known phenomena in the hole-doped cuprates
like breaking the rotational invariance, appearance of the
pseudogap, charge modulation and d-wave superconductivity
occur on a low energy scale of hundreds Kelvin. As it is not
quite clear how to obtain these phases in an unified way from
microscopic models of cuprates, we consider a low-energy
model of fermions interacting with close to critical
antiferromagnetic excitations. In contrast to a standard spin-
fermion model, we assume in agreement with ARPES data
that the fermion spectrum in the antinodal region is shallow,
such that the 8 hotspots merge at not very weak interaction
into 2 antinodal hot regions. In addition to the interaction via
antiferromagnetic fluctuations, a long range part of the
Coulomb interaction reducing the superconducting transition
temperature is taken into the consideration. It is
demonstrated in the mean field approximation that a variety
of phase transitions are possible depending on the chemical
potential and details of the electronic spectrum near the
antinodes. In addition to the d-wave superconductivity and
charge density wave with the diagonal modulation, we find a
nematic transition (Pomeranchuk instability) followed by a
transition to a charge density wave with a modulation along
the bonds and d-wave formfactor. Moreover, it is found that
an electron-hole pairing with a vector connecting to
neighboring antinodes (antiferromagnetic vector of cuprates)
is also possible. Remarkably, this pairing leads to circulating
currents rather than to a charge modulation. These currents
are similar to those proposed in DDW (d-density wave state).
Depending on the parameters of the electron spectrum one
can also obtain an incommensurate structure of circulating
currents. The nematic transition does not lead to formation of
the gap but the circulating currents do. This gap is located at
the antinodes and we associate this state with the pseudogap
state. The results of our theory can serve as an explanation
of recent experiments on cuprates performed with the help of
STM, NMR, hard and resonant soft X-ray scattering, neutron
scattering, sound propagation, and with some other
techniques.
