The phase diagram for coexisting d-wave superconductivity and charge-density waves: cuprates and beyond

Phase diagrams of d-wave superconductivity characterized by an order parameter Delta coexisting with charge-density waves (CDWs) characterized by an order parameter Sigma were constructed for the two-dimensional Fermi surface (FS) appropriate to, e. g., cuprates. CDWs were considered as an origin of the pseudogap appearing at antinodal FS sections of the d(x2-y2) superconductor. Two types of the Sigma-reentrance were found: with the temperature, T, and with the opening of the CDW sector, 2 alpha. The angular plots in the momentum space for the resulting gap profile over the FS ('gap roses') were obtained. The gap patterns are rather involved, giving insight into the difficulties of the interpretation of photoemission spectra. It was shown that the Sigma-Delta coexistence region exists even for the complete dielectric gapping due to the distinction between the superconducting and CDW order parameter symmetries. The checkerboard and unidirectional CDW configurations were examined, and both the phase diagrams and the behavior with T and alpha of the order parameters were found to differ. A more general case with a non-zero mismatch angle beta between the superconducting lobes and the CDW sectors was analyzed, the case beta = pi/4 corresponding to the d(xy) symmetry of the superconducting order parameter. The phase diagrams were found to be sensitive to beta-variations, showing that internal strains and external pressure can drastically affect the behavior of Sigma(T) and Delta(T).