Symmetry 2011, 3, 699-749; doi:10.3390/sym3040699 OPEN ACCESS symmetry ISSN 2073-8994 www.mdpi.com/journal/symmetry Article d-Wave Superconductivity and s-Wave Charge Density Waves: Coexistence between Order Parameters of Different Origin and Symmetry Toshikazu Ekino 1 , Alexander M. Gabovich 2,⋆ , Mai Suan Li 3 , Marek Pe ¸kala 4 , Henryk Szymczak 3 and Alexander I. Voitenko 2 1 Hiroshima University, Graduate School of Integrated Arts and Sciences, Higashi-Hiroshima 739-8521, Japan; E-Mail: ekino@hiroshima-u.ac.jp 2 Institute of Physics, National Academy of Sciences of Ukraine, 46, Nauka Ave., Kyiv 03680, Ukraine; E-Mail: voitenko@iop.kiev.ua 3 Institute of Physics, Al. Lotnik ´ ow 32/46, Warsaw PL-02-668, Poland; E-Mails: masli@ifpan.edu.pl (M.S.L.); szymh@ifpan.edu.pl (H.S.) 4 Department of Chemistry, University of Warsaw, Al. Zwirki i Wigury 101, Warsaw PL-02-089, Poland; E-Mail: pekala@chem.uw.edu.pl ⋆ Author to whom correspondence should be addressed; E-Mail: gabovich@iop.kiev.ua; Tel.: +38-044-525-0820; Fax: +38-044-525-1589. Received: 26 May 2011; in revised form: 8 October 2011 / Accepted: 11 October 2011 / Published: 20 October 2011 Abstract: A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-T c oxides. According to the cuprate specificity, the analysis is carried out for the two-dimensional geometry of the Fermi surface (FS). Phase diagrams on the σ 0 − α plane—here, σ 0 is the ratio between the energy gaps in the parent pure CDW and superconducting states, and the quantity 2α is connected with the degree of dielectric (CDW) FS gapping—were obtained for various possible configurations of the order parameters in the momentum space. Relevant tunnel and photoemission experimental data for high-T c oxides are compared with theoretical predictions. A brief review of the results obtained earlier for the coexistence between s-wave superconductivity and CDWs is also given. Keywords: order parameter symmetry; superconductivity; charge-density waves; phase diagrams