INSTITUTE OF PHYSICS PUBLISHING SUPERCONDUCTOR SCIENCE AND TECHNOLOGY Supercond. Sci. Technol. 14 (2001) R1–R27 www.iop.org/Journals/su PII: S0953-2048(01)08307-5 TOPICAL REVIEW Charge- and spin-density-wave superconductors A M Gabovich 1,4 , A I Voitenko 1,4 , J F Annett 2 and M Ausloos 3 1 Crystal Physics Department, Institute of Physics, National Academy of Sciences, prospekt Nauki 46, 03650 Kiev-28, Ukraine 2 University of Bristol, Department of Physics, H.H.Wills Physics Laboratory, Royal Fort, Tyndall Avenue, Bristol BS8 1TL, UK 3 SUPRAS, Institut de Physique B5, Universit´ e de Li` ege, Sart Tilman, B-4000 Li` ege, Belgium E-mail: collphen@iop.kiev.ua Received 8 June 2000, in final form 14 January 2001 Abstract This review deals with the properties of superconductors with competing electron spectrum instabilities, namely, charge-density waves (CDWs) and spin-density waves (SDWs). The underlying reasons of the electron spectrum instability may be either Fermi surface nesting or the existence of Van Hove saddle points for lower dimensionalities. CDW superconductors include layered dichalcogenides, NbSe 3 , and compounds with the A15 and C15 structures among others. There is much evidence to show that high-T c oxides may also belong to this group of materials. The SDW superconductors include URu 2 Si 2 and related heavy-fermion compounds, Cr–Re alloys and organic superconductors. We review the experimental evidence for CDW and SDW instabilities in a wide range of different superconductors, and assess the competition between these instabilities of the Fermi surface and the superconducting gap. Issues concerning the superconducting order parameter symmetry are also touched upon. The accent is put on establishing a universal framework for further theoretical discussions and experimental investigations based on an extensive list of available and up-to-date references. 1. Introduction The concept of a Fermi surface driven structural transition due to the electron–phonon interaction (commonly called the Peierls transition) has its roots in the 1930s [1], but only became widely appreciated after the publication of the book Quantum Theory of Solids [2]. At the same time, Fr ¨ ohlich [3] considered a possible sliding of the collective state involving electrons and lattice displacements in the one-dimensional (1D) metal as a manifestation of the superconductivity. The emergent energy gap was identified by him with a superconducting rather than with the dielectric Peierls gap [1, 2] as it should be. Even in the absence (practically inaccessible) of impurities, finite phonon lifetimes, three-dimensional (3D) ordering and the commensurability of the sliding wave with the background crystal lattice [4–9], the Fr¨ ohlich 1D metal would have really 4 Corresponding authors. become a so-called ‘ideal conductor’ with a zero resistance, rather than a true superconductor exhibiting the Meissner and Josephson effects [10, 11]. It is remarkable that the concept of the electron spectrum energy gap in the superconducting state had also been proposed by Bardeen [12] almost simultaneously with Fr¨ ohlich and before the full microscopic Bardeen– Cooper–Schrieffer (BCS) theory was developed [13]. The Fr¨ ohlich point of view [3] was revived after the sensational discovery of the giant conductivity peak in the organic salt TTF–TCNQ [14]. However, the coherent transport phenomena appropriate to these quasi-1D substances appeared to be a manifestation of a quite different collective state: charge-density waves (CDWs) coupled with periodic lattice distortions [4, 6, 8, 9, 15–18]. Their coherent properties now constitute a separate interesting branch of solid-state science, but lie beyond the scope of our review and will be touched upon hereafter only in specific cases where necessary. Here we 0953-2048/01/040001+27$30.00 © 2001 IOP Publishing Ltd Printed in the UK R1