Explicit and implicit experimental evidence for charge density wave (CDW) presence in high-Tcsuperconducting oxides is analyzed. The theory of CDW superconductors is presented. It is shown that the observed pseudogaps and dip-hump structures in tunnel and photoemission spectra are manifestations of the same CDW gapping of the quasiparticle density of states. Huge pseudogaps are transformed into modest dip-hump structures at low temperatures,T, when the electron spectrum superconducting gapping dominates. Heat capacity jumps at the superconducting critical temperature and the paramagnetic limit are calculated for CDW superconductors. For a certain range of parameters, the CDW state in ad-wave superconductor becomes reentrant withT, the main control quantity being a portion of dielectrcally gapped Fermi surface. It is shown that in the weak-coupling approximation, the ratio between the superconducting gap at zero temperatureΔ(T=0)andTchas the Bardeen-Cooper-Schrieffer value fors-wave Cooper pairing and exceeds the corresponding value ford-wave pairing of CDW superconductors. Thus, large experimentally found values2Δ(T=0)/Tc≈5÷8are easily reproduced with reasonable input parameter values of the model. The conclusion is made that CDWs play a significant role in cuprate superconductivity.

Differential conductance $G$ as the function of the bias voltage $V$ across the tunnel junction between a normal metal and an inhomogeneous superconductor with charge density waves (CDW’s) has been calculated by spatial averaging over random domains with varying superconducting- and normal-state properties. For these materials, irregularly distorted CDW patterns with spatially scattered values of various parameters were earlier shown to manifest themselves in a great body of experimental data. The results of the calculations were applied to explain the well-known dip-hump structure in the $G\left(V\right)$ dependence for ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ and other high-$T_c$ cuprates.

The properties of existing superconductors with ejectron spectrum instabilities, namely charge-density waves (CDWs) and spin-density waves (SDWs), are reviewed. In such substances the superconducting gap exists over the whole Fermi surface, whereas the dielectric gap emerges only on its nested sections. In particular, CDW superconductors include layered dichalcogenides, ${\mathrm{NbSe}}_{\mathrm{3}},$ compounds with the $\text{A15}$ and $\text{C15}$ structures, etc. There is a lot of evidence that high-$T_c$ oxides also belong to this group of materials. SDW superconductors include, e.g., ${\mathrm{URu}}_{\mathrm{2}}{\mathrm{Si}}_{\mathrm{2}}$ and related heavy-fermion compounds, Cr–Re alloys and organic superconductors. The theoretical description given in this review is based mostly on the Bilbro-McMillan model of the partially dielectrized metal. Various thermodynamic and electrodynamic properties are calculated in the framework of this model. The main subject of the review is the nonstationary Josephson effect in tunnel junctions involving CDW or SDW superconductors. A new effect of symmetry breaking in symmetrical tunnel junctions is predicted by the authors. A comparison with experiment is given.