Superconductivity on the density wave background with soliton-wall structure

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Superconductivity (SC) may microscopically coexist with density wave (DW) when the nesting of the Fermi surface (FS) is not perfect. There are, at least, two possible microscopic structures of a DW state with quasi-particle states remaining on the Fermi level and leading to the Cooper instability: (i) the soliton-wall phase and (ii) the small ungapped Fermi-surface pockets. The dispersion of such quasi-particle states strongly differs from that without DW, and so do the properties of SC on the DW background. The upper critical field $H_{c2}$ in such a SC state strongly increases as the system approaches the critical pressure, where superconductivity first appears. $H_{c2}$ may considerably exceed its typical value without DW and has unusual upward curvature as function of temperature. The results obtained explain the experimental observations in layered organic superconductors (TMTSF)$_{2}$PF$_{6}$ and $α$-(BEDT TTF)$_{2}$KHg(SCN)$_{4}$.
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