Bipolaronic superconductivity: Thermodynamics, magnetic properties, and possibility of existence in real substances

We examine systems where narrow-band electrons strongly couple to the lattice, resulting in the formation of locally bound pairs of small polarons, so-called bipolarons. Such systems present a hard-core charged Bose gas on a lattice. We study the strong dependence of the mass of these bosons and the interaction among themselves as a function of the characteristic phonon frequency. The conditions under which a phenomenological negative-U Hubbard model is applicable to such systems are established. We derive the phase diagram and excitation spectrum, fully taking fluctuations into account. It turns out that quantum fluctuations stabilize the homogeneous superconducting phase and suppress charge order. The specific heat in the superconducting phase shows a power-law behavior: $C_s$∼$T^{\alpha }$, with (3/2)≤α≤3, depending on the temperature. The specific heat in the normal phase for such heavy bosons on a lattice shows linear T dependence at low temperature and a $T^{\mathrm{-}2}$ behavior for high temperature. We demonstrate that the specific heats in the normal state for narrow-band bosons and fermions on a lattice are practically identical. The spin susceptibility of triplet-bipolarons shows Curie behavior at high temperature, but differs qualitatively from the Pauli susceptibility of narrow-band electrons at low temperature. We examine the electrodynamics of the superconducting phase. The equivalent of the Ginzburg-Landau theory for the narrow-band strong-coupling electron-lattice system is derived; this represents an equation of the order parameters of the charged interacting Bose gas which determines the upper critical field and coherence length, which are strongly dependent on the scattering mechanism for the bosons. In the case of impurity scattering they show unusual temperature dependence: $d^2$$H_{c2}$/${\mathrm{dT}}^2$>0. The possible application of our picture of heavy bosons to the description of certain A15 compounds, Chevrel phases, heavy-fermion systems, and ${\mathrm{BaBi}}_{\mathrm{x}}$${\mathrm{Pb}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{O}}_3$ is discussed.