High-temperature superconductivity from realistic Coulomb and Fröhlich interactions

Abstract

In the last years ample experimental evidence has shown that charge carriers in high-temperature superconductors are strongly correlated but also coupled with lattice vibrations (phonons), signaling that the true origin of high-Tc superconductivity can only be found in a proper combination of Coulomb and electron-phonon interactions. On this basis, we propose and study a model for high-Tc superconductivity, which accounts for realistic Coulomb repulsion, strong electron-phonon (Fröhlich) interaction and residual on-site (HubbardŨ ) correlations without any ad-hoc assumptions on their relative strength and interaction range. In the framework of this model, which exhibits a phase transition to a superconducting state with a critical temperature Tc well in excess of 100K, we emphasize the role ofŨ as the driving parameter for a BEC/BCS crossover. Our model lays a microscopic foundation for the polaron-bipolaron theory of superconductivity. We argue that the high-Tc phenomenon originates in competing Coulomb and Fröhlich interactions beyond the conventional BCS description.

Pseudogap in high-temperature superconductors from realistic Fröhlich and Coulomb interactions

“…As follows from Fig.1, for t/J p (Ũ ) ≈ 1 and forŨ ≫ 1 (J p (Ũ → ∞) → 0 [19]), the gap ∆ goes to zero. In this case bipolaron and unpaired polaron bands are completely overlapped with a single peak in the specific heat coefficient γ(T ) = C(T )/T leading to γ(T ) ∝ 1/T , Fig.3.…”

“…Importantly, it is worth noting that numerical data for R(x, T ) have been calculated by integrating the normalized conductivity σ(eV )/σ(∆), therefore do not depend on the particular choice of the tunnelling matrix elements B, and P in Eq.12. As one would expect, the only relevant quantities are t, J p (Ũ ),Ũ that, unlike in other theories, in the t-J p -Ũ model can be fixed from the measurable material properties [17][18][19].…”

“…The intensities A p,b of polaron and bipolaron contributions, calculated from the corresponding bandwidths w p,b , are both related to the ratio t/J p (Ũ ). The gap ∆, corresponding to the binding energy per polaron, is close to J p /2 for t/J p ≪ 1 and rapidly decreases with increasing ratio t/J p , vanishing at a critical value of U or t (Fig.1) when the bottom of the unpaired polaron band approaches the bipolaron ground-state energy [19]. Such an approximation is able to get an insight in a qualitative microscopic description of the pseudogap and also allows to obtain analytical expressions for all the relevant physical properties in terms of the model parameters.…”

“…that accounts for realistic Coulomb repulsion and strong electron-phonon (Fröhlich) interaction in terms of an exchange coupling J p [17,18] and a residual on-site correlationŨ which, limiting the double occupancy, reduces J p from its bare value [19]. Here c i , c into the chemical potential, but provides a more intuitive visualization of the spectrum (Fig.1).…”

“…In particular, the polaron band immediately follows from the first term in the Hamiltonian, and therefore has width 2w p = 8t. The bipolaron band instead can be obtained by means of exact diagonalization in the space of singlet pairs [18,19] which gives w b ∝ t 2 /J p for t ≪ J p .…”