Lorenz Number in High $T_c$ Superconductors: Evidence for Bipolarons

The strong electron-phonon interaction in cuprates has gathered support over the last decade in a number of experiments. While phonons remain almost unrenormalized, electrons are transformed into itinerant bipolarons and thermally excited polarons when the electron-phonon interaction is strong. We calculate the Lorenz number of the system to show that the Wiedemann-Franz law breaks down because of the interference of polaron and bipolaron contributions in the heat flow. The model fits numerically the experimental Hall Lorenz number, which provides direct evidence for bipolarons in the cuprates.

Figure 1

The experimental Hall Lorenz number [29] in ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6.95}$ fitted by the bipolaron theory, Eqs. (11, 12), with ${\Theta }_b/{\Theta }_p=0.44$. The upper inset shows the linear in-plane resistivity and the Hall ratio. The lower inset shows the ratio of the Hall Lorenz number to the Lorenz number as a function of temperature.