Influence of Van Hove singularities on the thermal conductivity of high-Tcsuperconductors

We calculate the electronic contribution ${\kappa }_e$ to the thermal conductivity of a two-dimensional $d_{x^2-y^2}$-wave superconductor presenting logarithmic Van Hove singularities (VHS) in the density of states. The influence of the position of these VHS from the Fermi level on the thermal conductivity peak observed below $T_c$ is investigated. Experimental results on different $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ compounds with various oxygen stoichiometry $x$ can be well described by this model with reasonable values of the physical parameters.