Estimation of the Quasiparticle Scattering Rate through Thermal Hall Conductivity in the Cuprate Superconductor Bi₂Sr₂CaCu₂O_δ+8

We present a study of the thermal conductivity κ_xx and thermal Hall conductivity κ_xy in the cuprate superconductor Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) across three doping regimes: underdoped, optimally doped, and overdoped. Our measurements reveal a significant increase in both κxx and κ_xy below the superconducting transition temperature T_c in the optimally doped and overdoped samples, indicating an increase in the electronic mean free path due to the suppression of electron-electron scattering as Cooper pairs form. By estimating the quasiparticle scattering rate 1/τ_s using a model previously applied to YBa₂Cu₃O_y (YBCO), we find that the magnitude of 1/τ_s at T = 0K is approximatively one order of magnitude higher in Bi-2212 than in clean YBCO, suggesting a significantly shorter mean free path in Bi-2212. Furthermore, the observed T² dependence of 1/τ_s contrasts with the theoretical T³ dependence expected for clean d-wave superconductors, providing insights into the scattering mechanisms and highlighting the role of κ_xy in probing the transport properties of these materials.