Thermal Hall conductivity as a probe of the quasiparticle mean free path in cuprate superconductors

The thermal Hall conductivity κxy offers a powerful probe of the scattering of d-wave quasiparticles in cuprate superconductors. Building on the semiclassical approach introduced by Zhang et al. [1], the magnitude and temperature dependence of κxy(T,H) give direct access to the quasiparticle mean free path, providing information that is difficult to obtain from longitudinal transport alone.

In this talk, I will present a comprehensive study of κxy across several major cuprate families, including the single-layer HgBa2CuO6+δ (Hg1201), the bilayers YBa2Cu3Oy (YBCO) and Bi2Sr2CaCu2O8+δ (Bi2212), and the trilayer HgBa2Ca2Cu3O8+δ (Hg1223), the cuprate with the highest Tc. Using κxy we extract their quasiparticle mean free paths and compare the intrinsic disorder levels of each material. Hg1223 is found to exhibit a mean free path as long as that of the cleanest YBCO crystals, consistent with a protective role of the outer CuO2 planes [2]. In contrast, Bi2212 shows a mean free path nearly an order of magnitude shorter, revealing a markedly stronger disorder potential [3].

Furthermore, in the cleanest materials (YBCO and Hg1223) the temperature dependence of the inferred scattering rate follows a cubic law, in excellent agreement with theoretical expectations for nodal quasiparticles in a d-wave superconductor [4,5]. These results demonstrate the effectiveness of κxy as a selective and sensitive probe of quasiparticle dynamics and highlight how crystallographic structure and intrinsic disorder shape the low-energy excitations of the cuprate superconductors.

[1] Zhang et al., Physical Review Letters 86, 890 (2001).

[2] Altangerel et al., Physical Review B 112, 014522 (2025).

[3] Campillo et al., arXiv:2508.05196 (2025).

[4] Walker and Smith, Physical Review B 61, 11285 (2000).

[5] Duffy, Hirschfeld and Scalapino, Physical Review B 64, 224522 (2001).