Origin of the large thermal Hall effect in the pseudogap phase and Mott-insulating cuprates
In plain words
Hole-doped cuprates show a large negative thermal Hall conductivity when they enter the pseudogap regime, and an even larger signal can appear in undoped Mott-insulating compounds where mobile electrons are absent. Measurements suggest that phonons carry much of the heat Hall current, but phonons are neutral and need some coupling to acquire chirality. The open problem is to identify the microscopic source of this phonon thermal Hall response and explain its sign, size, temperature dependence, and doping dependence.
Precise statement
What microscopic mechanism produces the observed phonon-dominated thermal Hall conductivities $\kappa_{xy}$ and $\kappa_{zy}$ in cuprates for dopings $p<p^\ast$ and in undoped Mott insulators such as $\mathrm{La_2CuO_4}$, including the large negative low-temperature value $|\kappa_{xy}|/T \sim 0.5\,\mathrm{mW\,K^{-2}\,m^{-1}}$ at $B=15\,\mathrm{T}$? Is the dominant contribution due to extrinsic skew scattering from defects or impurities, coupling of phonons to antiferromagnetic spin fluctuations, or coupling to a symmetry-breaking order parameter of the pseudogap phase?
What would settle it
A microscopic model that quantitatively reproduces the sign, magnitude, temperature dependence, doping dependence, and tensor components $\kappa_{xy}$ and $\kappa_{zy}$, together with decisive experiments using controlled disorder, substitution, and isotope changes that separate extrinsic defect contributions from intrinsic spin or order-parameter mechanisms.
References
1. G. Grissonnanche et al., Giant thermal Hall conductivity in the pseudogap phase of cuprate superconductors, Nature 571, 376 (2019).
2. G. Grissonnanche et al., Chiral phonons in the pseudogap phase of cuprates, Nature Physics 16, 1108 (2020).
3. M.-E. Boulanger et al., Thermal Hall conductivity in the cuprate Mott insulators Nd2CuO4 and Sr2CuO2Cl2, Nature Communications 11, 5325 (2020).