Origin of the large phonon thermal Hall effect in cuprates

This text mentions work from 2024 on. Those parts were partly written without a live literature search and have not been checked by an editor yet.

In plain words

In copper-oxide superconductors, phonons gain a large sideways heat flow below the doping where the pseudogap state appears and also in the undoped insulating parents. What gives phonons this handedness is unknown.

Precise statement

In hole-doped cuprates inside the pseudogap phase and in the Mott insulators $\mathrm{La_2CuO_4}$ and $\mathrm{Sr_2CuO_2Cl_2}$, a large negative $\kappa_{xy}$, present for heat flow both in the $\mathrm{CuO_2}$ planes and along $c$, is attributed to phonons (Grissonnanche et al. 2019, 2020); a planar thermal Hall response with $B$ in the plane was reported in 2024 (Chen et al., Physical Review X 14, 041011). Identify what couples phonons to $B$ (spin fluctuations of the antiferromagnetic background, defects, or charge-order domains) and predict the doping, field-direction and temperature dependence.

What would settle it

A microscopic coupling that predicts doping, field-direction and temperature dependence, checked across hole- and electron-doped cuprates and across defect densities.

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