The nature of the pseudogap phase of cuprates remains a major puzzle. Although there are indications that this phase breaks various symmetries, there is no consensus on its fundamental nature 1 . Although Fermi-surface 2 , transport 3 and thermodynamic 4 signatures of the pseudogap phase are reminiscent of a transition into a phase with antiferromagnetic order 5,6 , there is no evidence for an associated long-range magnetic order. Here we report measurements of the thermal Hall conductivity κ xy in the normal state of four different cuprates (La 1.6-x Nd 0.4 Sr x CuO 4 , La 1.8-x Eu 0.2 Sr x CuO 4 , La 2-x Sr x CuO 4 , and Bi 2 Sr 2-x La x CuO 6+δ ) and show that a large negative κ xy signal is a property of the pseudogap phase, appearing with the onset of that phase at the critical doping p*. Since it is not due to charge carriersas it persists when the material becomes an insulator, at low doping -or magnons -as it exists in the absence of magnetic order -or phonons -since skew scattering

The nature of the pseudogap phase of cuprates remains a major puzzle 1,2 . One ofnew signatures is a large negative thermal Hall conductivity κ xy , which appears for dopings p below the pseudogap critical doping p*, but whose origin is as yet unknown 3 . Because this large κ xy is observed even in the undoped Mott insulator La 2 CuO 4 , it cannot come from charge carriers, these being localized at p = 0. Here we show that the thermal Hall conductivity of La 2 CuO 4 is roughly isotropic, being nearly the same for heat transport parallel and normal to the CuO 2 planes, i.e. κ zy (T) ≈ κ xy (T). This shows that the Hall response must come from phonons, these being the only heat carriers able to move as easily normal and parallel to the planes 4 . At p > p*, in both La 1.6-x Nd 0.4 Sr x CuO 4 and La 1.8-x Eu 0.2 Sr x CuO 4 with

The heat carriers responsible for the unexpectedly large thermal Hall conductivity of the cuprate Mott insulator La2CuO4 were recently shown to be phonons. However, the mechanism by which phonons in cuprates acquire chirality in a magnetic field is still unknown. Here, we report a similar thermal Hall conductivity in two cuprate Mott insulators with significantly different crystal structures and magnetic orders – Nd2CuO4 and Sr2CuO2Cl2 – and show that two potential mechanisms can be excluded – the scattering of phonons by rare-earth impurities and by structural domains. Our comparative study further reveals that orthorhombicity, apical oxygens, the tilting of oxygen octahedra and the canting of spins out of the CuO2 planes are not essential to the mechanism of chirality. Our findings point to a chiral mechanism coming from a coupling of acoustic phonons to the intrinsic excitations of the CuO2 planes.

The thermal conductivity κ of the quasi-2D organic spin-liquid candidate EtMe3Sb[Pd(dmit)2]2 (dmit-131) was measured at low temperatures, down to 0.07 K. We observe a vanishingly small residual linear term κ0/T , in κ/T vs T as T → 0. This shows that the low-energy excitations responsible for the sizeable residual linear term γ in the specific heat C, seen in C/T vs T as T → 0, are localized. We conclude that there are no mobile gapless excitations in this spin liquid candidate, in contrast with a prior study of dmit-131 that reported a large κ0/T value [Yamashita et al., Science 328, 1246(2010]. Our study shows that dmit-131 is in fact similar to κ-(BEDT-TTF)2Cu2(CN)3, another quasi-2D organic spin-liquid candidate where a vanishingly small κ0/T and a sizeable γ are seen. We attribute heat conduction in these organic insulators without magnetic order to phonons undergoing strong spin-phonon scattering, as observed in several other spin-liquid materials. arXiv:1904.10402v3 [cond-mat.str-el]

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