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It has recently become clear that phonons generate a sizable thermal Hall effect in cuprates, whether they are undoped, electron-doped or hole-doped (inside the pseudogap phase). At higher doping, where cuprates are reasonably good metals, mobile electrons also generate a thermal Hall effect, the thermal equivalent of the standard electrical Hall effect. Here we show that in the cleanest crystals of the electron-doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_{4}$, at high doping, the phonon and electron contributions to the thermal Hall conductivity $\kappa_{\rm {xy}}$ are of comparable magnitude, but of opposite sign. In samples of lower quality, phonons dominate $\kappa_{\rm {xy}}$, resulting in a negative $\kappa_{\rm {xy}}$ at all temperatures. The fact that the negative phononic $\kappa_{\rm {xy}}$ in the metallic state is similar in magnitude and temperature dependence to that found in the insulating state at lower doping rules out any mechanism based on skew scattering of phonons off charged impurities, since a local charge should be screened in the metallic regime. The phononic $\kappa_{\rm {xy}}$ is found to persist over the entire doping range where antiferromagnetic correlations are known to be significant, suggesting that such correlations may play a role in generating the phonon thermal Hall effect in electron-doped cuprates. If the same mechanism is also at play in hole-doped cuprates, the presence of a phononic $\kappa_{\rm {xy}}$ below (and only below) the critical doping $p^{\star}$ would be evidence that spin correlations are a property of the pseudogap phase.

The recently discovered layered Kagome metals of composition AV3Sb5 (A = K, Rb, Cs) exhibit a complex interplay among superconductivity, charge density wave order, topologically non-trivial electronic band structure and geometrical frustration. Here, we probe the electronic band structure underlying these exotic correlated electronic states in CsV3Sb5 with quantum oscillation measurements in pulsed fields up to 86 T. The high-field data reveal a sequence of magnetic breakdown orbits that allows the construction of a model for the folded Fermi surface of CsV3Sb5. The dominant features are large triangular Fermi surface sheets that cover almost half of the folded Brillouin zone that have not yet been detected in angle resolved photoemission spectroscopy (ARPES). These sheets display pronounced nesting at the charge density wave (CDW) vectors, which may stabilize the CDW state. The Berry phases of the electron orbits have been deduced from Landau level fan diagrams near the quantum limit without the need for extrapolations, thereby unambiguously establishing the non-trivial topological character of several electron bands in this Kagome lattice superconductor., Comment: 28 pages, 10 figures, 1 table, Supplementary Materials added