  The nature of the pseudogap phase of cuprates remains a major puzzle. One of
its new signatures is a large negative thermal Hall conductivity $\kappa_{\rm
xy}$, which appears for dopings $p$ below the pseudogap critical doping $p^*$,
but whose origin is as yet unknown. Because this large $\kappa_{\rm xy}$ 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.
$\kappa_{\rm zy}(T) \approx \kappa_{\rm xy} (T)$. 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 . At $p > p^*$, in both
La$_{\rm 1.6-x}$Nd$_{\rm 0.4}$Sr$_x$CuO$_4$ and La$_{\rm 1.8-x}$Eu$_{\rm
0.2}$Sr$_x$CuO$_4$ with $p = 0.24$, we observe no c-axis Hall signal, i.e.
$\kappa_{\rm zy}(T) = 0$, showing that phonons have zero Hall response outside
the pseudogap phase. The phonon Hall response appears immediately below $p^* =
0.23$, as confirmed by the large $\kappa_{\rm zy}(T)$ signal we find in
La$_{1.6-x}$Nd$_{\rm 0.4}$Sr$_x$CuO$_4$ with $p = 0.21$. The microscopic
mechanism by which phonons become chiral in cuprates remains to be identified.
This mechanism must be intrinsic - from a coupling of phonons to their
electronic environment - rather than extrinsic, from structural defects or
impurities, as these are the same on both sides of $p^*$. This intrinsic phonon
Hall effect provides a new window on quantum materials and it may explain the
thermal Hall signal observed in other topologically nontrivial insulators.
