  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. Although Fermi-surface, transport
and thermodynamic signatures of the pseudogap phase are reminiscent of a
transition into a phase with antiferromagnetic order, there is no evidence for
an associated long-range magnetic order. Here we report measurements of the
thermal Hall conductivity $\kappa_{\rm xy}$ in the normal state of four
different cuprates (Nd-LSCO, Eu-LSCO, LSCO, and Bi2201) and show that a large
negative $\kappa_{\rm xy}$ 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 carriers -- as 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 is very weak, we
attribute this $\kappa_{\rm xy}$ signal to exotic neutral excitations,
presumably with spin chirality. The thermal Hall conductivity in the pseudogap
phase of cuprates is reminiscent of that found in insulators with spin-liquid
states. In the Mott insulator LCO, it attains the highest known magnitude of
any insulator.
