  The large thermal Hall conductivity recently detected in Mott insulating
cuprates has been attributed to chiral neutral spin excitations. A quantum spin
liquid with Majorana excitations, Chern number +/-4 and large thermal Hall
conductivity is found to be an excited state of a frustrated Heisenberg model
on the square lattice. Using a Majorana mean-field theory and exact
diagonalizations, we explore two possible routes to achieve this chiral quantum
spin liquid, an orbital effect of an applied magnetic field and spin orbit
couplings as present in cuprates. In particular, we show how only the orbital
magnetic field allows this topological phase to be the ground state, while it
remains an excited state of the Majorana mean field under the
Dzyaloshinskii-Moriya terms. We interpret the large thermal Hall effect
observed in Mott cuprates from their close proximity to a transition to a
Majorana chiral quantum spin liquid which can be induced by an external
magnetic field.
