  Mott insulators under sufficiently strong spin-orbit coupling can display
quantum spin liquid phases with topological order and fractional excitations.
Quantum magnets with pure Kitaev spin exchange interactions can host a gapped
quantum spin liquid with a single Majorana edge mode propagating in the
counter-clockwise direction when a small positive magnetic field is applied.
Here, we show how under a sufficiently strong positive magnetic field a
topological transition into a gapped quantum spin liquid with two Majorana edge
modes propagating in the clockwise direction occurs. The Dzyaloshinskii-Moriya
interaction is found to turn the non-chiral Kitaev's gapless quantum spin
liquid into a chiral one with equal Berry phases at the two Dirac points.
Thermal Hall conductance experiments can provide evidence of the novel
topologically gapped quantum spin liquid states predicted.
