  The quantum Hall effect (QHE) in two-dimensional (2D) electron gases, which
is one of the most striking phenomena in condensed matter physics, involves the
topologically protected dissipationless charge current flow along the edges of
the sample. Integer or fractional electrical conductance are measured in units
of $e^2/2\pi\hbar$, which is associated with edge currents of electrons or
quasiparticles with fractional charges, respectively. Here we discover a novel
type of quantization of the Hall effect in an insulating 2D quantum magnet. In
$\alpha$-RuCl$_3$ with dominant Kitaev interaction on 2D honeycomb lattice, the
application of a parallel magnetic field destroys the long-range magnetic
order, leading to a field-induced quantum spin liquid (QSL) ground state with
massive entanglement of local spins. In the low-temperature regime of the QSL
state, we report that the 2D thermal Hall conductance $\kappa_{xy}^{2D}$
reaches a quantum plateau as a function of applied magnetic field.
$\kappa_{xy}^{2D}/T$ attains a quantization value of $(\pi/12)(k_B^2/\hbar)$,
which is exactly half of $\kappa_{xy}^{2D}/T$ in the integer QHE. This
half-integer thermal Hall conductance observed in a bulk material is a direct
signature of topologically protected chiral edge currents of charge neutral
Majorana fermions, particles that are their own antiparticles, which possess
half degrees of freedom of conventional fermions. These signatures demonstrate
the fractionalization of spins into itinerant Majorana fermions and $Z_2$
fluxes predicted in a Kitaev QSL. Above a critical magnetic field, the
quantization disappears and $\kappa_{xy}^{2D}/T$ goes to zero rapidly,
indicating a topological quantum phase transition between the states with and
without chiral Majorana edge modes. Emergent Majorana fermions in a quantum
magnet are expected to have a major impact on strongly correlated topological
quantum matter.
