  The honeycomb Kitaev-Heisenberg model is a source of a quantum spin liquid
with Majorana fermions and gauge flux excitations as fractional quasiparticles.
In the quest of finding a pertinent material, $\alpha$-RuCl$_{3}$ recently
emerged as a prime candidate. Here we unveil highly unusual low-temperature
heat conductivity $\kappa$ of $\alpha$-RuCl$_{3}$: beyond a magnetic field of
$B_c\approx$ 7.5 T, $\kappa$ increases by about one order of magnitude,
resulting in a large magnetic field dependent peak at about 7 K, both for
in-plane as well as out-of-plane transport. This clarifies the unusual magnetic
field dependence unambiguously to be the result of severe scattering of phonons
off putative Kitaev-Heisenberg excitations in combination with a drastic
field-induced change of the magnetic excitation spectrum. In particular, an
unexpectedly large energy gap arises, which increases approximately linearly
with the magnetic field and reaches a remarkably large
$\hbar\omega_0/k_B\approx $ 50 K at 18 T.
