  In topological Weyl semimetals, the low energy excitations are comprised of
linearly dispersing Weyl fermions, which act as monopoles of Berry curvature in
momentum space and result in topologically protected Fermi arcs on the
surfaces. We propose that these Fermi arcs in Weyl semimetals lead to an
anisotropic magnetothermal conductivity, strongly dependent on externally
applied magnetic field and resulting from entropy transport driven by
circulating electronic currents. The circulating currents result in no net
charge transport, but they do result in a net entropy transport. This
translates into a magnetothermal conductivity that should be a unique
experimental signature for the existence of the arcs. We analytically calculate
the Fermi arc-mediated magnetothermal conductivity in the low-field
semiclassical limit as well as in the high-field ultra-quantum limit, where
only the chiral Landau levels are involved. By numerically including the
effects of higher Landau levels, we show how the two limits are linked at
intermediate magnetic fields. This work provides the first proposed signature
of Fermi arc-mediated thermal transport and sets the stage for utilizing and
manipulating the topological Fermi arcs in experimental thermal applications.
