  A Weyl semimetal hosts low-energy chiral surface states, which appear to
connect a pair of Weyl nodes in reciprocal space. As these chiral surface
states propagate in a given direction, a spontaneous circulating current is
expected to appear near the surface of a singly connected Weyl semimetal. This
possibility is examined by using a simple model with particle-hole symmetry. It
is shown that no spontaneous charge current appears when the Fermi level is
located at the band center. However, once the Fermi level deviates from the
band center, a spontaneous charge current appears to circulate around the
surface of the system and its direction of flow is opposite for the cases of
electron doping and hole doping. These features are qualitatively unchanged
even in the absence of particle-hole symmetry. The circulating charge current
is shown to be robust against weak disorder.
