  The Fermi arcs of topological surface states in the three-dimensional
multi-Weyl semimetals on surfaces by a continuum model are investigated
systematically. We calculated analytically the energy spectra and wave function
for bulk quadratic- and cubic-Weyl semimetal with a single Weyl point. The
Fermi arcs of topological surface states in Weyl semimetals with single- and
double-pair Weyl points are investigated systematically. The evolution of the
Fermi arcs of surface states variating with the boundary parameter is
investigated and the topological Lifshitz phase transition of the Fermi arc
connection is clearly demonstrated. Besides, the boundary condition for the
double parallel flat boundary of Weyl semimetal is deduced with a Lagrangian
formalism.
