  Topological boundary states, emerged at the spatial boundary between
topological non-trivial and trivial phases, are usually gapless, or commonly
referred as metallic states. For example, the surface state of a topological
insulator is a gapless Dirac state. These metallic topological boundary states
are typically well described by non-interacting fermions. However, the behavior
of topological boundary states with significant electron-electron interactions,
which could turn the gapless boundary states into gapped ordered states, e.g.,
density wave states or superconducting states, is of great interest
theoretically, but is still lacking evidence experimentally. Here, we report
the observation of incommensurable charge density wave (CDW) formed on the
topological boundary states driven by the electron-electron interactions on the
(001) surface of CoSi. The wavevector of CDW varies as the temperature changes,
which coincides with the evolution of topological surface Fermi arcs with
temperature. The orientation of CDW phase is determined by the chirality of the
Fermi arcs, which indicates direct association between CDW and Fermi arcs. Our
finding will stimulate the search of more interactions-driven ordered states,
such as superconductivity and magnetism, on the boundaries of topological
materials.
