  Chirality, a fundamental structural property of crystals, can induce many
unique topological quantum phenomena. In kagome lattice, unconventional
transports have been reported under tantalizing chiral charge order. Here, we
show how by deforming the kagome lattice to obtain a three-dimensional (3D)
chiral kagome lattice in which the key band features of the non-chiral 2D
kagome lattice - flat energy bands, van Hove singularities (VHSs), and
degeneracies - remain robust in both the $k_z$ = 0 and $\pi$ planes in momentum
space. Given the handedness of our kagome lattice, degenerate momentum points
possess quantized Chern numbers, ushering in the realization of Weyl fermions.
Our 3D chiral kagome lattice surprisingly exhibits 1D behavior on its surface,
where topological surface Fermi arc states connecting Weyl fermions are
dispersive in one momentum direction and flat in the other direction. These 1D
Fermi arcs open up unique possibilities for generating unconventional non-local
transport phenomena at the interfaces of domains with different handedness, and
the associated enhanced conductance as the separation of the leads on the
surface is increased. Employing first-principles calculations, we investigate
in-depth the electronic and phononic structures of representative materials
within the ten space groups that can support topological chiral kagome
lattices. Our study opens a new research direction that integrates the
advantages of structural chirality with those of a kagome lattice and thus
provides a new materials platform for exploring unique aspects of correlated
topological physics in chiral lattices.
