  The exploration of topological phases in carbon allotropes offers a
fascinating avenue to realize topological devices based on carbon materials.
Here, using first-principles calculations, we propose a novel metastable carbon
allotrope, which possesses exotically helical carbon chains bridged by
quadrangle-rings. This unique structure with sp2-sp3 bonding networks
crystallizes in a noncentrosymmetric face-centered orthogonal (fco) lattice
with six atoms in a unit cell, thus named fco-C6. The considerable stability of
fco-C6 is confirmed by phonon spectra, elastic constants, and ab initio
molecular dynamics simulations. More importantly, fco-C6 exhibits extraordinary
electronic properties with the minimum number of Weyl points in a time-reversal
preserved Weyl system. The symmetry arguments reveal that the Weyl points are
guaranteed to lie along the high-symmetry pathes and thus well separated in
momentum space, exhibiting the robustness of topologically protected features.
We investigate the topological surface states of fco-C6 projected on a
semi-infinite (010) surface. There are only nontrivial Fermi arcs across the
Fermi surface, which facilitates their measurements in experiments and further
applications in carbon allotropes.
