Almost ideal nodal-loop semimetal in monoclinic CuTeO$_3$ material

Nodal-loop semimetals are materials in which the conduction and valence bands cross on a one-dimensional loop in the reciprocal space. For the nodal-loop character to manifest in physical properties, it is desired that the loop is close to the Fermi level, relatively flat in energy, simple in its shape, and not coexisting with other extraneous bands. Here, based on the first-principles calculations, we show that the monoclinic CuTeO$_3$ is a realistic nodal-loop semimetal that satisfies all these requirements. The material features only a single nodal loop around the Fermi level, protected by either of the two independent symmetries: the $\mathcal{PT}$ symmetry and the glide mirror symmetry. The size of the loop can be effectively tuned by strain, and the loop can even be annihilated under stain, making a topological phase transition to a trivial insulator phase. Including the spin-orbit coupling opens a tiny gap at the loop, and the system becomes a $\mathbb{Z}_2$ topological semimetal with a nontrivial bulk $\mathbb{Z}_2$ invariant but no global bandgap. The corresponding topological surface states have been identified. We also construct a low-energy effective model to describe the nodal loop and the effect of spin-orbit coupling.