A Chern-Simons invariant of two-band topological nodal-line semimetals

Abstract We propose a Chern-Simons theory, which is constructed in terms of the inner structures of the U(1) gauge potential and corresponding field strength, for three-dimensional two-band systems to depict the topology of nodal-line semimetals (NLSMs). It is discovered that the nodal-lines are factually the line defects in the Brillouin zone. We provide a practical approach to obtain the proposed invariant depending on the self-linking and mutual-linking numbers, as well as the topological charges of the nodal-lines. A typical example is used to show the computation of the proposed invariant. Our theory can produce different invariants in previous literature, manifesting that it is promising for unifying the various topological invariants in the NLSMs.