Tunable charged domain wall from topological confinement in nodal-line semimetals

We study theoretically the electronic structure of topological nodal-line semimetals. We show that, in the presence of a gap-opening spatially dependent mass term that forms a domain wall, an in-gap charged localized mode emerges at the domain wall. It turns out that such a domain wall is realized by head-to-head (or tail-to-tail) bulk electric polarizations. The dispersion of the localized mode evolves from gapless to gapped as the bulk band gap increases, which means that its conductivity is tunable. The localized mode has a topological origin, i.e., a topological confinement is realized, which is understood by a semiclassical topological number defined in semiclassical momentum-real space. In contrast to previous studies, the origin of the charged domain wall in this study is purely electronic, i.e., due to the band topology. Moreover, this study demonstrates a topological confinement at the interface between two insulators without bulk topological numbers. We discuss a possible experimental realization of the stable, electrically tunable charged domain wall.