Charged Domain Wall of Electric Polarizations in Topological Nodal-Line Semimetals

We study theoretically the electronic structure of three-dimensional 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 localized mode has a topological origin, i.e., a topological confinement is realized, which is understood by a semiclassical topological number defined in the semiclassical momentum-real space. Namely, a stable charged domain wall of electric polarizations is realized in nodal-line semimetals. In sharp contrast to the well-known band bending mechanism, the origin of the charged domain wall in this study is purely electronic, i.e., due to the band topology. Moreover, in contrast to previous studies, our study demonstrates a topological confinement at the interface between two insulators without bulk topological numbers. The dispersion of the localized mode evolves from gapless to gapped as the bulk bandgap increases, which means that its conductivity is externally tunable. We discuss a possible experimental realization of the stable, electrically-tunable charged domain wall.