# Tunable Charged Domain Wall from Topological Confinement in Nodal-Line Semimetals

## TL;DR

This paper theoretically demonstrates the emergence of a topologically confined, electrically tunable charged mode at domain walls in nodal-line semimetals, with potential for experimental realization.

## Contribution

It introduces a novel topological confinement mechanism at insulator interfaces without bulk topological numbers, with tunable localized modes.

## Key findings

- Localized charged mode appears at domain walls with a topological origin.
- Mode dispersion can be tuned from gapless to gapped by adjusting the bulk bandgap.
- Potential for experimental realization of electrically tunable charged domain walls.

## Abstract

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 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. In contrast to previous studies, our study demonstrates a topological confinement at the interface between two insulators without bulk topological numbers. Moreover, 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.