Topological defects and Goldstone excitations in domain walls between ferromagnetic quantum Hall effect liquids

TL;DR

This paper investigates the low-energy excitations localized at domain walls in ferromagnetic quantum Hall liquids, revealing the presence of spin-waves and topological defects that influence transport properties.

Contribution

It introduces a detailed analysis of the spectrum of excitations at domain walls, including topological defects, in ferromagnetic quantum Hall systems with inhomogeneous Zeeman splitting.

Findings

Domain walls host localized spin-wave excitations with linear dispersion.

Topological defects at domain walls are charged and can dominate transport.

The spectrum includes a small gap due to spin-orbit coupling.

Abstract

It is shown that the low-energy spectrum of a ferromagnetic quantum Hall effect liquid in a system with a multi-domain structure generated by an inhomogeneous bare Zeeman splitting $\epsilon_{Z}$ is formed by excitations localized at the walls between domains. For a step-like $\epsilon_Z(r)$, the domain wall spectrum includes a spin-wave with a linear dispersion and a small gap due to spin-orbit coupling, and a low-energy topological defects. The latter are charged and may dominate in the transport under conditions that the percolation through the network of domain walls is provided.