Topological magnons and domain walls in twisted bilayer MoTe$_2$

TL;DR

This paper explores the topological properties of magnons and domain walls in twisted bilayer MoTe$_2$, revealing their spectrum, topology, and interactions, and proposing an effective spin model for these excitations.

Contribution

It introduces a comprehensive theoretical framework for understanding topological magnon and domain wall excitations in twisted bilayer MoTe$_2$, including a new effective spin model.

Findings

Identification of two low-energy topological magnon bands with opposite Chern numbers

Construction of a magnon tight-binding model analogous to the Haldane model

Calculation of domain wall energies and chiral edge states

Abstract

We theoretically investigate the magnetic excitations in the quantum anomalous Hall insulator phase of twisted bilayer MoTe$_2$ at a hole filling factor of $\nu=1$, focusing on magnon and domain wall excitations. Using a generalized interacting Kane-Mele model, we obtain the quantum anomalous Hall insualtor ground state with spin polarization. The magnon spectrum is then computed via the Bethe-Salpeter equation, revealing two low-energy topological magnon bands with opposite Chern numbers. To further explore the magnon topology, we construct a tight-binding model for the magnon bands, which is analogous to the Haldane model. We also calculate the energy cost of domain walls that separate regions with opposite Chern numbers and bind chiral edge states. Finally, we propose an effective spin model that describes both magnon and domain wall excitations, incorporating Heisenberg spin interactions and Dzyaloshinskii-Moriya interactions. The coupling constants in this model are determined from the numerical results for magnons and domain walls. This model accounts for the Ising anisotropy of the system, captures the magnon topology, and allows for the estimation of the magnetic ordering temperature. Our findings provide a comprehensive analysis of magnetic excitations in twisted MoTe$_2$ and offer new insights into collective excitations in moir\'e systems.