Higher-order Topological States in Chiral Split Magnons of Honeycomb Altermagnets

Abstract

We theoretically explore higher-order topological magnons in collinear altermagnets, encompassing a dimensional hierarchy ranging from localized corner modes to propagating hinge excitations. By employing antiferromagnetic interlayer coupling in bosonic Bogoliubov-de Gennes (BdG) Hamiltonian, our work reveals anisotropic surface states and spatially distributed hinge modes propagating along facet intersections. We track the adiabatic evolution of Wannier centers to identify the bulk-polarization with second-order topological magnon insulator (SOTMI), where various magnon spectra demonstrate symmetry-protected band structure beyond conventional topology. Leveraging the stability and propagative properties of hinge modes, these unconventional magnons demonstrate manipulability in atomic-scale modifications of termination. Our study integrate altermagnetism with higher-order topology, which advance magnon-based quantum computing processing energy-efficient integrated architectures and information transfer.

Figures (3)

• Figure 1: (a) Schematic representation of a honeycomb altermagnet in the unit cell of antiferromagnetic interlayer coupling, where $A, B, C, D$ are four different sublattices within magnetic Ne$\acute{e}$l order. (b) and (d), Brillouin zones (BZ) for the two-dimensional lattice and three-dimensional structure. (c) The black bonds are the NNN ferromagnetic coupling with strength $J_{2}$, while the red(blue) bonds indicate Heisenberg interaction with strength $J_{2}-\delta_{2}$($J_{2}+\delta_{2}$). $a_{1}$, $a_{2}$ and $a_{3}$ are lattice vectors along with the sublattice sites.
• Figure 2: (a) and (e) depict the magnon eigenvector probabilities $|\psi_{n}|^2$ of corner modes for $J_{2}'/J_{2}$=0.8, while $\delta_{1}$ and $\delta_{2}$ are both -0.4. (b) and (c) are edge spectra and local density of states (DOSs) for the zigzag and armchair nanoribbon respectively, where the parameters are chosen as before. (d) The Wannier center evolution is depicted as a function of $k_{y}$. Panels (f) and (g) illustrate the gapped altermagnetic honeycomb model with $J_{2}'/J_{2}$=1.2, $\delta_{2}$=-0.4 and $\delta_{1}$=-0.1, identifying the intrinsic second-order topological phase. (h) The Wannier center evolution corresponding to the nodal-line semimetal.
• Figure 3: (a) The bulk magnon band structure for $J_{z}=0.8J_{1}$, where the red (blue) bonds indicate right (left)-hand chirality. (b) Numerical simulations are performed on a finite-size lattice with dimensions $N_{x} \times N_{y} =20 \times 20$, revealing localized hinge modes that propagate unidirectionally along the edges. These topologically protected hinge modes are explicitly highlighted in red within the spectral plot, emphasizing their distinct energy dispersion relative to the bulk bands. (c) The magnon surface states in the $k_{x}-k_{z}$ plane with $N_{y}$ = 20 along y direction. (d) The hinge modes are marked by red arrows along the sample edges, indicative of topologically protected states.