High bosonic Bott index and transport of multi-band topological magnons

Magnons are bosonic quasiparticles in magnetically ordered systems. Bosonic Bott index has been affirmed as a real-space topological invariant for a two-band ferromagnetic model. In this work,we theoretically investigate the topology and transport of magnons in a multi-band bosonic Kagome ferromagnetic model. We demonstrate the validity of the bosonic Bott indices of values larger than 1 in multi-band magnonic systems by showing the agreement with Chern numbers in the clean limit and the bulk-boundary correspondence during the topological phase transition. For the high Bott index phase, the disorder-induced topological phase transition occurs in a multi-step manner. Using a generalized Landauer-Buttiker formalism, we reveal how the magnon transport depends on Gilbert damping and disorder under coherent excitation or temperature difference. The results further justify the bosonic Bott index as a robust real-space topological invariant for multi-band magnonic systems and provide insights into the transport of topological magnons.

💡 Research Summary

The manuscript investigates the topological characterization and transport behavior of magnons in a three‑band Kagome ferromagnet, focusing on the applicability of the real‑space Bott index when its absolute value exceeds one. Starting from a spin Hamiltonian that includes nearest‑neighbor Heisenberg exchange (J > 0), next‑nearest‑neighbor exchange (J′), site‑dependent easy‑axis anisotropy (K_i), and a pseudo‑dipolar interaction (F) arising from spin‑orbit coupling, the authors perform a Holstein‑Primakoff transformation and retain only linear terms. This yields a 6N × 6N bosonic Bogoliubov‑type Hamiltonian. Because the pseudo‑dipolar term generates anomalous pairing operators (a_i a_j and a_i† a_j†), the problem is pseudo‑Hermitian with a metric η = σ_z ⊗ I, which must be incorporated when defining topological invariants.

In the clean, translationally invariant limit the Hamiltonian is Fourier transformed, producing three positive magnon bands (and three corresponding negative‑energy partners). The authors compute both the momentum‑space Chern numbers C_n and the real‑space Bott indices B_n for each band using established formulas. They find (C₁, C₂, C₃) = (‑1, 2, ‑1) and the same set of Bott indices, thereby confirming that a Bott index of magnitude two can arise in a bosonic system and that it matches the Chern number when translation symmetry is present.

To explore richer topological phases, a staggered anisotropy Δ is introduced such that K_A = K, K_B = K + Δ, K_C = K ‑ Δ. Varying the pseudo‑dipolar strength F and Δ produces a phase diagram with distinct Bott‑index triples: (‑1, 2, ‑1), (‑1, 1, 0), and (0, 0, 0). In the (‑1, 1, 0) phase only the lower gap hosts chiral edge states, illustrating how a high Bott index does not guarantee edge modes in every gap but still obeys bulk‑boundary correspondence.

Disorder is modeled by adding a random on‑site anisotropy term ΔK uniformly distributed in