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

TL;DR

This work extends real-space topology to multi-band magnonic systems by using the bosonic Bott index on a Kagome ferromagnet with a nontrivial bosonic metric. It demonstrates that Bott indices for the three magnon bands reproduce the Chern numbers in the clean limit and align with bulk-boundary behavior during disorder-driven transitions, including higher Bott index phases under engineered interactions. Transport is analyzed via a generalized Landauer-Buttiker formalism, revealing how Gilbert damping and disorder shape edge versus bulk magnon currents for coherent and thermal excitations. Overall, the paper establishes the bosonic Bott index as a robust descriptor of topological magnonics and provides practical insights into robust edge-state transport in realistic, dissipative, disordered systems.

Abstract

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.

Figures (9)

• Figure 1: (a) Schematic diagram of Kagome lattice. The red,green and blue atoms represent the A,B and C sublattices in a unit cell. $\mathbf{a}_i$ and $\bm{\rho}_i$ denote the NN and NNN vectors, respectively. (b) Topological phase diagram in $F-\Delta$ parameter space. (c) Magnon spectrum for infinite sample, strip sample, and $40\times 40$ finite sample (from left to right, respectively). The parameters are $K=20J$ and $F=5J$. $C_{1,2,3}$ denote Chern numbers and $\mathcal{B}_{1,2,3}$ denote Bott indices for the corresponding bands.
• Figure 2: (a) Schematic diagram of the lead-sample-lead device for magnon transport calculation. The colors of the circles illustrate the anisotropy at the spin sites. (b) Topological phase with respect to pseudodipolar interaction strength $F$ and disorder strength $W$ for $K=20J$. (c)(d) Magnon transmission $T$ calculated at the center of the (c) upper gap and (d) lower gap, compared with the Bott index of (c) the third band and (d) the first band. The parameters are $F=5J$, $K=20J$, and 50 samples are averaged. $C_{1,2,3}$ and $\mathcal{B}_{1,2,3}$ denote the Chern numbers and Bott indices of the corresponding bands.
• Figure 3: The Bott index of the second band $\mathcal{B}_2$ for different disorder strength for (a) $\Delta=4.7J$ [$(0,0,0)$ phase when $W=0$], and (b) $\Delta=5.5J$ [$(-1,1,0)$ phase when $W=0$]. Sample size is $30 \times 30$ and 50 samples are averaged.
• Figure 4: (a) The magnon transmission $T$ across the device divided by the value of clean case $T(W=0)$ for different disorder strength. (b)(c) The transmission functions for $W=0$ and different damping $\alpha$. (b) The transmission from left lead to right lead $T_L$. (c) The transmission from left lead to central sample $T_L^{\prime}$.
• Figure 5: Magnon currents at the two interfaces for different damping and disorder strength for different excitations. (a)(b)(c) External frequency in the left lead of (a) $\hbar\omega=29.65J$ (in the upper gap), (b) $\hbar\omega=20.11J$ (in the lower gap), and (c) $\hbar\omega=14.5J$ (in the bulk band). (d) Temperature difference $t_L=1.2t_C$ and $t_R=0.8t_C$.