Bosonic Bott Index and Disorder-Induced Topological Transitions of Magnons

Abstract

We investigate the role of disorder on the various topological magnonic phases present in deformed honeycomb ferromagnets. To this end, we introduce a bosonic Bott index to characterize the topology of magnon spectra in finite, disordered systems. The consistency between the Bott index and Chern number is numerically established in the clean limit. We demonstrate that topologically protected magnon edge states are robust to moderate disorder and, as anticipated, localized in the strong regime. We predict a disorder-driven topological phase transition, a magnonic analog of the "topological Anderson insulator" in electronic systems, where the disorder is responsible for the emergence of the nontrivial topology. Combining the results for the Bott index and transport properties, we show that bulk-boundary correspondence holds for disordered topological magnons. Our results open the door for research on topological magnonics as well as other bosonic excitations in finite and disordered systems.

6 pages, 3 figures (main text) + 4 pages, 4 figures (supplemental material)

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• Topological Anderson insulators with different bulk states in quasiperiodic chains
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• Observation of squeezed Chern insulator in an acoustic fractal lattice
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
• Zero-frequency chiral magnonic edge states protected by non-equilibrium topology
• Time-dependent strain-tuning topological magnon phase transition
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• Inducing a topological transition in graphene nanoribbons superlattices by external strain
• Topological Higgs Amplitude Modes in Strongly Interacting Superfluids
• Recent progress on disorder-induced topological phases
• Connecting Topological Anderson and Mott Insulators in Disordered Interacting Fermionic Systems
• Quantum geometry, localization, and topological bounds of spin fluctuations
• Type-II Weyl Excitation in Vortex Arrays
• Multiple topological phases of magnons induced by Dzyaloshinskii-Moriya and pseudodipolar anisotropic exchange interactions in Kagome ferromagnets
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Topological Invariant for Bosonic Bogoliubov-de Gennes Systems with Disorder