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arXiv:2604.10483

Topological Magnon-Phonon Hybrid Bands in Ferromagnetic Skyrmion Crystals

Doried Ghader, Bilal Jabakhanji

cond-mat.mes-hallquant-phSubmitted Apr 12, 2026• Announced Apr 14, 2026
v1 · Apr 12, 2026v2 · Oct 27, 2026
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Abstract

We investigate magnon-phonon (MP) excitations in a Neel-type two-dimensional ferromagnetic skyrmion crystal (SkX) stabilized on a triangular spin lattice by Dzyaloshinskii-Moriya interaction (DMI). Although the lowest two magnon bands of the bare SkX are topologically trivial, we show that coupling to lattice vibrations reconstructs the low-energy sector and generates topological MP hybrid bands. Starting from a spin-lattice Hamiltonian in which phonons couple to magnons through fluctuations of the DMI vectors, we derive the bosonic Hamiltonian for the SkX and compute the hybrid band structure by Bogoliubov diagonalization. MP coupling opens gaps at low-energy magnon-phonon crossings, lifts phonon degeneracies associated with supercell folding, and yields nontrivial Chern numbers for the lowest hybrid bands. The resulting low-energy topology and associated edge states remain robust under magnetic-field variation, while higher-energy hybrid bands can undergo field-driven topological phase transitions. These results extend topological magnon-phonon hybridization to noncoplanar SkXs.

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We investigate magnon-phonon (MP) excitations in a Neel-type two-dimensional ferromagnetic skyrmion crystal (SkX) stabilized on a triangular spin lattice by Dzyaloshinskii-Moriya interaction (DMI). Although the lowest two magnon bands of the bare SkX are topologically trivial, we show that coupling to lattice vibrations reconstructs the low-energy sector and generates topological MP hybrid bands. Starting from a spin-lattice Hamiltonian in which phonons couple to magnons through fluctuations of the DMI vectors, we derive the bosonic Hamiltonian for the SkX and compute the hybrid band structure by Bogoliubov diagonalization. MP coupling opens gaps at low-energy magnon-phonon crossings, lifts phonon degeneracies associated with supercell folding, and yields nontrivial Chern numbers for the lowest hybrid bands. The resulting low-energy topology and associated edge states remain robust under magnetic-field variation, while higher-energy hybrid bands can undergo field-driven topological phase transitions. These results extend topological magnon-phonon hybridization to noncoplanar SkXs.
Recent experiments in moiré quantum materials exhibit quantized Hall states without an external magnetic field, motivating continuum mechanisms based on smooth moiré-periodic pseudospin textures. We present a controlled theory of skyrmion Chern bands generated by such textures. An exact local SU(2)SU(2)SU(2) transformation reveals an emergent non-Abelian gauge field; for large branch splitting we perform an operator-level Schrieffer-Wolff expansion, yielding a single-branch Hamiltonian together with systematically dressed physical operators that define the projected interacting theory beyond strict adiabaticity. The leading dynamics is governed by a U(1)U(1)U(1) Berry connection whose flux is set by the skyrmion density, while controlled non-adiabatic corrections are fixed by the texture's real-space quantum geometric tensor. In a Landau-level representation built from the averaged emergent field, moiré-periodic modulations induce Umklapp-resolved deformations of Girvin-MacDonald-Platzman kinematics and microscopic sources of excess optical quantum weight above the topological lower bound. Assuming a gapped Hall phase, we further derive a skyrmion-crystal effective field theory with a universal Berry-phase term and a noncommutative magnetophonon. Our results provide experimentally accessible signatures for twisted transition-metal dichalcogenide homobilayers and rhombohedral graphene aligned with hexagonal boron nitride.
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A magnetic impurity embedded in a metal is collectively screened by Fermi-surface quasiparticles into a many-body spin-singlet ground state, forming a Kondo cloud of size ξK∼ℏvF/(kBTK)ξ_{\rm K}\sim\hbar v_F/(k_B T_{\rm K})ξK​∼ℏvF​/(kB​TK​). This kinematic picture collapses in flat bands, where vF=0v_F=0vF​=0 and the hierarchy of dispersive energy shells is absent. Here we show that the missing organizing principle is quantum geometry. A magnetic impurity coupled to an isolated flat band selects a single active bath mode: a coherent superposition of flat-band Bloch states weighted by the hybridization factor v(k)v(\mathbf{k})v(k), while all orthogonal flat-band modes remain dark. The resulting flat-band Kondo problem is a quantum geometric molecule, with an algebraic Kondo scale set by the total projected hybridization strength rather than a logarithmic-renormalization scale. In real space, the impurity-bath spin correlation defines a quantum geometric Kondo cloud. Its cloud-size tensor admits a gauge-invariant decomposition into a hybridization-weighted quantum metric, a dressed Berry-connection covariance, and a positive hybridization-gradient term, yielding the lower bound ξK2≥∑kρ(k)Tr g(k)ξ_{\rm K}^2\geq \sum_{\mathbf{k}}ρ(\mathbf{k}){\rm Tr}\,g(\mathbf{k})ξK2​≥∑k​ρ(k)Trg(k), where ρ(k)=∣v(k)∣2/∑k∣v(k)∣2ρ(\mathbf{k})=|v(\mathbf{k})|^2/\sum_{\mathbf{k}}|v(\mathbf{k})|^2ρ(k)=∣v(k)∣2/∑k​∣v(k)∣2. Our result reveals that, in flat bands, Kondo screening is governed by the quantum geometry and interference structure of the impurity-selected Bloch wave packet, rather than Fermi-surface kinematics.
We study the ground-state topology and quasiparticle properties in bosonic Mott insulators with two-dimensional spin-orbit couplings in cold atomic optical lattices. We show that the many-body Chern and spin-Chern number can be expressed as an integral of the quasihole Berry curvatures over the Brillouin zone. Using a strong-coupling perturbation theory, for an experimentally feasible spin-orbit coupling, we compute the Berry curvature and the spin Chern number and find that these quantities can be generated purely by interactions. We also compute the quasiparticle dispersions, spectral weights, and the quasimomentum space distribution of particle and spin density, which can be accessed in cold-atom experiments and used to deduce the Berry curvature and Chern numbers.
We investigate topological transport in spin-orbit coupled bosonic Mott insulators. We show that interactions can lead to anomalous quasiparticle dynamics even when the spin-orbit coupling is Abelian. To illustrate the latter, we consider the spin-orbit coupling realized in the experiment of Lin et al. [Nature (London) 471, 83 (2011)]. For this spin-orbit coupling, we compute the quasiparticle dispersions and spectral weights, the interaction-induced momentum-space Berry curvature, and the momentum-space distribution of spin density, and propose experimental signatures. Furthermore, we find that, for a generic spin orbit coupling, in our approximation for the single-particle propagator, the ground state can in principle support an integer Hall conductivity if the sum of the Chern numbers of the hole bands is nonzero.