Quantum topological phase transitions in skyrmion crystals

Abstract

Topological order is important in many aspects of condensed matter physics, and has been extended to bosonic systems. In this Letter we report on the nontrivial topology of the magnon bands in two distinct quantum skyrmion crystals appearing in zero external magnetic field. This is revealed by nonzero Chern numbers for some of the bands. As a bosonic analog of the quantum anomalous Hall effect, we show that topological magnons can appear in skyrmion crystals without explicitly breaking time-reversal symmetry with an external magnetic field. By tuning the value of the easy-axis anisotropy at zero temperature, we find eight quantum topological phase transitions signaled by discontinuous jumps in certain Chern numbers. We connect these quantum topological phase transitions to gaps closing and reopening between magnon bands.

arXiv comment6+17 pages, 2+3 figures, includes supplemental material, accepted in Physical Review Research

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• Momentum-space theory for topological magnons in 2D ferromagnetic skyrmion lattices
• Spin-orbit coupled Hubbard skyrmions
• Skyrmionic Schrödinger cat states in monoaxial chiral magnets
• Topological magnons in a non-coplanar magnetic order on the triangular lattice
• Mechanism for Nodal Topological Superconductivity on PtBi${}_2$ Surface
• Impact of the honeycomb spin-lattice on topological magnons and edge states in ferromagnetic 2D skyrmion crystals