Topological phase transitions driven by polarity change and next-nearest-neighbor hopping in skyrmion crystals

Abstract

By considering the bulk-edge correspondence of the skyrmion crystal this work focused on the relation of the topological properties to the polarity ($Q_{\mathrm{sk}}$), next-nearest-neighbor hopping ($t^{\prime }$), and exchange coupling ($J$). We found that by continually increasing polarity of the skyrmions from 1 to 2, the monopole-lattice phase and the dipole-lattice phase both span a wide range in the parameter space demonstrating topological robustness. While the next-nearest-neighbor-hopping of the electrons coexists with the nearest-neighbor hopping the flux pattern of the emergent magnetic field traversing the two-dimensional SkX is reshaped giving rise to different topological Hall effect. By increasing $t^{\prime }$ from 0 to $t$ with the polarity fixed to be 1, we found Chern numbers of the electronic bands change from unity to indefinite values demonstrating a phase transition. We also considered the effect of finite $J$ and found the results obtained in the adiabatic limit hold to around $J=t$.

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Cited by in corpus (2)

• Klein tunneling of the electronic states in the gate voltage modulated skyrmion crystal
• A $C^{\ast }$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals