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 sk ), next-nearest-neighbor hopping (t ′ ), 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 ′ 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.