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

Abstract

By considering the topological Hall conductivity and the nanoribbon edge states, i.e., the bulk-boundary correspondence of the skyrmion crystal (SkX), this work focused on the relation of the topological properties to the next-nearest-neighbor (nnn) hopping (t′), the exchange coupling strength (J), and the topological number of the skyrmion (Qsk). When the nnn hopping of the electrons coexists with the nearest-neighbor hopping, the flux pattern of the emergent magnetic field traversing the SkX is reshaped giving rise to different topological Hall effect. By increasing t′ from 0 to t, we found the Chern numbers of the electronic bands change from unity to indefinite values demonstrating a phase transition. By continually increasing Qsk from 1 to 2, we found topological phase transitions occur at Qsk=1.3 and 1.7. We also considered the effect of finite J and found the results obtained in the adiabatic limit (J≫t) hold to around J=t.