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

摘要

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 (Q(sk)). 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 Q(sk) from 1 to 2, we found topological phase transitions occur at Q(sk) = 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.

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