Electric field tunable band topology and topological Hall conductivity in skyrmion crystals

In recent years, magnetic skyrmions have attracted significant attention due to their role in unconventional electron transport driven by topology. One such property is the topological Hall effect (THE), which is the transport of electronic charge along the transverse direction. Here, using the many-body model Hamiltonian on a two-dimensional (2D) skyrmion crystal, we study THE under various spin-orbit couplings (SOC) such as Rashba, Dresselhaus, and Weyl. We find that at an optimal SOC strength, a nearly uniform emergent magnetic field distribution is achieved at which subband dispersions and quantization plateaus of THE closely resemble the Landau levels and plateaus of quantum Hall effect in 2D crystal under a uniform magnetic field, respectively. Moreover, varying SOC alters band topology that enables transition between ordinary and Chern insulating states. Also, it changes the Chern number from negative to positive, which results in a flip of the edge current direction. Interestingly, varying SOC also reverses the sign of THE at a critical point. Since Rashba and Dresselhaus SOC can be tuned by electric fields, these results could pave the way for future quantum devices and create new avenues for controlled charge transport in skyrmions.