Quantized topological Hall effect in skyrmion crystal

We theoretically study the quantized topological Hall effect (QTHE) in skyrmion crystal (SkX) without external magnetic field. The emergent magnetic field in SkX could be gigantic, as much as 40000. 28em{0ex}T, when its lattice constant is 10. 28em{0ex}nm. The band structure is not flat but has a finite gap in the low electron-density regime. We also study the conditions to realize the QTHE for the skyrmion size, carrier density, disorder strength, and temperature. Comparing the SkX and the system under the corresponding uniform magnetic field, the former is more fragile against the temperature compared with the latter since the gap is reduced by a factor of 1/5, while they are almost equally robust against the disorder. Therefore, it is expected that the QTHE of the SkX system is realized even with strong disorder at room temperature when the electron density is of the order of 1 per skyrmion.