Unconventional topological Hall effect in high-topological-number skyrmion crystals

Abstract

Skyrmions with the topological number Q equal an integer larger than 1 are called hightopological-number skyrmions or high-Q skyrmions. In this work, we theoretically study the topological Hall effect in square-lattice high-Q skyrmion crystals (SkX) with Q = 2 and Q = 3.As a result of the emergent magnetic field, Landau-level-like electronic band structure gives rise to quantized Hall conductivity when the Fermi energy is within the gaps between adjacent single band or multiple bands intertwined. We found that different from conventional (Q = 1) SkX the Hall quantization number increases by 1/Q in average when the elevating Fermi energy crosses each band. We attribute the result to the fact that the Berry phase C is measured in the momentum space and the topological number of a single skyrmion Q is measured in the real space. The reciprocality does not affect the conventional SkX because Q = 1 = 1/Q.

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

“…The topological properties of the monopole and dipole are sharply distinct. We recently found that different from the conventional monopolelattice SkX, the Hall conductivity quantization number of the dipole-lattice SkX increases by 0, 1, 0, 1, • • • consecutively when the elevating Fermi energy crosses each band 15 . Both the skyrmion profile and the topological Hall conductivity show that the monopole lattice and dipole lattice are two distinct topological phases, with the polarity value their distinguishing index.…”