Unconventional topological Hall effect in skyrmion crystals caused by the topology of the lattice

The hallmark of a skyrmion crystal (SkX) is the topological Hall effect\n(THE). In this Article, we predict and explain an unconventional behavior of\nthe topological Hall conductivity in SkXs. In simple terms, the spin texture of\nthe skyrmions causes an inhomogeneous emergent magnetic field whose associated\nLorentz force acts on the electrons. By making the emergent field homogeneous,\nthe THE is mapped onto the quantum Hall effect (QHE). Consequently, each\nelectronic band of the SkX is assigned to a Landau level. This correspondence\nof THE and QHE allows to explain the unconventional behavior of the THE of\nelectrons in SkXs. For example, a skyrmion crystal on a triangular lattice\nexhibits a quantized topological Hall conductivity with steps of $2 \\cdot\ne^2/h$ below and with steps of $1 \\cdot e^2/h$ above the van Hove singularity.\nOn top of this, the conductivity shows a prominent sign change at the van Hove\nsingularity. These unconventional features are deeply connected to the topology\nof the structural lattice.\n