The quantum skyrmion Hall effect in f electron systems

The flow of electric current through a two-dimensional material in a magnetic field gives rise to the family of Hall effects. The quantum versions of these effects accommodate robust electronic edge channels and fractional charges. Recently, the Hall effect of skyrmions, classical magnetic quasiparticles with a quantized topological charge, has been theoretically and experimentally reported, igniting ideas on a quantum version of this effect. To this end, we perform dynamical mean field theory calculations on localized $f$ electrons coupled to itinerant $c$ electrons in the presence of spin-orbit interaction and a magnetic field. Our calculations reveal localized nano quantum skyrmions that start moving transversally when a charge current in the itinerant electrons is applied. The results show the time-transient build-up of the quantum skyrmion Hall effect, accompanied by an Edelstein effect and a magnetoelectric effect that rotate the spins. This work motivates studies about the steady state of the quantum skyrmion Hall effect, looking for eventual quantum skyrmion edge channels and their transport properties.