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.Comment: 12 pages, 9 figure

Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains

Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor—also known as Shiba chains—up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.publishe