Transport properties of the electronic states in the gate voltage-modulated skyrmion crystal

In this work, we investigated transport properties of the electronic states in the gate voltage-modulated skyrmion crystal (SkX). Dynamics of conducting electrons in the SkX can be described by the double-exchange model or the so-called $$t-J$$ t - J model, with the t term measuring the hopping energy of the electrons between neighboring sites and J term measuring the strength of the on-site Hund’s coupling between the spin of conducting electrons and local magnetization. As a result of the Hund’s coupling, the band structure of the conducting electrons in the SkX shares similar topological properties with that of gapped graphene, such as its cone-like shape, nonzero band Chern number, and edge states. By linear fitting the cone-shape energy dispersion of the electronic states in the SkX, one can obtain a gapped Dirac model similar to that of the gapped graphene. We use the Green’s function technique and calculate the transmission probability of the electrons tunneling through an electrostatic barrier in the SkX expressed by the double-exchange model. Numerical results of the transport properties of the SkX by the double-exchange model reproduced analytic results from the Dirac model. We further interpreted the resemblance between the transport properties of the two models by the likeness in their wave functions. Graphical Abstract