A theory showing that the low-energy electronic minibands formed when a topological insulator's Dirac surface states are proximity-coupled to a triangular skyrmion lattice are captured by a chiral network model on a kagome lattice. The out-of-plane magnetization opens a position-dependent Dirac mass; along the zero-mass lines encircling each skyrmion the surface hosts confined chiral modes, and tunneling between adjacent skyrmions broadens them into delocalized minibands whose links form the kagome medial lattice of the skyrmion-boundary honeycomb. A naive energy-independent scattering network spuriously predicts a chiral Floquet phase impossible without external driving; applying 'band reconstruction' (accounting for the energy dependence of the network parameters) removes the artifact and accurately reproduces the surface minibands and their topological transitions, establishing band reconstruction as essential for the broad class of network models describing nanostructure electronics.
A theory of the electronic states that arise when the Dirac surface states of a topological insulator are proximity-coupled to the triangular skyrmion lattice of an adjacent insulating magnet. The ou…