Top-down patterning of topological surface and edge states using a focused ion beam

The conducting boundary states of topological insulators appear at an interface where the characteristic invariant ℤ₂ switches from 1 to 0. These states offer prospects for quantum electronics; however, a method is needed to spatially-control ℤ₂ to pattern conducting channels. It is shown that modifying Sb₂Te₃ single-crystal surfaces with an ion beam switches the topological insulator into an amorphous state exhibiting negligible bulk and surface conductivity. This is attributed to a transition from ℤ₂= 1 → ℤ₂= 0 at a threshold disorder strength. This observation is supported by density functional theory and model Hamiltonian calculations. Here we show that this ion-beam treatment allows for inverse lithography to pattern arrays of topological surfaces, edges and corners which are the building blocks of topological electronics.