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 ℤ 2 switches from 1 to 0. These states offer prospects for quantum electronics; however, a method is needed to spatially-control ℤ 2 to pattern conducting channels. It is shown that modifying Sb 2 Te 3 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 ℤ 2  = 1 → ℤ 2  = 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.