Topological surface states in deformed quantum wires

We show that a cylindrical quantum wire whose lateral surface is deformed may support surface states localized on the deformation. This surface localization can be studied upon writing the single-particle Schrödinger equation in a curvilinear coordinates system on the surface. The energies of these localized states depend on the parameters that characterize the surface and numerical results for a deformed quantum wire show that the more the deformation is pronounced, the more the wave functions are localized on it. The relative alignment of both volume confined and surface states is discussed with a view to porous silicon. Insights are given on the relation between the formation of localized surface states and the nanostructure surface reactivity to a gas environment in the framework of nanostructured materials sensor applications.