Curvature effects on valley splitting and degeneracy lifting: The case of Si/Ge rolled-up nanotubes

We numerically investigate electronic states, degeneracy lifting, and valley splitting in the conduction band of rolled-up Si/Ge nanotubes. Results are derived from a tight-binding model where the input equilibrium positions of the atoms are obtained by means of continuum elasticity theory. We find three inequivalent Δ valleys. The lifting of their energy degeneracy and the spatial distribution of the corresponding states are interpreted in terms of nonbiaxial strain and confinement effects. The intervalley interaction in Si/Ge nanotubes is studied as a function of the thickness and curvature of the tube. We demonstrate that the curvature affects the intervalley interaction, in close analogy to what happens with the application of a perpendicular electric field in planar quantum well Si/Ge systems.