Curvature effects on valley splitting and degeneracy lifting: 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 Delta 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.