Quantum twin spectra in nanocrystalline silicon

Using inelastic neutron-scattering spectroscopy, we have identified twin-split scattering spectra in hydrogen-terminated nanocrystalline silicon. We show that this duality originates from the cooperative motion of hydrogen and silicon. Our formalism for the inelastic neutron-scattering spectrum, which is derived from the Hermite orthogonal wave functions in terms of the normal coordinates, elucidates the physical origin of the observed quantum twin spectra and predicts the possible occurrence of this behavior in other materials such as metal hydrides.