Development of a Debye heat capacity model for vibrational modes with a gap in the density of states

Low-energy vibrational modes that have a gap in the density of states (DOS) have often been observed in heat capacity data in the form of 'boson' peaks, but the functions used to model these modes are often inadequate or are not physically meaningful. We have adapted the Debye model to represent these gapped modes and have derived the heat capacity equations for these modes in one, two, and three dimensions. Applying these equations to the low-temperature heat capacity data fitting for a large variety of materials substantially improves the fit quality relative to conventional fits. From the fitting parameters, the underlying DOS were estimated, which we show to be comparable to those reported in the literature. This model expands the methods of theoretical low-temperature heat capacity data analysis and improves the procedure of approximating a material's DOS from its low-temperature heat capacity.