Critical point analysis of the interband transition strength of electrons

Optical and electron-energy-loss spectroscopies are well established methods of probing the electronic structure of materials. Comparison of experimental spectroscopic results with theory is complicated by the fact that the experiments extract information about the interband transition strength of electrons, whereas theoretical calculations provide information about individual valence and conduction bands. Based on the observation that prominent features in the optical response arise from critical points in the joint density of states, critical point modelling was developed to gain an understanding of these spectral features in terms of specific critical points in the band structure. These models were usually applied to derivative spectra and restricted to the consideration of isolated critical points. The authors present a new approach to critical point modelling of the undifferentiated spectra and interpret the model in terms of balanced sets of critical points which describe the interband transition strength arising from individual pairings of valence and conduction bands. This approach is then applied to achieve a direct, quantitative comparison of theoretical and experimental data on aluminium nitride.