The discussion centers on the relationship between the imaginary part of the dielectric function, denoted as ε₂, and the joint density of states (JDOS). It is established that ε₂ is almost directly proportional to JDOS, with exact proportionality occurring when the matrix element for transitions is independent of k-space position. For anisotropic materials, the matrix element's dependence on the polarization vector alters the relationship, requiring consideration of the coupling between conduction and valence bands. Additionally, the factor of 1/E² in the ε₂ equation suggests that JDOS is almost proportional to E²ε₂.
PREREQUISITESPhysicists, materials scientists, and researchers in solid-state physics focusing on electronic properties and the behavior of dielectric materials.
genneth said:Epsilon_2 is *almost* directly proportional to the JDoS. It is exactly proportional if the matrix element for the transition is independent of the position in k-space on the surface that defines the energetically allowed transition. For most purposes in crystals, the matrix element is only weakly dependent, and people like to just move it outside of the integral and replace it with an averaged matrix element.