Instabilities and the response function in low dimensional materials
Detecting the presence of charge and spin instabilities in a material is an important step to make predictions about the superconducting transition temperature. Typically, the evidence of sharp peaks in the real part of the static dielectric response function is used as an indication that such instabilities exist. However, there are persistent misconceptions that Fermi surface (FS) nesting guarantees a peak in the response function like in one-dimensional systems, and, in addition, response function matrix elements between empty and occupied states are of secondary importance and set to unity like in the free electron gas case. We explicitly show, through model systems and real materials, within the framework of density functional theory, that predictions about the peaks in the response function, using FS nesting and constant matrix elements yields erroneous results. In all the cases studied, other than the one-dimensional case, we find that the inclusion of matrix elements washes out the structure found with constant matrix elements. Our conclusion is that it is imperative to calculate the full response function, with matrix elements, when making predictions about instabilities in novel materials.