Dielectric properties and plasmon modes of gapped momentum systems of different dimensionality

The concept of the energy gap is a fundamental characteristic of the band structure of a material and it determines its physical properties. Formally the energy gap appears in the dispersion relation Ek, where the vector k is determined on the whole momentum space. However, today the gapped momentum materials are in the focus of research in which the so-called momentum or k gap can emerge; i.e., some lacunae of momentum space are excluded from the domain of the function Ek. One such example presents the non-Hermitian systems. Within the random phase approximation we study the dielectric properties of the momentum gapped materials in one, two, and three dimensions for cases of both zero and finite temperatures. We find the corresponding plasmon modes and determine the unusual behavior of the appropriate dispersion relations for each dimensionality. Based on these findings we evaluate the absorption coefficient of gapped momentum media and provide some numerical estimations of its value for the practical applications.