First-principles study on the dielectric response of solids

Abstract

The dielectric response function is investigated using the first-principles pseudopotential method within the local density functional approximation. The dielectric matrix is calculated through a perturbative approach employing an analytic continuation of the response function. Calculations are performed for three different materials; semiconductor - Si, simple metal - Al, and transition metal - Nb. The local field and exchange-correlation effects on the linear response in these materials are discussed and compared with each other. The static dielectric matrices for Si, Al, and Nb are calculated. Comparison with previously reported results on Si show good agreement. In the case of Si and Nb, the local fields substantially weaken the screening effects, thus, reducing the macroscopic dielectric function. The role of the exchange-correlation in the dielectric response depending on the probe of the response is discussed. The screening potentials of external perturbations caused by the addition of point charges at several positions in the unit cell are calculated with information for the full elements of the dielectric matrix. The results well illustrate the role of the local fields in the screening. The dynamical response function and plasmon excitations are investigated for Si and Al. Analytic continuation using Taylor expansion is successfully applied in the calculation of the dynamical response function. A new type of analytic continuation technique using the N-point Pade approximant is developed. The applicability of this scheme is tested on the dynamical response function of Al and Si. As an application of the dielectric response to superconductivity, the Coulomb pseudopotential $μ^*$ is calculated for Al and Nb. The $μ^*$ is calculated for various cases of dielectric screening illustrating the effects of the local-field and exchange-correlation on the magnitudes of $μ^*$.