Macroscopic Dielectric Function Research Articles

Longitudinal dielectric function for Bloch electrons in a uniform magnetic field

The macroscopic longitudinal dielectric function for Bloch electrons in a uniform magnetic field is obtained from the canonical density matrix. The effect of the periodic field of the crystal is described by an anisotropy mass tensor. It is shown that the canonical density matrix method for calculating the dielectric function is equivalent to the treatment of Lindhard (1954), and Ehrenreich and Cohen (1959), in the static and zero-temperature case. The screening effects are discussed and an effective Coulomb potential is found in the Thomas-Fermi approximation. The limit of weak magnetic field is also considered.

Local-Field Effects in the Optical Spectrum of Silicon

We have calculated the dielectric response matrix ${\ensuremath{\epsilon}}_{\stackrel{\ensuremath{\rightarrow}}{G},{\stackrel{\ensuremath{\rightarrow}}{G}}^{\ensuremath{'}}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}=0, \ensuremath{\omega})$ for silicon and have obtained the macroscopic frequency-dependent dielectric function. Contrary to recent calculations, local-field corrections do not shift the prominent peak positions of the imaginary part of the dielectric function; further the calculated dielectric function is improved as compared with experiments at higher energies. In particular, agreement with measured energy-loss spectra is significantly better when local-field effects are included.

On the relation between macroscopic and microscopic nonlinear susceptibilities

A general formulation of the relationship between macroscopic and microscopic nonlinear dielectric response functions is presented. The results are in agreement with and justify previous theoretical and experimental data for local field corrections for the nonlinear susceptibilities χ 2 and χ 3, and for a contribution proportional to (χ 2); 2 to χ 3 eff,.