First-principles study of electronic structure and optical properties of semiconductor surfaces unified approach for exact calculation of coupling coefficients of quantum angular momenta.

摘要

We compute the surface dielectric function anisotropy (SDA) and reflectance-difference (RD) spectra of Si(001)(2 x 1):As/Sb surfaces. The calculations are based on the local density approximation (LDA) scheme and utilize a novel set of basis functions, which are the products of delocalized plane waves in the surface planes and localized Gaussian functions in the direction normal to the surface. We identify and interpret the SDA and RD spectra in terms of interband transitions, and find that these transitions are mainly related to the electronic surface bands and surface induced bands. Considering that the calculations based on the LDA of density functional theory (DFT) usually underestimate the band gaps for semiconductors, we make the many-body self energy correction by shifting the related energy bands and then calculate the dielectric function anisotropy and reflectance difference spectra. We also take into consideration the excitonic and local-field effects with a contact-potential model. The finally calculated result for Si(001)(2 x 1):As surface is in a very good agreement with experimental observation.;We present schemes to reformulate all the 3j, 6j and 9j symbols in a form which is the product of two factors. One is a prefactor which is the square root of integer products and quotients. The other is the summation of the products of binomial coefficients. In the calculation of these factors, we utilize two types of number representation: the prime number representation for the prefactor, and the 32768-base number representation for the summation terms. This makes it possible to tabulate or exactly calculate the coupling and recoupling coefficients for any large angular momenta. Instead of evaluating a large number of factorials of integers, we also compute the binomial coefficients recursively at every stage, which dramatically increases the efficiency of calculation. Hence, a direct method for very fast and exact calculation of coupling and recoupling coefficients for all range of quantum angular momenta is established.;We present accurate results for the dynamics of an initially localized two-level (TLS) system coupled to a generic dissipative environment and driven by a periodic force which in the semiclassical limit is equivalent to a continuous-wave electromagnetic field. The time evolution is calculated via iterative evaluation of the path integral. We show that in the case where the temperature of the environment is high with respect to the energy splitting of the tunneling doublet, the delocalization rate is largely independent of the friction of the environment and of the specifics of the driving force, depending only on its overall strength. This robust behavior implies that localized states can be stabilized in these systems without much finetuning of external conditions. Our numerical results are interpreted in light of non-adiabatic rate theory.