Final Report of Strongly Interacting Fermion Systems Page: 1 of 14
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Final Report for DE-FG02--88ER45347
I. Final Report (11/15/95-11/14/99)
There has been significant progress is three broad areas: (A) Optical properties, (B)
Large-scale computations, and (C) Many-body systems. In this summary the emphasis is
primarily on those papers that point to the research plans. At the same time, some important
analytic work is not neglected, some of it even appearing in the description of large-scale
computations. Indeed one of the aims of such computations is to give new insights which
lead to development of models capable of simple analytic or nearly analytic analysis.
A.. Optical Properties
The relevant papers can be roughly divided into three topics: local-field corrections,
improving upon local density theory, and magnetic circular dichroism.
This report represents the end of nearly a decade of work on optical properties on bulk,
undefected materials. In that time a group of collaborators have pioneered efficient ways to
compute the nonlinear and other optical properties of semiconductors and insulators. Over
two dozen different materials have been studied for a variety of crystal structures and optical
properties. Two features characterized the work:
o Local fields. Our calculations were the first to include local-field corrections within
first-principles band structure calculations. Recently an alternate formulation for local-
field corrections of the second-harmonic susceptibility has appeared.t We have showed
f that this new formulation is equivalent to the sum-over-states method we have been
using for years.14 While the new formulation is algebraically simpler than ours, its
relative computational efficiency awaits verification. For our code, successive algorithmic
a improvements have reduced the same-platform computational time nearly two orders of
1 omgnitude, allowing us to explore increasingly larger systems.
issor operator. That the Local-Density Approximation (LDA) substantially under-
ge inmates the energy gap causes straight-forward computation to seriously overestimate
~ ical properties, which depend strongly on the inverse powers of the energy gap. The
issors operator" was introduced to uniformly shift all conduction bands upward by
>'-j amount equal to the difference between the measured energy gap and the computed
o_ E tA gap. This correction, which also included a concomitant correction to the current
_ orator, works very well for small- and medium-gap semiconductors, but is less suc-
S mcsful for large-gap semiconductors and insulators. The next subsection of this progress
report introduces a next step in the argument and points to the proposal section. There
are two greater difficulties with the scissors operator:
Materials by design. For prospective new semiconductors or heterostructures
the scissors approach is a non-starter since the measured energy gap is necessarily
t A. Dal Corso, F. Mauri and A. Rubio, Physical Review B 53, 15368 (1996).
The reference numbers refer to numbering of DOE publications listed in Section I.D.
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Wilkins, J. W. Final Report of Strongly Interacting Fermion Systems, report, June 25, 2001; United States. (digital.library.unt.edu/ark:/67531/metadc777342/m1/1/: accessed September 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.