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Phonon-assisted optical absorption in silicon from first principles
The phonon-assisted interband optical absorption spectrum of silicon is
calculated at the quasiparticle level entirely from first principles. We make
use of the Wannier interpolation formalism to determine the quasiparticle
energies, as well as the optical transition and electron-phonon coupling matrix
elements, on fine grids in the Brillouin zone. The calculated spectrum near the
onset of indirect absorption is in very good agreement with experimental
measurements for a range of temperatures. Moreover, our method can accurately
determine the optical absorption spectrum of silicon in the visible range, an
important process for optoelectronic and photovoltaic applications that cannot
be addressed with simple models. The computational formalism is quite general
and can be used to understand the phonon-assisted absorption processes in
general
Energy Gaps in Graphene Nanoribbons
Based on a first-principles approach, we present scaling rules for the band
gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs
considered have either armchair or zigzag shaped edges on both sides with
hydrogen passivation. Both varieties of ribbons are shown to have band gaps.
This differs from the results of simple tight-binding calculations or solutions
of the Dirac's equation based on them. Our {\it ab initio} calculations show
that the origin of energy gaps for GNRs with armchair shaped edges arises from
both quantum confinement and the crucial effect of the edges. For GNRs with
zigzag shaped edges, gaps appear because of a staggered sublattice potential on
the hexagonal lattice due to edge magnetization. The rich gap structure for
ribbons with armchair shaped edges is further obtained analytically including
edge effects. These results reproduce our {\it ab initio} calculation results
very well
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