35,592 research outputs found
Interaction between graphene and SiO2 surface
With first-principles DFT calculations, the interaction between graphene and
SiO2 surface has been analyzed by constructing the different configurations
based on {\alpha}-quartz and cristobalite structures. The single layer graphene
can stay stably on SiO2 surface is explained based on the general consideration
of configuration structures of SiO2 surface. It is also found that the oxygen
defect in SiO2 surface can shift the Fermi level of graphene down which opens
out the mechanism of hole-doping effect of graphene absorbed on SiO2 surface
observed in experiments.Comment: 17 pages, 7 figure
Standard model plethystics
We study the vacuum geometry prescribed by the gauge invariant operators of the minimal supersymmetric standard model via the plethystic program. This is achieved by using several tricks to perform the highly computationally challenging Molien-Weyl integral, from which we extract the Hilbert series, encoding the invariants of the geometry at all degrees. The fully refined Hilbert series is presented as the explicit sum of 1422 rational functions. We found a good choice of weights to unrefine the Hilbert series into a rational function of a single variable, from which we can read off the dimension and the degree of the vacuum moduli space of the minimal supersymmetric standard model gauge invariants. All data in Mathematica format are also presented
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