We report electrical transport measurements on a suspended ultra-low-disorder graphene nanoribbon(GNR) with nearly atomically smooth edges that reveal a high mobility exceeding 3000 cm2 V-1 s-1 and an intrinsic band gap. The experimentally derived ba
ndgap is in quantitative agreement with the results of our electronic-structure calculations on chiral GNRs with comparable width taking into account the electron-electron interactions, indicating that the origin of the bandgap in non-armchair GNRs is partially due to the magnetic zigzag edges.
In this paper, we prove that a non-semisimple Hopf algebra H of dimension 4p with p an odd prime over an algebraically closed field of characteristic zero is pointed provided H contains more than two group-like elements. In particular, we prove that
non-semisimple Hopf algebras of dimensions 20, 28 and 44 are pointed or their duals are pointed, and this completes the classification of Hopf algebras in these dimensions.
One dimensional nanobeam photonic crystal cavities are fabricated in silicon dioxide with silicon nanocrystals. Quality factors of over 9 x 10^3 are found in experiment, matching theoretical predictions, with mode volumes of 1.5(lambda/n)^3 . Photolu
minescence from the cavity modes is observed in the visible wavelength range 600-820 nm. Studies of the lossy characteristics of the cavities are conducted at varying temperatures and pump powers. Free carrier absorption effects are found to be significant at pump powers as low as a few hundred nanowatts.
