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The valence band structure of α-phase crystalline films of cobalt phthalocyanine (CoPc) grown on Au(111) is investigated by using angle-resolved photoemission spectroscopy (ARPES) with synchrotron radiation. The photo-induced change in the ARPES peaks is noticed in shape and energy of the highest occupied molecular orbital (HOMO, C 2p) and HOMO-1 (Co 3d) of CoPc, and is misleading the interpretation of the electronic properties of CoPc films. From the damage-free normal-emission ARPES measurement, the clear valence-band dispersion has been first observed, showing that orbital-specific behaviors are attributable to the interplay of the intermolecular ρ-ρ and ρ-d interactions. The HOMO band dispersion of 0.1 eV gives the lower limit of the hole mobility for α-CoPc of 28.9 cm² V-1 s-1 at 15 K. The non-dispersive character of the split HOMO-1 bands indicates that the localization of the spin state is a possible origin of the antiferromagnetism. [ABSTRACT FROM AUTHOR]

Let H be the quantum double of a Nichols algebra of diagonal type. We compute the R-matrix of 3-tuples of modules for general finite-dimensional highest weight modules over H. We also calculate a multiplicative formula for the universal R-matrix when H is finite dimensional. We show the unicity of a PBW basis (or a Lusztig-type Poincaré-Birkhoff-Witt basis) with a given convex order. [ABSTRACT FROM AUTHOR]