  Electronic transport in a zig-zag-edge graphene nanoribbon (GNR) and its
modification by adsorbed transition metal porphyrins is studied by means of
density functional theory calculations. The detachment reaction of the metal
centre of the porphyrin is investigated both in the gas phase and for molecules
adsorbed on the GNR. As most metal porphyrins are very stable against this
reaction, it is found that these molecules bind only weakly to a perfect
nanoribbon. However, interaction with a single-atom vacancy in the GNR results
in chemical bonding by the transition metal centre being shared between
nitrogen atoms in the porphyrin ring and the carbon atoms next to the vacancy
in the GNR. For both the physisorbed and the chemisorbed geometry, the
inclusion of van der Waals interaction results in a significant enlargement of
the binding energy and reduction of the adsorption height. Electronic transport
calculations using non-equilibrium Greens functions show that the conductivity
of the GNR is altered by the chemisorbed porphyrin molecules. Since the metal
centers of porphyrins carry an element-specific magnetic moment, not only the
net conductance, but also the spin-dependent conductance of the GNR is
affected. In particular, the adsorption of Ru-porphyrin on the single-atom
vacancy results in a very large spin polarization of the current of 88% at
small applied source-drain voltages. Based on our results, we suggest that a
spin valve constructed from a GNR with ferromagnetic contacts could be used as
a sensitive detector that could discriminate between various metal porphyrins.
