content_image/425510.jpg content_image/425520.jpg content_image/425511.jpg
<img src='content_image/425510.jpg'>

states can be substantial and translate into a magnetore- sistive response as large as 100% for distances between the H atoms of the order of few nanometers. Practical implications of these results are discussed in Sec. IV and a brief summary is presented in Sec. V 

For the calculation of the electronic structure of hydro- genated AGNR’s we use both ab initio techniques within the local spin density approximation (LSDA), aided by the CRYSTAL03 package $^{23}$, and a one-orbital ( π ) first- neighbor tight-binding model where the electronic repul- sion is treated by means of a Hubbard-like interaction U in the mean field approximation: 

<img src='content_image/425520.jpg'>

The first term represents the kinetic energy with first neighbors hopping t between π orbitals. The remain- ing terms account for the electronic interactions where 

## II. COMPUTATIONAL DETAILS 

<img src='content_image/425511.jpg'>

ˆ n$_{iη}$ = ˆ c + $_{iη}$ˆ c$_{iη}$ are the number operators associated to each π orbital with spin η . These two different lev- els of approximation to the electronic structure have been shown to yield similar results for nanoribbons 24 and nanographenes 13 where a full passivation by H of the σ bonds is assumed. 

The bulk adsorption geometry of a H atom has been obtained by relaxing the C atom bonded to the H and the nearest C atoms until the characteristic sp 3 hybridization is obtained [see inset in Fig. 1(a)]. The bonding between a H atom and a C atom results in the effective removal of the π orbital from the low energy sector, so that the H adsorption is simulated by simply removing a site in the one-orbital mean-field Hubbard model [see Fig. 1(b- d)]. Our results, as shown below, provide further support to the use of the Hubbard model in graphene systems, as an alternative to the computationally more demand- ing LSDA and extend the range of applicability of Lieb’s theorem 25 to a wider set of situations. 

To calculate the transport properties we use the standard Green’s function partitioning method as im- plemented, e.g., in the quantum transport package ALACANT $^{26}$. To this purpose, the infinite system is 

