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Motivated by the very recent fabrication of sub-10-nm-wide semiconductinggraphene nanoribbons [X. Li et al., Science 319, 1229 (2008)], whose band gapsextracted from transport measurements were fitted to density functional theorypredictions for magnetic ordering along zigzag edges that is responsible forthe insulating ground state, we compute current-voltage (I-V) characteristicsof finite-length zigzag graphene nanoribbons (ZGNR) attached to metalliccontacts. The transport properties of such devices, at source-drain biasvoltages beyond the linear response regime, are obtained using thenonequilibrium Green function formalism combined with the mean-field version ofthe Hubbard model fitted to reproduce the local spin density approximationdescription of magnetic ordering. Our results indicate that magnetic orderingand the corresponding band gap in ZGNR can be completely eliminated by passinglarge enough DC current through it. The threshold voltage increases with theZGNR length (e.g., reaching $\approx 0.8$ V for $\simeq 13$ nm long ZGNR) whichprovides possible explanation of why the recent experiments [Wang et al., Phys.Rev. Lett. 100, 206803 (2008)] on $\sim 100$ nm long GNR field-effecttransistors with bias voltage less than 1 V did not detect the I-V curvesignatures of the band gap collapse. Thus, observation of predicted abrupt jumpin the I-V curve of two-terminal devices with short ZGNR channel andtransparent contacts will confirm its zigzag edge magnetic ordering viaall-electrical measurements, as well as a current-flow-drivenmagnetic-insulator--nonmagnetic-metal nonequilibrium phase transition.

I-V curve signatures of nonequilibrium-driven band gap collapse in magnetically ordered zigzag graphene nanoribbon two-terminal devices