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

Motivated by the very recent fabrication of sub-10-nm-wide semiconducting graphene nanoribbons [X. Li et al., Science 319, 1229 (2008)], where some of their band gaps extracted from transport measurements were closely fitted to density-functional theory predictions for magnetic ordering along zigzag edges that is responsible for the insulating ground state, we compute current-voltage $(I\text{\ensuremath{-}}V)$ characteristics of finite-length zigzag graphene nanoribbons (ZGNRs) attached to metallic contacts. The transport properties of such devices, at source-drain bias voltages beyond the linear-response regime, are obtained using the nonequilibrium Green's function formalism combined with the mean-field version of the Hubbard model fitted to reproduce the local spin-density approximation description of magnetic ordering. Our results indicate that magnetic ordering and the corresponding band gap in ZGNR can be completely eliminated by passing large enough direct current through it. The threshold voltage for the onset of band gap collapse depends on the ZGNR length and the contact transparency. If the contact resistance is adjusted to experimentally measured value of $\ensuremath{\simeq}60\text{ }\text{k}\ensuremath{\Omega}$, the threshold voltage for sub-10-nm-wide ZGNR with intercontact distance of $\ensuremath{\simeq}7\text{ }\text{nm}$ is $\ensuremath{\approx}0.4\text{ }\text{V}$. For some device setups, including $60\text{ }\text{k}\ensuremath{\Omega}$ contacts, the room-temperature $I\text{\ensuremath{-}}V$ curves demonstrate steplike current increase by one order of magnitude at the threshold voltage and can exhibit a hysteresis as well. On the other hand, poorly transmitting contacts can almost completely eliminate abrupt jump in the $I\text{\ensuremath{-}}V$ characteristics. The threshold voltage increases with the ZGNR length (e.g., reaching $\ensuremath{\approx}0.8\text{ }\text{V}$ for $\ensuremath{\simeq}13\text{-nm}$-long ZGNR) which provides possible explanation of why the recent experiments [Wang et al., Phys. Rev. Lett. 100, 206803 (2008)] on $\ensuremath{\sim}100\text{-nm}$-long GNR field-effect transistors with bias voltage $<1\text{ }\text{V}$ did not detect the $I\text{\ensuremath{-}}V$ curve signatures of the band gap collapse. Thus, observation of predicted abrupt jump in the $I\text{\ensuremath{-}}V$ curve of two-terminal devices with short ZGNR channel and transparent metallic contacts will confirm its zigzag edge magnetic ordering via all-electrical measurements, as well as a current-flow-driven magnetic-insulator--nonmagnetic-metal nonequilibrium phase transition.