Magnetotransport through graphene nanoribbons

We investigate magnetotransport through graphene nanoribbons as a function of gate and bias voltage, and temperature. We find that a magnetic field systematically leads to an increase in the conductance on a scale of a few tesla. This phenomenon is accompanied by a decrease in the energy scales associated to charging effects, and to hopping processes probed by temperature-dependent measurements. All the observations can be interpreted consistently in terms of strong-localization effects caused by the large disorder present, and exclude that the insulating state observed in nanoribbons can be explained solely in terms of a true gap between valence and conduction bands.

Figure 1

(Color online) (a) Conductance $G$ as a function of the gate voltage $V_{bg}$, showing a transport gap at low charge densities. The inset shows a scheme of the device geometry (the substrate is highly doped silicon covered by a 285 nm ${\text{SiO}}_2$ layer). Panels (b) and (c) zoom in on the Coulomb-blockade peaks present in the transport gap at $B=0\text{T}$ and 8 T, respectively.

Figure 2

(Color online) Panels (a) and (b) show the color plots of $\text{log}\left(G\right)$ as a function of gate $\left(V_{bg}\right)$ and bias $\left(V_{sd}\right)$, respectively, at $B=0$ and 8 T (the measurements are taken at $T=4.2\text{K}$; $G_0=e^2/h$). The comparison of the two panels shows how in a magnetic field the extent of the high-resistance part is suppressed.

Figure 3

(Color online) Coulomb diamonds measured in the transport gap at $T=4.2\text{K}$, at (a) $B=0\text{T}$ and (b) $B=8\text{T}$. The typical height $\Delta V_{sd}$ and width $\Delta V_{bg}$ of the diamonds at high field are smaller than at zero field.

Figure 4

(Color online) (a) Color plot of $\text{log}\left(G\right)$ as a function of $V_{bg}$ (in the transport gap) and of $B$ (measurements done at $T=4.2\text{K}$). The average peak conductance and the number of Coulomb peaks increase with increasing magnetic field [consistent with Figs. 1b, 1c and Fig. 3]. Panel (b) shows the average of conductance over gate voltage, as a function of magnetic field. Noticeably, this quantity increases with increasing $B$ up to approximately 3 T (irrespective of the ribbon width), and saturates for higher-field values.

Figure 5

(Color online) The average conductance $⟨G⟩$ in the transport gap as a function of $T^{-1/2}$ at $B=0\text{T}$ and $B=8\text{T}$. The dashed lines are linear fits to the data. In the inset, the same data is plotted as a function of $T^{-1}$.