Shot noise suppression and hopping conduction in graphene nanoribbons

We have investigated shot noise and conduction of graphene field-effect nanoribbon devices at low temperature. By analyzing the exponential $I\text{−}V$ characteristics of our devices in the transport gap region, we found out that transport follows variable range hopping laws at intermediate bias voltages $1<V_{bias}<12\text{mV}$. In parallel, we observe a strong shot noise suppression leading to very low Fano factors. The strong suppression of shot noise is consistent with inelastic hopping, in crossover from one- to two-dimensional regime, indicating that the localization length $l_{loc}<W$ in our nanoribbons.

Figure 1

(Color online) (a) Schematics of an etched GNR. (b) False color scanning electron micrograph of sample A, highlighting the graphene and the GNR (in blue/dark gray) and the leads (in yellow/light gray).

Figure 2

(Color online) [(a) and (b)] $G$ versus $V_{gate}$ at various temperatures for sample A and B, respectively. [(c) and (d)] Color map of $\frac{dI}{dV}$ versus $V_{bias}$ and $V_{gate}$ with step of 0.2 and 0.3 V between each biasing at $T=4.9$ and 5.2 K for sample A and B, respectively.

Figure 3

(Color online) $I\text{−}V$ characteristics of sample A and B plotted using hopping law at high bias (a), Eq. (1), at $V_{gate}=25.4$ and 11 V at $T=4.9$ and 5.2 K for sample A and B, respectively (△ and ◻). The plot shows linear behavior in the log scale with $1/V_{bias}^{1/2}$ above the gap [flat part of (b) and (c)] and below $V_0$, i.e., where the data stats to deviate from linear in (a). (b) and (c) are the corresponding normal $I\text{−}V$ plots of sample A and B, respectively.

Figure 4

(Color online) (a) $S_I$ versus $I$ averaged over three gate values around $V_{gate}=25.4\text{V}$ and $T=4.9\text{K}$ for sample A (△), and $V_{gate}=11\text{V}$ and $T=5.2\text{K}$ for sample B (◻). We show a low-bias fit for sample B using the Khlus formula with $F$ as the only fitting parameter. $F$ decreases at higher bias (see text). [(b) and (c)] $S_I$ versus $I$ zoomed in the low-bias region.