Coulomb gap in graphene nanoribbons

We investigate the density- and temperature-dependent conductance of graphene nanoribbons with varying aspect ratio. Transport is dominated by a chain of quantum dots forming spontaneously due to disorder. Depending on ribbon length, electron density, and temperature, single or multiple quantum dots dominate the conductance. Between conductance resonances, cotunneling transport at the lowest temperatures turns into activated transport at higher temperatures. The density-dependent activation energy resembles the Coulomb gap in a quantitative manner. Individual resonances show signatures of multilevel transport in some regimes, and stochastic Coulomb blockade in others.

Figure 1

(a) Scanning force micrograph of the nanoribbon investigated here ($L=200$ nm, $W=75$ nm). (b) $G(V_{\mathrm{BG}}$) in a large density range showing the transport gap around $V_{\mathrm{BG}}=-2$ V. The measurement was taken at $T=1.25$ K with a source-drain bias of $V_{\mathrm{bias}}=500$ $\mu$V. (c) Finite-bias measurement inside the transport gap [same temperature as (b)].

Figure 2

(a) $T$ dependence of $G$ inside the transport gap at $V_{\mathrm{bias}}=100$ $\mu$V. Different curves are taken at $T=1.25$ K to $T=45$ K (lowermost to uppermost line). Inset: Coulomb resonances (gray solid line) reconstructed by a convolution of three Lorentzians with the derivative of the Fermi distribution (red dotted line). (b) Zoom into two exemplary peaks of (a). The left-hand peak is broadened and grows with increasing $T$, and the right-hand peak exhibits an overall decrease of $G$ with temperature. (c) $G$ as a function of $1/T$ at three positions in $V_{\mathrm{BG}}$ indicated by arrows in (b). Solid lines are fits to the data according to Eq. (1).

Figure 3

Back-gate dependence of fitting parameters: (a) $E_a$, (b) $G_{\mathrm{off}}$ (upper dotted line) and $G_0$ (lower dotted line). In (a) and (b) the black solid curve shows $G$ at base temperature. Insets: Coulomb diamonds reconstructed from $E_a$ for two regimes. (c) Comparison of a Coulomb diamond [representing $E_c\left(V_{\mathrm{BG}}\right)$] and $E_a$ determined for this $V_{\mathrm{BG}}$ interval. (d) $G_0\left(E_a\right)$ for the transport gap. Colored branches indicate $G_0/E_a$ pairs that originate from the same conductance valleys [arrows in (b)].