Correlation between resistance fluctuations and temperature dependence of conductivity in graphene

It is known that monolayer graphene has an extraordinarily high intrinsic mobility of the charge carriers. An important complication is the presence of strong mesoscopic resistance fluctuations (MRFs) that, in graphene, persist to relatively high temperatures. These reproducible fluctuations are seen as a function of gate voltage but they are not expected to be seen as a function of temperature $T$. However, we propose that the monotonic increases or decreases in resistance $R\left(T\right)$ that we observe in graphene flakes as $T$ increases from 4.2 K to around 70 K arise from the decay of the magnitude of the MRFs due to progressive dephasing of the interfering scattered electron waves. Using the field effect transistor configuration, we demonstrate that this explanation is correct by measurements of $R\left(T\right)$ at different constant gate voltages $V_{\text{G}}$ tuned to different features of the MRFs observed in $R\left(V_{\text{G}}\right)$ at constant temperature. We find that the $T$ dependence of the MRF magnitude is, surprisingly, best fitted by an exponential decay.

Figure 1

(Color online) (a) Resistance with MRFs of the graphene flake as a function of gate voltage at 4.2 K before (black) and after (gray) a $T$ cycle up to 245 K and back down again to 4.2 K; the inset shows the peak on an expanded scale. (b) Resistance during the $T$ cycle carried at a constant gate voltage $V_{\Delta }=-0.6\text{V}$ [indicated by vertical lines in (a)]. Inset: optical image of the pattern of gold electrodes on top of a monolayer graphene sample (indicated by the dotted lines).

Figure 2

(Color online) (a) Resistance as a function of gate voltage showing the decrease in magnitude of each extremum of the MRFs as temperature increases. (b) Rms magnitude of the MRFs as a function of temperature averaged over all gate voltages, showing the close agreement with an exponential decay.

Figure 3

(Color online) (a) Resistance $R\left(T\right)$ as a function of temperature at gate voltage $V_{\Delta }=0$ at an MRF maximum value at the NP, indicated by the vertical line in the inset. Inset: resistance $R\left(V_{\Delta }\right)$ showing strong resistance fluctuations as a function of gate voltage near the NP. (b) Resistance as a function of $T$ at a MRF minimum value near the NP at $V_{\Delta }=-0.4\text{V}$. The fit lines in (a) and (b) are fits of the $R\left(T\right)$ data for an exponentially decaying MRF term and other terms in Eq. (1), as discussed in the text. (c) Resistance $R\left(T\right)$ far from the NP (i.e., at large charge-carrier densities) at a minimum of the resistance fluctuation pattern as a function of gate voltage (as indicated in the inset). (d) Resistance $R\left(T\right)$ far from the NP at a maximum of the MRF pattern. The fit lines in (c) and (d) are fits to Eq. (1) without the activation term but with phonon-scattering terms as discussed in the text.