Suspending Effect on Low-Frequency Charge Noise in Graphene Quantum Dot

Charge noise is critical in the performance of gate-controlled quantum dots (QDs). Such information is not yet available for QDs made out of the new material graphene, where both substrate and edge states are known to have important effects. Here we show the 1/f noise for a microscopic graphene QD is substantially larger than that for a macroscopic graphene field-effect transistor (FET), increasing linearly with temperature. To understand its origin, we suspended the graphene QD above the substrate. In contrast to large area graphene FETs, we find that a suspended graphene QD has an almost-identical noise level as an unsuspended one. Tracking noise levels around the Coulomb blockade peak as a function of gate voltage yields potential fluctuations of order 1 μeV, almost one order larger than in GaAs/GaAlAs QDs. Edge states and surface impurities rather than substrate-induced disorders, appear to dominate the 1/f noise, thus affecting the coherency of graphene nano-devices.


Suspension of the device
shows a SEM image of a graphene nanoribbon, which is in contact with the substrate. (This device is not used in the experiment.) Figure S2(a) shows a SEM image of a suspended graphene nanoribbon device after transport measurement. Clearly, the nanoribbon is not pulled down to the substrate during the transport measurement, which is different from the situation in Figure S1. Even though a dc voltage of up to 7 V was applied to the back gate, the graphene nanoribbon still remains suspended. Figure  S2(b) shows a SEM image of the same device in Figure S2(a) after AFM measurement. The graphene nanoribbon is tapped down, in contact with the substrate, which is similar with Figure S1.

Lever arm
We measure the noise level of five graphene nano-devices, both suspended and regular (unsuspended). As suspend the device above the substrate, the electrical environment is changed, resulting in the difference between the lever arms of the device.
We obtain the lever arm from standard Coulomb diamonds measurement. S1 As shown in Table S1, we find regular devices have a lever arm almost twice as much as those of suspended devices.  Table S1. Lever arms of five different nano-devices labeled in Figure 5. 3. Noise spectra analysis using another method Figure S3 shows two different noise spectra, calculated using the method described in Ref. [S2]. The spectra (red and black) were measured at different regions of the Coulomb peak, labeled A and B in the inset (similar as in Figure 3). The figure is plotted in log-log scale. All the data points near 50 Hz were removed as they were induced by electricity from the mains. The blue and green dashed lines are the noise spectra obtained from regular and suspended graphene FETs respectively (see Ref. [S2]), showing a difference of an order of magnitude. However, in our experiment, no difference was observed between regular and suspended graphene QDs using this method.
To compare our results to graphene FETs, we focus our attention on spectrum A, since electrons tunnel through the graphene QD at A. Clearly, the noise at A is one (two) order(s) of magnitude larger than the result obtained from regular (suspended) GFETs, respectively. Figure S3. Two different noise spectra measured at different regions of the Coulomb peak, labeled A and B in the inset. The figure is plotted in log-log scale. The blue and green dashed lines are the noise spectra obtained from regular and suspended graphene FETs, respectively (see Ref. [S2]).
We also compared our results to which described in Ref. [S3]. Fitting the spectra with the formula S I 2 /I 2 =A/f, we find that the noise power A of our graphene nano-devices (both suspended and unsuspended) is of the order of 10 -6 to 10 -5 , which is about one (two) order(s) of magnitude larger. Furthermore, we obtained our area-scaled noise amplitude (device area ( 2 )×noise power A), as 10 -2 ×10 -5 (10 -6 )=10 -7 (10 -8 ). Since we only consider the area of the nanoribbon, the effective area should also include the area of the connection part between the nanoribbon and source-drain contacts, results in larger area-scaled noise amplitude. Compared to the Figure 3 in Ref. [S3], our result is one (two) order(s) of magnitude larger. This result is also consisted with the comparison in the Figure S3, indicating some new sources of noise, such as edge states and surface impurities, influence the performance of the graphene QDs.