## 3 Results and Discussion  
After the SLB formation on the GO/SiO\({}_{2}\)/Si substrate, the position of the GO flakes was recognized in the AFM topographies as shown in Figure 2a,b. The regions with GO flakes were higher than the surrounding SiO\({}_{2}\) region by \(\sim\)6.5 nm or \(\sim\)1.5 nm. They are assigned to double layers and a single layer of the SLB as with the previous study [29]. The typical height of a GO flake on a SiO\({}_{2}\)/Si solid substrate in the AFM topographies is approximately 1.5 nm, which includes the thicknesses of GO and a water layer confined between the GO flake and the substrate [29]. Since the SiO\({}_{2}\)/Si substrate is covered with a single layer of SLB, the height difference of 1.5 nm indicates a single layer of SLB existing on the GO flake, and that of 6.5 nm indicates another SLB layer, whose typical thickness is approximately 5 nm [12; 29; 40], stacking on the first SLB on GO. The domains of the PEG-DSPE appeared as depressed regions in Figure 2a,b as reported in the previous study [41]. The DOPC-SLB with C\({}_{\text{PEG}}\) = 5.0 mol% and 7.0 mol% on the SiO\({}_{2}\)/Si substrate without GO are shown in Figure 2c,d, respectively, for comparison. The depressed region increased with C\({}_{\text{PEG}}\). The apparent AFM topography of the PEG-DSPE domains is highly force-dependent: in the force range of the conventional intermittent contact mode, they appear lower than the surrounding SLB region where diffusing PEG-DSPE molecules exist [41; 42]. It is interesting that the PEG-DSPE domains were localized on the GO flakes (Figure 2a,b) probably due to the difference in the substrate-SLB interaction between GO and SiO\({}_{2}\). Hydration repulsion on a SiO\({}_{2}\) surface, which is due to the hydrogen-bonded water layer to the surface hydroxy groups, reduces with the decrease in the surface hydrophilicity [43]. The surface of GO is partially hydrophobic because of the pristine graphene patches [13; 14]; therefore, it induces less hydration repulsion compared to the SiO\({}_{2}\) surface. Hydrophilic polymers, including PEG, cause thermal fluctuation repulsions [41; 42; 44]; therefore, we surmise that the PEG-DSPE preferred the less repulsive GO region than the SiO\({}_{2}\) region. The QD was conjugated to the SLB with \(C_{\text{PEG}}\) = 5.0 mol% on the GO/SiO\({}_{2}\)/Si substrate, to perform the SPT. Each QD appeared as bright spots in the SPT movie, as shown in Video S1 of the Supplementary Materials and its snapshot in Figure 3a. Mobile bright spots (Figure 3a, indicated by a white arrow) were QDs conjugated with one or a few DPPTE molecules in the SLB, while immobile ones (Figure 3b, indicated by black arrows) were QDs with an excessively multivalent conjugation or those nonspecifically adsorbed on the SLB. The shape of the GO flakes was recognized because of the fluorescence from GO, but its intensity was sufficiently lower than that from QDs. QDs conjugated on the SLB surface were visible in the GO region even under the effect of the fluorescence quenching by GO. The fluorescence intensity of the QDs was not homogeneous as seen in Figure 3a. It may be because of the heterogeneous conjugation states of the QDs that possibly affect the fluorescence intensity by itself and also the effects of dissolved oxygen in the buffer solution. Oxygen induces various effects on the fluorescence of QDs including quenching, brightening, and blinking [45]. Figure 2: AFM topographies of DOPC-SLB containing PEG-DSPE on the SiO\({}_{2}\)/Si substrates (**a,b**) with and (**c,d**) without GO, and their cross-section profiles at the white lines. \(C_{\text{PEG}}\) = (**a,c**) 5.0%, and (**b,d**) 7.5%. Scale bar = 500 nm. Figure 3b shows the trajectory of a mobile QD that diffused from the GO region (depicted in blue in Figure 3b) to the SiO\({}_{2}\) region without GO (depicted in red in Figure 3b). The fluorescence intensity of this QD during the diffusion in Figure 3b was obtained from the SPT movie (Video S1) and plotted as the time trace in Figure 3c.