Figure 6: Gating efficiency for various gating methods.

(a) Pinch-off back-gate voltage, V_BG, as a function of V_EDL. The dashed line is a guide for eyes. (b) Comparison of the lever-arm factors for various gating methods. The lever-arm factor is defined as the conversion ratio of the gate voltage to the shift in the energy levels. The lever-arm factor for the side gate was derived from Deacon et al.¹³ and Kanai et al.¹⁵ The lever-arm factor for the back-gate was derived from this work (α_BG ~70 meV V⁻¹) and Takahashi et al.¹⁴ The lever-arm factor for the top-gate structure was derived from Supplementary Fig. S9. The efficiency of EDL gating (350 meV V⁻¹) is about 6, 9 and 90 times higher than that of the back gating (60 meV V⁻¹), the top gating (40 meV V⁻¹) and the side gating (4 meV V⁻¹), respectively. In order to compare the lever-arm factors for different gating methods, we carefully chose the samples with almost the same nano-gap size (50 nm) and the QD location relative to the nano-gap electrodes (The QD is located at the centre of nano-gap metal electrodes as shown in Fig. 1c).