## 3 Results and Discussion  
We have employed dynamic and static STM-BJ methods to characterize single-molecule TMC isomers conductance and to study the effect of the EEF generated by the STM bias voltage, on the conductance of the TMC single-molecule junction. Briefly, in the dynamic BJ approach (Figure 1c), the STM tip electrode is repeatedly moved into and out of contact with the substrate electrode at a constant piezo voltage ramp at 0.5 V/s with the STM piezo servo-feedback loop off. The junction conductivity is captured via the current versus time (or displacement) traces in the retraction stage. During the contact process (stage 1 in Figure 1c), the two metal electrodes (STM tip and substrate) are in contact, which the corresponding current saturation due to high conductive nature of the metal/metal contact, and individual carotenoid molecules in solution spontaneously attach to them through the -SMe terminal groups that have a high affinity for Au [26]. When the tip is retracted from the substrate, the metallic contact breaks and makes it possible for a TMC molecule to bridge the nanoscale gap (stage 2 in Figure 1c). In such cases, the current trace exhibits characteristic step-like features or plateaus corresponding to the quantum conductance of the molecular junction. Upon further retraction of the tip, the molecule detaches from one electrode (stage 3 in Figure 1c). The collapse of the molecular junction (open gap) is accompanied by a sharp drop in current. In a typical dynamic BJ experiment, we collect thousands of current traces, and an automated selection process designed in LabVIEW selects the decays that show plateaus (formation of a molecular junction and accumulates them into 1D semi-logarithmic conductance histograms [26]. The same selection criteria to build all histograms are applied throughout all experimental series. The yield of decay curves showing plateaus that meet the selection criteria is typically around 25% of the total number of collected curves [43]. The data selection process results in 1D conductance histograms that show peaks above the tunnelling background baseline, providing an averaged single-molecule conductance value, G. G is defined as G = Istep/Vbias, where Istep is the current plateau and Vbias is the voltage applied between the two Au electrodes. In the static approach (Figure 1d) [5], a fixed inter-electrode distance (electrode-electrode separation) is established between the STM tip and the substrate by setting a defined tunnelling current, It, to flow between them. When the gap has stabilized and shows a constant It versus time signal, the It feedback is turned off and the actual tunnelling current monitored (stage 1 in Figure 1d). A sudden current increase to Im appears when a target molecule is spontaneously caught in the gap and transiently forms a molecular junction, lowering the resistance between the electrodes (stage 2 in Figure 1d) [44]. This sudden increase in current is commonly referred to as a _blink_. A current blink is characterized by its conductance value and by its lifetime. The (spontaneous) collapse of the junction (i.e., molecule detaches from one electrode) is evidenced by a sudden drop of the Im to It [5,45,46] (stage 3 in Figure 1d). The number of individual blinks per fraction of time defines the accumulation yield and hundreds of them are plotted as 1D and 2D conductance histograms with a common x-axis time origin. All blinks are accumulated for evaluation without any selection using an automated process designed in LabVIEW. This process provides the averaged single-molecule conductance as a peak in the 1D histograms and prominent coloured regions of higher counts in the 2D blinking conductance-map histograms. The current corresponding to a trapped molecule (Iblink) is defined as Iblink = Im - It. Conductance values G are extracted from Iblink divided by the Vbias.