This yields E c ≈ 0.6 meV for SWNT1, which requires a temperature T < 7 K for CB to occur. However, the scaling law is observed up to at least 10 K, which suggests that the observed scaling, at least above 7 K, could be indeed a TLL behavior. It is noted from Figure 6b that for bias voltages less than about 9 mV at 2 and 5 K, there is an increase in the resistance that could be attributed to enhanced CB effect with reducing bias voltages. This change in R versus V at low-bias voltages could be attributed to a crossover between the TLL and CB regimes . Nevertheless, to experimentally confirm the CB effect, a gate voltage VE-822 mouse is required to modulate the SWNT’s energy levels in order to possibly observe single electron tunneling
as evidence for CB [37, 40], which is beyond our current experimental setup. Figure 6 Tomonaga-Luttinger liquid and Coulomb blockade scaling analysis. Log-log plots for sample SWNT1 of (a) the low-bias
resistance versus temperature, with data points in circles is the extracted resistance from IV curves at different temperatures, and the solid line is a power law fit R ~ T -α . (b) High-bias differential resistance versus voltage at 2, 5, and 10 K. The solid line is a power law fit dV/dI ~ V -α . The inset shows the same data at higher temperatures. (c) and (d) are the same log-log plots for sample SWNT2. The solid line in the inset of (d) indicates the independence of dV/dI versus temperature. The same TLL and CB scaling analysis is applied to sample SWNT2 as shown in Figure 6c,d. For R vs T plot, a fit to T -α at high temperatures satisfying the low-bias click here condition eV < < k B T, yields an α ≈ 0.5. On the other hand, R vs V plot at the high-bias regime eV > > k B T leads to a power fit V -α , with α ≈ 2. Since the exponents from the two regimes are different, it is concluded that SWNT2 behavior is not consistent with TLL or CB. Figure 6d shows a dramatic increase in resistance at low bias for temperatures below or equal to 10 K. At higher temperatures, as shown in the inset of Figure 6d, the
resistance is SN-38 cell line basically independent of the applied voltage, which is consistent with GPX6 the linear IVs measured at higher temperature as shown in Figure 5b. The measured very high values of the resistance at low temperatures and low bias (in the order of GΩs) suggest the presence of an insulating state in this region. To explore this possibility, the current is plotted against voltage at the temperatures 2, 5, and 10 K, and low bias, as shown in Figure 7. Indeed, voltage thresholds separating a zero-resistance state (within the noise level of the measurements) and a conductive state at higher voltages are observed. The extracted values of these energy barriers are 82, 63, and 58 meV, for 2, 5, and 10 K, respectively, which are clearly much higher than the thermal energies k B T at these temperatures. Such insulating state in individual SWNTs have been observed by some other groups [50, 51].