Since its temperature dependence is similar to Equation 2 but inv

Importantly, for the pure AL term, regardless of the thickness. Then the total sheet resistance above T c is given by the following equation: (3) The experimental data were fitted excellently using Equations 1 to 3 with R n,res, C, a, R 0, and T c being fitting parameters, as shown in Selleckchem BMS202 Figure 2 (yellow line, S1; green

line, S2). Since Equation 2 is only valid for T>T c , the data of the normal state region (defined as R □>50 Ω) were used for the fitting. All parameters thus determined are listed in Table 1 for the seven samples. We note that the obtained values for R 0 are

all smaller by a factor of 2.4 to 5.4 BI 10773 manufacturer than R 0=65.8 kΩ for the AL term. This indicates that the observed fluctuation-enhanced conductivities originate see more from both AL and MT terms. We also tried to fit the data by explicitly including the theoretical form for the MT term [13], but this resulted in poor fitting convergence. Table 1 Summary of the fitting analysis on the resistive transition of the ( )-In surface Sample R 0 (kΩ) R n,res (Ω) T c (K) b Δ R □/R n,res(%) S1 12.1 293 2.64 1.80 8.0 S2 20.0 171 2.99 1.54 10.8 S3 15.6 146 2.81 1.78 12.6 S4 17.6 108 2.76 1.67 15.3 S5 27.7 394 2.76 1.86 5.0 S6 14.3 160 2.67 1.69 11.5 S7 20.9 124 2.88 1.48 13.7 The determined T c ranges from 2.64 to 2.99 K. This is in reasonable agreement with the previously determined value of T c =2.8 K, but there are noticeable variations among the samples. The normal residual resistance R n,res also shows significant variations, ranging from 108 to 394 Ω. These two quantities, T c and R n,res, could be correlated because a strong impurity electron scattering might cause interference-driven electron localization MRIP and suppress T c [23]. However, they are poorly correlated, as shown in the inset of Figure 2. This is ascribed to possible different impurity scattering mechanisms determining R n,res and T c as explained in the following. Electron scattering should be strong

at the atomic steps because the surface layer of ( )-In is severed there. Therefore, they contribute to most of the observed resistance [8, 24]. However, the interference between scatterings at the atomic steps can be negligibly weak if the average separation between the atomic steps d av is much larger than the phase relaxation length L ϕ . This is likely to be the case because d av≈400 nm for our samples, and L ϕ is several tens of nanometer for typical surfaces [25]. In this case, electron localization and resultant suppression of T c are dominated by other weaker scattering sources within the size of L ϕ , not by the atomic steps that determine R n,res. The exponent a was determined to be 1.48 to 1.85 in accordance with feature (i).

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