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These temperatures have been chosen so that one can extract the residual resistance Rres in Hall bars [i.e., minimize Re-ph (T) as well as RAA (T)] [see Eq. in Sec.]
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It is also possible to obtain a diffusion coefficient from quasi-1D wires which is 1.5 times larger than that from Hall bars. Plotting the data as a function of D from the wires rather than the 2D Hall bars would simply shift all the data by a fixed value. This does not change the D dependence as well as the interpretation of the data at all. Nevertheless, we have chosen to plot all the data as a function of D from the 2D Hall bars because it is difficult to obtain, for example, ne and le only from the wires. In order to define the regime (semiballistic or diffusive), it is necessary to know le. Therefore, we have determined D from the Hall bars.
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It is also possible to obtain a diffusion coefficient from quasi-1D wires which is 1.5 times larger than that from Hall bars. Plotting the data as a function of D from the wires rather than the 2D Hall bars would simply shift all the data by a fixed value. This does not change the D dependence as well as the interpretation of the data at all. Nevertheless, we have chosen to plot all the data as a function of D from the 2D Hall bars because it is difficult to obtain, for example, n e and l e only from the wires. In order to define the regime (semiballistic or diffusive), it is necessary to know l e. Therefore, we have determined D from the Hall bars.
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The residual resistance R res defined here is for 20 wires in parallel. The resistance per 1 wire is 20 times larger. When R res > 8 k Ω, the resistance exponentially increases with decreasing temperature, which indicates that the electron system enters the strongly localized regime as detailed in Sec..
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The residual resistance R res defined here is for 20 wires in parallel. The resistance per 1 wire is 20 times larger. When R res > 8 k Ω, the resistance exponentially increases with decreasing temperature, which indicates that the electron system enters the strongly localized regime as detailed in Sec..
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In metallic wires, the three-dimensional formula of the GZ theory is applied since all geometric dimensions ( L, w, and film thickness t) are larger than le.
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It is difficult to distinguish clearly between the variable range hopping model and the self-consistent theory from our results. The same analyses for the conductivity in the strongly localized regime have been performed by Minkov (Ref.). But they could not identify a reliable mechanism of the conductivity, either.
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It is difficult to distinguish clearly between the variable range hopping model and the self-consistent theory from our results. The same analyses for the conductivity in the strongly localized regime have been performed by Minkov (Ref.). But they could not identify a reliable mechanism of the conductivity, either.
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Note that Eq. is valid only in the weakly localized regime and should not be applicable in the strongly localized regime.
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Note that Eq. is valid only in the weakly localized regime and should not be applicable in the strongly localized regime.
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Although L for weff =1130nm wide wire is smaller than weff above T=100mK, the WL curves can still be fitted well by the 1D WL theory, Eq. , over the whole temperature range
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Although L for w eff = 1130 nm wide wire is smaller than w eff above T = 100 mK, the WL curves can still be fitted well by the 1D WL theory, Eq., over the whole temperature range.
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In Figs. , we have already corrected the electron temperature below 60 mK by using the AA law for another diffusive wire or Hall bar at the same diffusion coefficient D
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In Figs., we have already corrected the electron temperature below 60 mK by using the AA law for another diffusive wire or Hall bar at the same diffusion coefficient D.
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