Dephasing time and one-dimensional localization of two-dimensional electrons inGaAs/AlxGa1−xAsheterostructures

Low-field magnetoresistance measurements are made on the two-dimensional (2D) electron gas in $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures to study the size effects on weak localization and the phase-breaking rate ($\frac{1}{{\tau }_{\phi }}$) as a function of sample width ($W$) and potential probe spacing ($L$). When $L$ and $W$ are larger than $\pi l_{\phi }$ and $\pi L_T$, where $l_{\phi }$ is the phase-breaking length and $L_T$ is the thermal diffusion length, $\frac{1}{{\tau }_{\phi }}$, deduced from experiment using the 2D localization theory, has some agreement with the theoretical 2D phase-breaking rate due to electromagnetic fluctuations and disagrees with the energy relaxation rate. When $W<\mathrm{}\pi l_{\phi }$ and $\pi L_T$, both the localization effect and the determined $\frac{1}{{\tau }_{\phi }}$ are one dimensional. When $L$ is small and comparable to $l_{\phi }$ a new dimensional crossover for localization is observed. In such small samples, we also observe the predicted conductance fluctuations of order $\frac{e^2}{h}$.