Gate-controlled transport in narrow GaAs/AlxGa1−xAs heterostructures

The transport of two-dimensional electrons in the narrow channel, realized by the split gate of a GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterojunction field-effect transistor, is investigated from 4.2 to 1.3 K as a function of the gate voltage $V_g$. Results from Shubnikov–de Haas effect and low-field magnetoresistance measurements show that the channel width W and the electron density $n_s$ decrease linearly with $V_g$ and that the mobility μ decreases with $n_s$ to the power (3/2). The phase-breaking length $l_i$ in the one-dimensional weak-localization regime is studied as a function of $V_g$. We find that the functional dependence of $l_i$ on the channel conductance is in good agreement with theory.