The effect of split gate dimensions on the electrostatic potential and 0.7 anomaly within one-dimensional quantum wires on a modulation doped GaAs/AlGaAs heterostructure

We use a multiplexing scheme to measure the conductance properties of 95 split gates of 7 different gate dimensions fabricated on a GaAs/AlGaAs chip, in a single cool down [1]. The number of devices for which conductance is accurately quantized reduces as the gate length increases. However, even the devices for which conductance is accurately quantized in units of $2e^2/h$ show no correlation between the length of electrostatic potential barrier in the channel and the gate length, using a saddle point model to estimate the barrier length. Further, the strength of coupling between the gates and the 1D channel does not increase with gate length beyond 0.7 $\mu$m. The background electrostatic profile appears as significant as the gate dimension in determining device behavior. We find a clear correlation between the curvature of the electrostatic barrier along the channel and the strength of the ``0.7 anomaly'' which identifies the electrostatic length of the channel as the principal factor governing the conductance of the 0.7 anomaly. \newline $^{*}$ Present address: Wisconsin Institute for Quantum Information, University of Wisconsin-Madison, Madison, WI. \newline [1] L. W. Smith \emph{et al.}, arXiv:1508.03085