Superballistic electron flow through a point contact in a Ga[Al]As heterostructure

We measure electronic transport through point contacts in a high-mobility electron gas in a Ga[Al]As heterostructure at different temperatures and bulk electron densities. The conductance through all point contacts increases with increasing temperature in a temperature window around $T\sim 10\mathrm{K}$ for all investigated electron densities and point contact widths. For high electron densities this conductance exceeds the fundamental ballistic limit (Sharvin limit). These observations are in agreement with a viscous electron transport model and previous experiments in graphene.

Figure 1

(a) Bulk conductance of the sample (all top gates are grounded) as a function of temperature for electron densities from $1.5\times {10}^{11}$ to $2.7\times {10}^{11}{\mathrm{cm}}^{-2}$ changed in steps of $0.3\times {10}^{11}{\mathrm{cm}}^{-2}$. (b) Bulk mobility of the 2DEG. (c) Conductance $G$ of the narrowest PC ($d=0.75\mu \mathrm{m}$) and (d) conductance of the widest PC ($d=2.5\mu \mathrm{m}$) as a function of temperature; horizontal lines show the calculated Sharvin limit of PC conductance for the lithographic (dashed lines) and effective electronic (dotted lines) widths at the highest and lowest displayed charge densities, see color code.

Figure 2

Extraction of channel conductance and electron-electron scattering length from experimentally measured conductance and model simulations, all for the highest electron density $2.7\times {10}^{11}{\mathrm{cm}}^{-2}$. (a) and (b) Measured PC conductance as a function of temperature (thick black line) and the sum of ballistic $G_{\mathrm{Sh}}$ and viscous $G_{\mathrm{vis}}$ contributions (thin colored lines; subtracted diffusive contribution $G_{2\mathrm{DEG}}$ calculated numerically). Different colors correspond to different radii of the excluded circle of 2DEG $R$ around the PC in the model. (c) Estimate of $l_{\mathrm{ee}}$ for different $R$ and $d$. Effective width of the PCs calculated numerically. (d) Estimate of $l_{\mathrm{ee}}$ for different $R$ and $d$. Effective width of the PCs calculated as a low temperature limit of the experimental data.