Interaction effects in a one-dimensional constriction

We have investigated the transport properties of one-dimensional (1D) constrictions defined by split-gates in high quality ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures. In addition to the usual quantized conductance plateaus, the equilibrium conductance shows a structure close to ${0.7(2e}^2/h)$, and in consolidating our previous work [K. J. Thomas et al., Phys. Rev. Lett. 77, 135 (1996)] this 0.7 structure has been investigated in a wide range of samples as a function of temperature, carrier density, in-plane magnetic field $B_{\Vert },$ and source-drain voltage $V_{\mathrm{sd}}.$ We show that the 0.7 structure is not due to transmission or resonance effects, nor does it arise from the asymmetry of the heterojunction in the growth direction. All the 1D subbands show Zeeman splitting at high $B_{\Vert },$ and in the wide channel limit the $g$ factor is $|g|\approx 0.4$, close to that of bulk GaAs. As the channel is progressively narrowed we measure an exchange-enhanced $g$ factor. The measurements establish that the 0.7 structure is related to spin, and that electron-electron interactions become important for the last few conducting 1D subbands.