Spin splitting of one-dimensional subbands in high quality quantum wires at zero magnetic field

We have studied the transport properties of a high quality one-dimensional constriction formed in an undoped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructure and therefore largely free of the random potential of ionized donors. We induce an electron gas electrostatically and are able to vary the sheet carrier density ${(n}_{2\mathrm{D}})$ by a factor of at least seven. The constriction shows resonance-free integer conductance plateaus and the additional “0.7 structure,” a plateaulike feature, the conductance of which decreases from about 0.80 towards $0.5\times {2e}^2/h$ at low and high $n_{2\mathrm{D}}.$ This low value is unaffected by a high in-plane magnetic field, supporting previous evidence and theories that the breaking of the spin degeneracy at high fields persists in some form, even at zero field. The height of the feature generally seen at a conductance of about $0.85\times {2e}^2/h$ at high dc bias also varies, and we show that this is in reasonable agreement with a simple relation linking the conductances of the two features. We use a source-drain bias to study the spin splitting of the lowest one-dimensional subbands, and find a spin gap that is independent of $n_{2\mathrm{D}}$ for the first subband. We discuss possible reasons for the splitting, and show how various models for the 0.7 structure can be applied in the finite bias regime.