Interaction Effects at Crossings of Spin-Polarized One-Dimensional Subbands

We report conductance measurements of ballistic one-dimensional (1D) wires defined in GaAs/AlGaAs heterostructures in an in-plane magnetic field, $B$. When the Zeeman energy is equal to the 1D subband energy spacing, the spin-split subband $N\uparrow$ intersects $(N+1)\downarrow$, where $N$ is the index of the spin-degenerate 1D subband. At the crossing of $N=1\uparrow$ and $N=2\downarrow$ subbands, there is a spontaneous splitting giving rise to an additional conductance structure evolving from the $1.5(2e^2/h)$ plateau. With further increase in $B$, the structure develops into a plateau and lowers to $2e^2/h$. With increasing temperature and magnetic field the structure shows characteristics of the 0.7 structure. Our results suggest that at low densities a spontaneous spin splitting occurs whenever two 1D subbands of opposite spins cross.

Figure 1

Differential conductance, $G(V_g)$, traces at $B_{\parallel }$ incremented in steps of 0.6 T. For clarity, successive traces are offset horizontally. Inset: Schematic energy diagram for a linear Zeeman splitting of 1D subbands and subsequent crossings.

Figure 2

(a) Gray-scale plot of transconductance, $dG/d{V}_g$, as a function of $V_g$ and $B_{\parallel }$ for sample B. (b) $G(V_g)$ traces (offset horizontally) for $B_{\parallel }=10\mathrm{T}$ to $13\mathrm{T}$ incremented by $0.2\mathrm{T}$ (sample B, different cooldown). (c) gray-scale plot as in (a), for sample A. (d) $G(V_g)$ traces as in (b), for sample A.

Figure 3

(a) Gray-scale plot of $dG/d{V}_g$ as a function of $V_g$ and $B_{\parallel }$ for sample B, showing the splitting of five 1D subbands. (b) Calculated Zeeman splitting with diamagnetic shift of the 1D subbands. The solid lines represent parallel spin and the dotted lines represent antiparallel spin.

Figure 4

Temperature dependence of $G(V_g)$ for sample B [same cooldown as Fig. 2b] at 10 and 13 T. Inset: The height of the 0.7 analog as a function of $B_{\parallel }$ for various temperatures.