Spin-Incoherent Transport in Quantum Wires

When a quantum wire is weakly confined, a conductance plateau appears at $e^2/h$ with decreasing carrier density in zero magnetic field accompanied by a gradual suppression of the $2e^2/h$ plateau. Applying an in-plane magnetic field $B_{\parallel }$ does not alter the value of this quantization; however, the $e^2/h$ plateau weakens with increasing $B_{\parallel }$ up to 9 T, and then strengthens on further increasing $B_{\parallel }$, which also restores the $2e^2/h$ plateau. Our results are consistent with spin-incoherent transport in a one-dimensional wire.

Figure 1

Differential conductance $G(V_{\mathrm{tg}})$ measured at $T=50\mathrm{mK}$ with fixed $V_{\mathrm{sg}}$, ranging from $-1.7\mathrm{V}$ on the right-hand side to $-0.52\mathrm{V}$ on the left-hand side. A structure evolves at $e^2/h$ on the left-hand side accompanied by the suppression of the $2e^2/h$ degenerate plateau. Moving from right to left sc, ic, and wc mark the strong-, intermediate-, and weak-confinement regimes described in the text. The arrow at the bottom of the figure indicates the onset of a plateau at $e^2/h$, corresponding to the arrow shown in Fig. 2.

Figure 2

Gray-scale plot of transconductance $dG/d{V}_{\mathrm{tg}}$. Gradual suppression of the $2e^2/h$ plateau and strengthening of the $e^2/h$ plateau are marked by a thin light line bridging the two adjacent light lines at the bottom. Inset: Schematic diagram of the device (not to scale) showing the split gates (sg) and top gate (tg) separated by a dielectric layer (PMMA).

Figure 3

Differential conductance $G(V_{\mathrm{tg}})$ in the wc regime at fixed $B_{\parallel }$, incremented from 0 to 16 T in steps of 1 T. The $e^2/h$ plateau initially weakens up to 9 T, but no appreciable change in the quantized value is observed.

Figure 4

Gray-scale plot of $dG/d{V}_{\mathrm{tg}}$ with $B_{\parallel }$. Diverging pairs of light lines for $V_{\mathrm{tg}}>-0.62\mathrm{V}$ indicate Zeeman splitting for subbands $N\ge 2$. The sharp light line on the left-hand side at $V_{\mathrm{tg}}=-0.69\mathrm{V}$ corresponds to spin-incoherent electrons. It appears to be the spin-split branch of $N=1$; however, note that at 9 T, a branch comes out to the right of this line, at which point the transport becomes spin coherent.

Figure 5

(a) $G(V_{\mathrm{sd}})$ showing a zero-bias anomaly peak for $G<e^2/h$ and its suppression above $e^2/h$. (b) $G(V_{\mathrm{sd}})$ measured at fixed $B_{\parallel }$. The ZBA shows no discernible splitting up to $B_{\parallel }=7\mathrm{T}$, beyond which the peak is completely suppressed.

Figure 6

Dependence of the $e^2/h$ plateau on the lattice temperature. There is overall thermal averaging, a 0.7 structure evolves at higher $T$. Inset: Temperature dependence of $G$ at various carrier densities ($V_{\mathrm{tg}}$); the top trace is for the midpoint of the plateau.