Phenomenological model for the 0.7 conductance feature in quantum wires

One-dimensional (1D) quantum wires exhibit a conductance feature near $0.7\times 2e^2∕\mathrm{h}$ in connection with many-body interactions involving the electron spin. With the possibility of exploiting this effect for novel spintronic device applications, efforts have focused on uncovering a complete microscopic theory to explain this conductance anomaly. Here we present conductance calculations based on a simple phenomenological model for a gate-dependent spin gap that are in excellent agreement with experimental data taken on ultra-low-disorder quantum wires. Taken together the phenomenology and experimental data indicate that the 0.7 feature depends strongly on the potential profile of the contact region, where the reservoirs meet the 1D wire. Microscopic explanations that may underpin the phenomenological description are also discussed.

Figure 1

(Color online) Conductance calculations based on the model. In (a) $\gamma =d\Delta E_{\uparrow \downarrow }∕d{V}_S$ is small in comparison to (b). Low temperature is shown in blue $(\Delta E∕kT=80)$ and high temperature in red $(\Delta E∕kT=15)$. Inset to (a) is an AFM image of a QW device showing the 1D and 2D regions. $V_T$ and $V_S$ are the top gate and side gates respectively. Inset to (b) is a schematic of the model showing the Fermi level $E_F$ and the spin gap $\Delta E_{\uparrow \downarrow }$ opening with gate bias, $V_S$.

Figure 2

(Color online) (a) The calculated temperature dependence of the 0.7 feature in the regime of Fig. 1a. The highest temperature trace exhibits a broader tail near pinch-off. (b) Data taken on a point contact device at temperatures $T=0.5–3\mathrm{K}$ (black to red) $n_{2D}=2.1\times {10}^{11}∕{\mathrm{cm}}^2$ (taken from Ref. 5). (c) Calculated conductance for the low temperature case of Fig. 1b (dashed) and data taken on a $l=1\mu \mathrm{m}$ long wire at $T=100\mathrm{mK}$, $n_{2D}=4.6\times {10}^{11}∕{\mathrm{cm}}^2$ (solid). (d) The calculated in-plane magnetic field dependence of the 0.7 feature. $B=0$ (left) to $B=0.1\Delta E$ (right); traces are offset for clarity.

Figure 3

Comparison of data taken on a $l=1\mu \mathrm{m}$ wire with calculations based on the model. (a) Data taken at $T=100\mathrm{mK}$ for $n_{2D}=2-4.6\times {10}^{11}∕{\mathrm{cm}}^2$ right to left. Vs is the voltage applied to both side gates. (b) Calculations for $\Delta E∕kT=54$, with $\gamma$ increasing (arb. units) right to left. Due to the electrostatics of the devices the experimental data shifts in $V_S$ with increasing $n_{2D}$ and in-turn the calculated traces have also been offset to aid in comparison with the data.

Figure 4

Comparison of data taken on a $l=0.5\mu \mathrm{m}$ wire (right) with calculations based on the model (inset). In the experiment $n_{2D}$ is fixed at $\sim 5\times {10}^{11}∕{\mathrm{cm}}^2$ and $V_{S2}$ is swept negative, reducing the conductance (see inset diagram for gate configuration). Traces from left to right correspond to $V_{S2}$ sweeps, as $V_{S1}$ is stepped more negative. For calculations (inset) $\gamma$ is increased in linear steps from left to right with $\Delta E∕kT=54$ (traces offset).

Figure 5

(Color online) (a) $di∕dv$ data taken on a $l=0.5\mu \mathrm{m}$ QW at $T=100\mathrm{mK}$. Each trace is for a different side gate bias, $V_S$. (b) Calculations based on the phenomenological model. $di∕dv$ is plotted as a function of the difference in S-D potential in units of the sub-band spacing $\Delta E$. (c) Schematic showing how the positions of S and D relate to the observed conductance features.