Zero-bias anomaly in quantum wires

We use quantum wires fabricated on undoped GaAs/AlGaAs heterostructures in which the average impurity separation is greater than the device size to compare the behavior of the zero-bias anomaly against predictions from Kondo and spin-polarization models. Both theories display shortcomings, the most dramatic of which is the linear electron-density dependence of the zero-bias anomaly spin splitting at fixed magnetic field $B$ and the suppression of the Zeeman effect at pinch off.

Figure 1

(a) Measured (spheres) and calculated (dashed line) $\mu -n_{2\text{D}}$ relation for T622. For comparison, we simulate an otherwise identical 2DEG with a $\delta$-doped layer 80 nm above. (b) $G$ vs $V_{\text{sd}}$ incrementing $V_{\text{gate}}$ (in steps of 0.3 mV) of a quantum wire in an undoped heterostructure $\left(T=60\text{mK}\right)$. A ZBA can be observed in the riser of the $2e^2/h$ plateau.

Figure 2

(Color online) (a) $G$ vs $V_{\text{sd}}$ incrementing $V_{\text{gate}}$ for eight quantum wires, labeled (i)–(viii). (b) For a wide range of $G$ (on a log scale), the ZBA occurs far beyond the ballistic regime $\left(T\approx 150\text{mK}\right)$. (c) $T$ dependence of the 0.7 structure at $V_{\text{sd}}=0$. (d) $\Delta h_{\text{ZBA}}$ (defined in main text) for various $T$. A local minimum appears as $T$ increases.

Figure 3

(Color online) $G$ vs $V_{\text{sd}}$ incrementing $V_{\text{gate}}$ $\left(T\approx 150\text{mK}\right)$ for: (a) $V_{\text{top}}=+4\text{V}$ $\left(n_{2\text{D}}=0.8\times {10}^{11}{\text{cm}}^{-2}\right)$ and (b) $V_{\text{top}}=+7\text{V}$ $\left(n_{2\text{D}}=1.6\times {10}^{11}{\text{cm}}^{-2}\right)$. (c) $\Delta h_{\text{ZBA}}$ for $V_{\text{top}}=4–7\text{V}$. (d) Sketch showing $\text{FWHM}\propto \text{max}\left[T,T_K\right]$ as $T$ increases. (e) FWHM of the ZBA for $T=60\text{mK}$ and 250 mK. (f) FWHM for $V_{\text{top}}=4–7\text{V}$ from the data set in panel (c).

Figure 4

(Color online) $G$ vs $V_{\text{sd}}$ incrementing $V_{\text{gate}}$ $\left(T=60\text{mK}\right)$ for: (a) $B=0\text{T}$, (b) $B=1\text{T}$, and (c) $B=2\text{T}$. (d) Sketch of the expected splitting of the ZBA at constant $B$ and $T$ for the singlet Kondo effect as $T_K$ alone is decreased from top to bottom (traces offset vertically). (e) Enlarged view of the ZBA being barely spin split near pinch off for device (vii). (f) Zeeman splitting of the ZBA as a function of $B$ for the red (●) and green (◇) traces in panels (a)–(c). The black solid line shows the expected peak splitting $g{\mu }_B/e=25\mu \text{V}/\text{T}$ (for $\left|g\right|=0.44$). The blue squares (◼) are extracted from the same family of traces as shown in panel (e). (g) Color scale of the data from panel (c). The white “×” symbols mark the location of the spin-split ZBA peaks.

Figure 5

(Color online) At $T\approx 150\text{mK}$, a clean, “classic” 0.7 structure (a) can be distinguished from disorder effects (b) by laterally shifting the conducting 1D channel by differentially biasing the left and right gates by $\Delta V_g=V_{\text{left}}-V_{\text{right}}$ (traces offset laterally). Blue $(\ast )$ traces in both panels correspond to $\Delta V_g=0$, and the leftmost (rightmost) trace to $\Delta V_g=+1.2\text{V}$ $\left(-1.2\text{V}\right)$. (c) $G$ vs $V_{\text{sd}}$ incrementing $V_{\text{gate}}$ corresponding to the red, blue, and green traces from panel (b). The apparent splitting at high $G$ is related to disorder.