Two-step breakdown of a local $\nu =1$ quantum Hall state

We report quantum Hall effect breakdown of a local filling factor $v_{\mathrm{local}}=1$ state formed in a bulk $v_{\mathrm{bulk}}=2$ system in an AlGaAs/GaAs heterostructure. When a finite source-drain bias is applied across the local system, the breakdown occurs in two steps. At low bias, quantized conductance through the $v_{\mathrm{local}}=1$ system breaks down due to interedge electron tunneling. At high bias, the incompressibility of the $v_{\mathrm{local}}=1$ system breaks down because the spin gap closes. The two steps are resolved by combining measurements of resistively detected nuclear magnetic resonance and shot noise, which allows one to evaluate electron spin polarization in the local system and spin-dependent charge transport through the system, respectively.

Figure 1

(a) Local $v_{\mathrm{local}}=1$ QH system formed in a bulk $v_{\mathrm{bulk}}=2$ system. (b) Schematic of experimental setup. Inset: scanning electron micrograph of the device. (c) Pinch-off traces of the split gate measured at several $V_{\mathrm{in}}$ values.

Figure 2

(a) Color plot of $g$ as a function of $V_{\mathrm{g}}$ and $V_{\mathrm{in}}$. (b) $V_{\mathrm{in}}$ dependence of $g$ measured in 20-mV (solid lines: $0\mathrm{V}\le V_{\mathrm{g}}\le -1.1\mathrm{V}$) and 4-mV (dashed lines: $-1.024\mathrm{V}\le V_{\mathrm{g}}\le -1.036\mathrm{V}$) steps of $V_{\mathrm{g}}$. Each trace was measured by sweeping $V_{\mathrm{in}}$ with a slow speed of 0.067 mV/min. (c),(d) Schematics of the interedge tunneling at (c) high and (d) low $V_{\mathrm{g}}$.

Figure 3

(a) $V_{\mathrm{in}}$ dependence of $G$ at $V_{\mathrm{g}}=-0.96\mathrm{V}$. (b) $V_{\mathrm{in}}$ dependence of $\mathrm{\Delta }{S}_2$. Solid and dashed curves are $S_{\mathrm{shot}}$ calculated assuming $F_{\mathrm{c}}=1$ for fully spin-degenerate and spin-resolved transport, respectively. In general cases, $S_{\mathrm{shot}}$ appears in the green area. (c) $V_{\mathrm{in}}$ dependence of $P_n=K/K_{max}$. Error bars indicate fitting errors for the NMR spectra in Fig. 3. (d) Representative NMR spectra. Blue lines are fitted curves.

Figure 4

(a) $V_{\mathrm{in}}$ dependence of ${\alpha }_{\mathrm{shot}}$ and $P_n$. Inset: schematics of the lowest Landau levels in the constriction at low- (left) and high-bias (right) regimes. (b) $V_{\mathrm{g}}$ dependence of $V_{\mathrm{th}1}$ and $V_{\mathrm{th}2}$. (c) $V_{\mathrm{g}}$ dependence of ${\alpha }_{\mathrm{th}}$.

Figure 5

(a) $V_{\mathrm{in}}$ dependence of $T_{\uparrow }, T_{\downarrow }$, and $T_{\uparrow }+T_{\downarrow }$ estimated assuming $P_n=P_{\mathrm{T}}$. (b) $\mathrm{\Delta }{S}_2$ [same data as in Fig. 3] and $S_{\mathrm{shot}}$ curves for $F_{\mathrm{c}}=1$ and $F_{\mathrm{c}}=1/3$ calculated using $T_{\uparrow }$ and $T_{\downarrow }$ in Fig. 5. (c) $V_{\mathrm{in}}$ dependence of $F_{\mathrm{c}}$.