Metallic and insulating states at a bent quantum Hall junction

A nonplanar geometry for the quantum Hall (QH) effect is studied, whereby two quantum Hall systems are joined at a sharp right angle. When both facets are at equal filling factor $\nu$ the junction hosts a channel with nonquantized conductance, dependent on $\nu$. The state is metallic at $\nu =1∕3$, with conductance along the junction increasing as the temperature $T$ drops. At $\nu =1,2$ it is strongly insulating, and at $\nu =3,4$ shows only weak $T$ dependence. Upon applying a dc voltage bias along the junction, the differential conductance again shows three different behaviors. Hartree calculations of the dispersion at the junction illustrate possible explanations, and differences from planar QH structures are highlighted.

Figure 1

(Color) (a) Schematic of the bent quantum well subjected to a quantizing $B$ field. The electrons in the facets (blue and red) and corner accumulation wire (green) are colored according to their dispersions in (c). (b) Scanning electron micrograph of a diagnostic structure with $\mathrm{AlAs}$ (dark) and $\mathrm{GaAs}$ (light) bands. The corner curvature $R$ is sharper than the $10\mathrm{nm}$ resolution limit.[16] (c) Hartree calculations of the dispersion at a sharp corner (black) from Eq. (1), overlaid with left- (blue) and right-facing (red) sharp QH edge dispersions and an accumulation wire dispersion (green). Vertical dotted lines represent the effective hard walls seen by the edge states.

Figure 2

(Color) Sample A. Longitudinal resistance $R_{xx}$ within each facet (gray), and cross-corner voltages $V_{\mathrm{cc}}$ (red) and $V_{\mathrm{cc}}^{\prime }$ (green). Nonzero $V_{\mathrm{cc}}$ minima indicate finite conduction along the junction. Inset: schematic of edge states and backscattering of current along the junction.

Figure 3

(Color) Bent QH junction conductance $G$ vs $\nu$. (a) (Sample A) Landau index $m$ and spin quantum number $\sigma$ are indicated above each integer $\nu$ revealing a pairwise similarity. Circled $\nu$ are measured as a function of temperature and voltage in Figs. 4a, 4b. (b) (Sample B) Length dependence of the bent QH junction conductance $G$. The $L_1=4.2\mathrm{mm}$ corner junction was first characterized (red and green, dotted lines), and then scribed to a length $L_2=0.45\mathrm{mm}$ and remeasured (red and green, solid lines). Note: for the longer $L_1$ length conductance to be at all measurable, elevated temperatures were required for $\nu =3,4$.

Figure 4

(Color) Sample A. (a) Temperature dependence of the bent QH junction conductance $G$ vs $T$ at the $\nu$ circled in Fig. 3. $\nu =1,2$ are strongly insulating; $\nu =3,4$ weakly insulating; and the fractional $\nu =1∕3$ metallic. (b) The dc voltage dependence $V_s$ of the differential conductance $dI∕dV$ for the same $\nu$. For $\nu =1∕3$ four temperatures are shown, whose peak values at $V_s=0$ correspond to the black squares in (a). Power laws $T^{-0.4}$ and $V^{-0.4}$ plotted for comparison (dotted line).