Topological defects in the edge-state structure in a bilayer electron system

We experimentally demonstrate formation of pointlike topological defects in the edge-state structure in the quantum Hall effect regime. By using of a selective population technique, we investigate equilibration processes between the edge states in bilayer electron structures with a high tunneling rate between layers. Unexpected flattening of the $I\text{−}V$ curves in a perpendicular magnetic field at a specific filling factor combination and the recovery of the conventional nonlinear $I\text{−}V$ characteristics in tilted fields give a strong evidence for the existence of topological defects.

Figure 1

(a) Schematic diagram of the gate-gap region in the pseudo-Corbino geometry. The shaded area represents the Schottky gate. In a quantizing magnetic field at total filling factor $\nu$, one set of the edge states (the number is equal to the filling factor under the gate, $g$; $g<\nu$) is propagating under the gate along the etched edge of the sample, while the other edge states (their number is $\nu -g$) are going along the gate edge. In the gate-gap region, both sets of the edge states are running in parallel. (b) A quantum well subband diagram at zero gate voltage (solid line) and at smaller electron concentration, near bilayer onset (dashed line), is shown.

Figure 2

Energy subband diagram of the sample edge for the filling factors $\nu =3$ and $g=2$ with no voltage applied between the ES: (a) in the gate-gap region in perpendicular and tilted magnetic fields; (b) under the gate in a single-layer regime (sample $B$) and the resulting ES structure in the gate gap; (c) under the gate in a bilayer regime (sample $A$) and the resulting ES structure in the gate gap. Symbols $t$, $b$, $s$, $\uparrow$, $\downarrow$ indicate the isospin (top, bottom, symmetric) and the spin (up and down) states of the ES. Ohmic contacts, connected to different ES, are denoted by gray bars.

Figure 3

$I\text{−}V$ curves for samples $B$ (a) and $A$ (b) for filling factors $\nu =3$ and $g=2$ at different tilt angles equal to $\theta =0$ (solid line), $\theta =30°$ (dashed line), $\theta =45°$ (dotted line), $\theta =50°$ [dash-dot-dot, only the (a) panel], $\theta =60°$ (dash-dot line). A perpendicular magnetic field is constant and is equal to 6.6 T for the sample $B$ and 5.9 T for the sample $A$. The insets demonstrate $I\text{−}V$ curves for samples $B$ and $A$ at filling factors $\nu =3$ and $g=1$ in a perpendicular magnetic field.