Quasiparticle Tunneling across an Exciton Condensate

The bulk properties of the bilayer quantum Hall state at total filling factor one have been intensively studied in experiment. Correlation induced phenomena such as Josephson-like tunneling and zero Hall resistance have been reported. In contrast, the edge of this bilayer state remains largely unexplored. Here, we address this edge physics by realizing quasiparticle tunneling across a quantum point contact. The tunneling manifests itself as a zero bias peak that grows with decreasing temperature. Its shape agrees quantitatively with the formula for weak quasiparticle tunneling frequently deployed in the fractional quantum Hall regime in single layer systems, consistent with theory. Interestingly, we extract a fractional charge of only a few percent of the free electron charge, which may be a signature of the theoretically predicted leakage between the chiral edge and the bulk mediated by gapless excitations.

Figure 1

(a) Schematic illustration of the quantum Hall bilayer device and the measurement configuration. The upper-left inset sketches the quasiparticle tunneling between two counterpropagating edges of the ${\nu }_{\mathrm{tot}}=1$ state. (b) Hall, longitudinal, and diagonal resistances as a function of magnetic field for the GaAs bilayer in the balanced case measured at the base temperature of the dilution refrigerator. The dotted curve is the calculated average $(R_D+|R_D^{-}|)/2$. (c) Diagonal resistance $R_D$ as a function of dc bias current at different magnetic fields (filling factors are indicated). (d) $\mathrm{\Delta }{R}_D$ (see text) as a function of temperature. The dotted line is a fit to the data points. The inset shows the temperature dependence of the full width at half maximum (FWHM) of the tunneling peak.

Figure 2

(a) Tunnel conductance (solid curve) as a function of dc current for ten different temperatures. Also shown are fit curves (dashed lines) generated with a single set of optimized fit parameters obtained by simultaneously fitting the formula for weak quasiparticle tunneling for all traces and minimizing the total error. The fitted $g$ and $e^{*}$ are 0.30 and $0.036e$. (b) Normalized fit error [48] as a function of $g$ and $e^{*}/e$. The circle marks the best fit point. The contours correspond to relative errors of 1, 1.1, and 1.2, as indicated by the arrows.

Figure 3

Tunnel conductance as a function of bias current at different temperatures and for different degrees of imbalance between the layers. $V_g$ is varied from 0.9 V (top leftmost panel) to 1.25 V (bottom rightmost panel) in 0.05 V steps. The estimated filling factor in the top (${\nu }_t$) and bottom (${\nu }_b$) layer have been included in each panel. The split gate voltage to form the QPC is kept constant at $V_s=0.5\mathrm{V}$ after cycling to $-1.5\mathrm{V}$ at base temperature.

Figure 4

Fitted values of $g$ and $e^{*}/e$ for the ${\nu }_{\mathrm{tot}}=1$ state near the balance point. Data points for $\nu =5/2$ from Refs. [38, 40, 41, 42] and for $\nu =1/3$ from Ref. [37] are also shown. The error bar for one of the $\nu =5/2$ data points stems from a variation of the confinement while fixing $e^{*}/e=1/4$ during fitting [42]. Empty squares for $\nu =5/2$ are extracted by varying the QPC gate voltage [41] at a fixed magnetic field (we avoid taking the points in the accidental resonant situation). Vertical dotted lines at $1/4$ and $1/3$ correspond to the expected ratio of $e^{*}/e$ for the $5/2$ and $1/3$ FQH states, respectively.