Interplay between coherent and incoherent transport in quantum Hall bilayers

We systematically study the coherent transport (Josephson tunneling and counterflow current) and its breakdown which leads to incoherent charge flow in the excitonic BCS condensate formed in GaAs bilayers at ${\nu }_{\mathrm{tot}}=1/2+1/2$. The Josephson currents in samples with three different interlayer distances vary by four orders of magnitude. In contrast, the breakdown thresholds for the ${\nu }_{\mathrm{tot}}=1$ quantum Hall state are comparable. Furthermore, Coulomb drag in a Corbino ring reveals that the coherent counterflow current coexists with the dissipative charge transport.

Figure 1

Interlayer $I\text{−}V$ characteristics at ${\nu }_{\mathrm{tot}}=1$ obtained from three bilayers with comparable sample sizes but different barrier thicknesses showing their effect of the Josephson currents which are signalled by the steep current increases terminated by critical values near zero voltage.

Figure 2

(a)–(c) Three measurement configurations on a bilayer with a Hall bar geometry and the corresponding line styles of the data: (a) interlayer tunneling experiment: dash-dotted; (b) intralayer study on the top (bottom) layer: solid (dotted); (c) intralayer study on both layers: dashed. (d) $I\text{−}V$ characteristics of the sample with $b=8$ nm at ${\nu }_{\mathrm{tot}}=1$ measured using the respective configurations on the top. (e) Intralayer transport studies at ${\nu }_{\mathrm{tot}}=1$ on samples with 10 and 12 nm barriers. For comparison, the interlayer $I\text{−}V$ characteristic obtained from the sample with $b=10$ nm is shown (circles).

Figure 3

(a) Intralayer $I\text{−}V$ characteristics at ${\nu }_{\mathrm{tot}}=1$ on Corbino samples with $b=8$ and 10 nm. Curves are obtained when contacting only the top layer. The dashed curve is measured when the Corbino sample with $b=8$ nm is rotated by 75 degrees while keeping the perpendicular $B$ field fixed. (b) $I\text{−}V$ characteristics obtained with the Coulomb drag configuration (top inset). Current directions are defined by the arrows. Under a tilt angle of 75 degrees, the ${\nu }_{\mathrm{tot}}=1$ state is found at a total $B$ field of 9.5 T. Inset in the middle compares the drive and drag voltages recorded simultaneously.

Figure 4

(a) Normalized critical current as a function of ${\Delta }_{\text{SAS}}$. Filled data points are obtained from the curves shown in Figs. 1–1. For each ${\Delta }_{\text{SAS}}$ value, results for several $d/l_B$ ratios are plotted. From top to bottom: $d/l_B=1.46,1.48,1.62$ for $b=12$ nm; $d/l_B=1.42,1.56,1.65$ for $b=10$ nm; $d/l_B=1.39,1.68$ for $b=8$ nm (from two wafers). The dashed line shows the trend: $I\propto {\Delta }_{\text{SAS}}^2$. The left inset gives a sketch of the conduction band profile. The single particle tunneling amplitude ${\Delta }_{\text{SAS}}$ is defined as the energy spacing between the lowest symmetric and antisymmetric subbands. The right inset shows the dependence of the evaluated ${\Delta }_{\text{SAS}}$ on the interlayer distance $d$. The solid line is a linear fit. (b) Critical Hall electric fields for the ${\nu }_{\mathrm{tot}}=1$ quantum Hall state.