Dominant parameters for the critical tunneling current in bilayer exciton condensates

We will discuss the relevant conditions to observe a critical tunneling current [New J. Phys. 10, 045018 (2008)] in electron double-layer systems at a total filling factor of 1 and find they are related to the effective layer separation and the temperature. Our studies suggest that the intensity of the critical tunneling behavior is also directly linked to the area of the sample.

Figure 1

(Color online) (a) Measured four-terminal voltage $V_{4t}$ (c) and the measured total current $I$ as a function of the applied two-terminal voltage $V_{2t}$ at ${\nu }_{tot}=1\left(d/l_B=1.42\right)$. When the current is plotted over $V_{4t}$, the curve (c) collapses onto subfigure (d). The absolute values of the negative and positive critical currents $\pm I_C$, however, remain unchanged and translate now into the maximal currents around $V_{4t}=0$. Subfigure (b) is a cartoon of the measurement setup with S and D being the source and drain contacts and A and B being the voltage probes. Hall bar sample of $0.88\times 0.08{\text{mm}}^2$ (wafer $\alpha$) at $T<20\text{mK}$.

Figure 2

(Color online) (a) Tunnel characteristics for several total filling factors, i.e., the electron density remains constant while $I/V$ characteristics are measured at several magnetic fields around ${\nu }_{tot}=1$. The eight most inner curves are marked with symbols. (b) Maximal (critical) currents as a function of the total filling factor [data from labeled curves in subfigure (a) are used)]. At exactly ${\nu }_{tot}=1$ the effective layer separation is 1.42. Hall bar sample of $0.88\times 0.08{\text{mm}}^2$ (wafer $\alpha$) and $T_{bath}<20\text{mK}$.

Figure 3

(Color online) (a) Critical current as a function of the effective layer separation $d/l_B$ at fixed temperature and (b) the inverse temperature at fixed effective layer separation. (c) and (d) illustrate some corresponding four-terminal $I/V$ curves to allow comparison.

Figure 4

(a) Critical currents as a function of the circumference $U$ (right-hand side) and the ${\nu }_{tot}=1$ sample area $A$ (left-hand side) for $d/l_B\approx 1.6$ for samples from wafer $\alpha$ and $\beta$. Fitting yields a linear dependence on the area. See text for further discussions. (b) Corresponding four-terminal $I/V$ curves. The sample dimensions are (from largest to smallest): Corbino ring; $d_{outer}=860\mu \text{m}$ and $d_{inner}=270\mu \text{m}$, Hall bar type 1; $0.88\times 0.08{\text{mm}}^2$, and Hall bar type 2; $0.15\times 0.05{\text{mm}}^2$.