Activated Transport in the Separate Layers that Form the ${\nu }_T=1$ Exciton Condensate

We observe the total filling factor ${\nu }_T=1$ quantum Hall state in a bilayer two-dimensional electron system with virtually no tunneling. We find thermally activated transport in the balanced system with a monotonic increase of the activation energy with decreasing $d/{\ell }_B$ below 1.65. In the imbalanced system we find activated transport in each of the layers separately, yet the activation energies show a striking asymmetry around the balance point, implying a different excitation spectrum for the separate layers forming the condensed state.

Figure 1

(top) ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{e},xx}$ and ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{g},xx}$ and (bottom) ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{e},xy}$ and ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{g},xy}$ vs magnetic field at 50 mK and matched densities ($n_U=n_L=2.22\times {10}^{14}{\mathrm{m}}^{-2}$ corresponding to $d/{\ell }_B=1.57$). At ${\nu }_T=1$ both longitudinal components tend to zero, while both Hall components tend to $h/e^2$. The inset plots the counterflow experiment; ${\rho }_{xx}$ and ${\rho }_{xy}$ both tend to zero.

Figure 2

Activation energies of the ${\nu }_T=1$ state obtained from ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{e},xx}$ with balanced layer densities for various $d/{\ell }_B$. The inset shows Arrhenius plots of some of the data with corresponding symbols in the main panel; lines are fits to ${\rho }_{xx}\propto \exp (-{\Delta }_{\nu =1}/k_{B}T)$.

Figure 3

Arrhenius plot of the lower layer ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{e},xx}$ for five different imbalances $(\equiv [n_L-n_U]/n_T)$ indicated in the right of the figure. The inset plots the lower layer ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{e},xx}$ at 50 mK vs magnetic field for these five imbalances. The total electron density is fixed at $4.44\times {10}^{14}{\mathrm{m}}^{-2}$, corresponding to $d/{\ell }_B=1.57$.

Figure 4

Activation energies of the ${\nu }_T=1$ state vs density imbalance. (□) and ($\blacksquare$) correspond to the activation energy determined from the longitudinal resistance in the lower and upper layer, respectively. ($▴$) denotes the activation energy obtained from the longitudinal drag.