Quantum Hall Exciton Condensation at Full Spin Polarization

Using Coulomb drag as a probe, we explore the excitonic phase transition in quantum Hall bilayers at ${\nu }_T=1$ as a function of Zeeman energy $E_Z$. The critical layer separation $(d/\ell {)}_c$ for exciton condensation initially increases rapidly with $E_Z$, but then reaches a maximum and begins a gentle decline. At high $E_Z$, where both the excitonic phase at small $d/\ell$ and the compressible phase at large $d/\ell$ are fully spin polarized, we find that the width of the transition, as a function of $d/\ell$, is much larger than at small $E_Z$ and persists in the limit of zero temperature. We discuss these results in the context of two models in which the system contains a mixture of the two fluids.

Figure 1

Hall and longitudinal Coulomb drag at ${\nu }_T=1$ vs $d/\ell$ at $T=30\mathrm{mK}$. Dots, $\theta =0$; triangles, $\theta =66°$. Solid curves in (b) are Gaussian fits.

Figure 2

Longitudinal drag $R_{xx,D}$ vs $d/\ell$ and $\eta =E_Z/(e^2/ϵ\ell )$ at ${\nu }_T=1$ and $T=50\mathrm{mK}$. Color scale: purple, $R_{xx,D}=0$; red, $R_{xx,D}=2\mathrm{k}\Omega$. Solid dots: phase boundary, $(d/\ell {)}_c$ vs $\eta$. Dashed line: approximate location of knee in drag contours. Left and right boundaries of colored region: $\theta =0$ and $\theta =66°$ trajectories, respectively.

Figure 3

(a) Width, $\Delta (d/\ell )$, of the longitudinal drag peak at ${\nu }_T=1$ and $T=50\mathrm{mK}$ versus normalized Zeeman energy $\eta$ at the peak center. (b) Temperature dependence of $\Delta (d/\ell )$ at $\theta =0$ (blue squares) and $\theta =66°$ (red triangles).