# Synopsis: A superfluid of excitons

Researchers explore how the excitonic condensate phase in a bilayer electron gas depends on the relative electron densities of the two layers.

When a magnetic field is applied to a bilayer two-dimensional electron system with sufficiently close spacing, a collective phase emerges if the total electron density is equal to the degeneracy, $e\phantom{\rule{0}{0ex}}B/h$, of a single Landau level (or, equivalently, a “filling factor” of 1/2 per layer). The system shows spontaneous phase coherence that extends across the layers even when the electron tunneling between the layers is weak. This state can be described as a Bose-Einstein condensate of interlayer electron-hole pairs or an excitonic superfluid.

A signature of this condensate is that it takes zero energy for electrons to conduct from one layer to the next. Moreover, when current flows in opposite directions in the two layers the resistance of each layer goes to zero.

Writing in Physical Review B, Alex Champagne and colleagues at the California Institute of Technology, in collaboration with Bell Laboratories, show that an interlayer Bose-Einstein condensate is realized even when the densities of each layer are not the same. The filling factor imbalance can be as high as $\mathrm{\Delta }\phantom{\rule{0}{0ex}}\nu =\nu 1-\nu 2=1/2$, corresponding to a filling factor of 3/4 and 1/4 for each layer. The authors also report the first observation of a direct phase transition from a coherent excitonic phase at $\mathrm{\Delta }\phantom{\rule{0}{0ex}}\nu =1/3$ to a pair of single-layer fractional quantum Hall states at $\nu =2/3,1/3$ as a function of layer spacing. – Sarma Kancharla

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