The exciton condensate state in electronic bilayers



The 2d electron gases in the quantum-Hall-effect state may harbor a BCS condensate of excitons. The BCS state is well-known from superconductors, atomic gases and liquid 3He at extremely low temperatures. Electrons or atoms interact with each other and form Cooper pairs which condense into a quantum state with macroscopic coherence. In the case of the quantum-Hall effect systems one finds a BCS condensation of of excitons which consist of a filled and an vacant electron state. These excitons are not excited by the absorption of light. Instead one uses half filled Landau levels in 2 dimensional electron gases to host the charges of which the excitons consist.

Landau levels of a 2 dimensional electron system form if it is exposed to a magnetic field of sufficient strength. If the Landau level is half full then it can be considered to consist of an equal number of  electrons and holes. To achieve the BCS state one must use two adjacent layers of 2 dimensional electron gases with a relative distance of about 20 nm. Under this condition the formation of excitons composed of the opposite charges from the two layers is possible.

At temperatures below about 300 mK one observes the condensation into a BCS-like state. The condensed phase shows the nearly dissipationless transport of the ground state excitons and the Josephson effect. The requirement to observe these properties is the  MBE-growth of extremely high purity III-V materials and the ability to electrically contact the two layers separately. 

Molecular beam epitaxy (MBE) of III-V heterostructures

Two MBE systems for growing heterostructures of the  GaAs/AlGaAs system were operated by this research group. The wafers are used for magneto-transport measurements by researchers within and also outside the institute. Much effort is put into the development of the highest possible mobility. In our systems we achieved mobilities close to 20 million cm²/Vs. These activities are now continued in cooperation with Prof. W. Wegscheider at the ETH Zürich.

Surface acoustic waves

The damping and the dispersion of surface acoustic waves is an alternative way to measure the conductance of a two-dimensional charge gas. In contrast to the more conventional voltage probes at the sides of sample, the surface acoustic waves is sensitive to the average over the bulk of the sample. The difference became significant at the fractional quantum Hall effect at 2/3 filling where a spin transition leads to a significant resistance maximum. This maximum vanished with the surface acoustic waves. This is most likely caused by the domain structure at the spin transition where domain boundaries cause a significant voltage drop in the conventional experiments but contribute little to the acoustic attenuation because the domain areas are much larger than the boundaries between them.  In contrast, acoustic measurements of the excitonic condensate state showed no differences between the conventional and the acoustic results meaning that this is a homogeneous state.

Decorating „Hot Spots“ at the integer quantum Hall effect

In the quantum Hall effect regime, the longitudinal resistance tends to vanish while the Hall resistance shows quantized values. This means that inside the sample the lines of constant electric potential must run parallel to the edges of the sample. However, to match the potential landscape at the contacts where the potential lines run perpendicular to the current, one has to invoke “hot spots” in one corner of each contact. In these hot spots nearly all dissipation of the quantum-Hall effect takes place.

Using the fountain effect of superfluid helium, we managed to visualize the hot spots.  This effect leads to an easily visible drop in the helium film covering the sample at the hot spots. The animation shows the effect of turning the current on (drops visible) and off (no drops can be seen).