Probing Composite Fermions with a Wigner Crystal and Vice-Versa
نویسندگان
چکیده
Two-dimensional electron gases in high magnetic fields have proven to be a remarkably rich playground for the study of strongly-correlated quantum many-body systems. In two dimensions with a strong magnetic field, the cyclotron motion of the electrons completely quenches the particle kinetic energy into Landau levels which are macroscopically degenerate–the number of states in a Landau level is equal to the number of flux quanta from the external field that penetrate the sample. This degeneracy is lifted solely by Coulomb interactions (and by weak disorder) making the system automatically strongly correlated. Remarkably, there is a huge zoo of correlated states that occur at different rational values of the fractional filling of the (highest occupied) Landau level. For simple filling fractions like 1/3 and 2/5, the Laughlin liquid states are most stable. For very small filling fractions the potential energy is minimized by placing the electrons into a spatially ordered Wigner crystal. Near filling factor 1/2, it is useful to view the system as consisting of ‘composite fermions’ (CFs are electrons or holes with two quantized flux tubes or vortices attached [1, 2, 3]). At the mean-field level, the flux attachment transformation creates a pseudo magnetic field which cancels the physical magnetic field when the filling factor is precisely one-half. Slightly away from filling factor 1/2, the composite fermions behave as if they are in a weak magnetic field and hence move in cyclotron orbits with relatively large radius (on the micron scale, which is large compared to the mean distance between particles). The dynamics on this new characteristic length scale can be probed with surface acoustic waves [4], but it is challenging to launch phonons with wavelengths on this scale and to continuously vary that wavelength. In a remarkable experiment, Jo et al. use a double quantum well to form a quantum Hall bilayer system (for holes). By means of an intrinsic doping asymmetry in the sample and application of a tunable voltage gradient normal to the plane of the bilayer, they can bias one layer to have low filling factor and the other to have filling factor near 1/2. The holes in the low filling-factor layer form a triangular Wigner crystal which induces a spatially periodic potential on the composite fermions in the other layer. Because of their larger mass
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