Competing correlated phases in orbitally mixed half-filled Landau levels

An astounding array of correlated phases have been experimentally realized in high quality two-dimensional electron systems (2DES). By exploiting the quantizing effects of a magnetic field, these systems form an ideal platform for studying the competition between compressible, incompressible and nematic liquids owing to a tunable Landau level index (N) which influences the nature of the ground state. Here, I will present data taken on state-of-the-art MgZnO/ZnO heterostructures that offer the ability to tune N while remaining at a constant Landau level filling. By rotating the sample within a magnetic field, it is possible to selectively decouple the Zeeman and cyclotron energy terms and induce a level crossing between opposing spin branches of the neighboring N=1 and 0 levels. In contrast to the naive expectation of a first-order spin flop transition, an unexpectedly complex cascade of phases is resolved as we incrementally shift the spin and orbital polarization of carriers between levels while remaining at ν=5/2 filling. Transport signatures associated with two instances of incompressibility are observed, in addition to two compressible phases and an unanticipated anisotropic phase which breaks rotational symmetry. Our experiments indicate that the depolarization process is gradual and complex. In addition to level polarized states, the unexpected incompressible and anisotropic phases observed in the orbitally mixed regime open questions concerning the possibility of novel interlevel coherence occurring at fractional fillings in systems with strongly mixed levels.