Striped Quantum Hall Phases

While a large number of fractional quantized Hall states have been discovered in the lowest Landau level, such states become increasingly rare in higher Landau levels. Few quantized Hall states have been observed in the first Landau level (Landau level filling factor 2 ≤ ν < 4) and no such states have so far been found for filling factors ν ≥ 4. Correspondingly, the role of electron-electron interactions in this filling factor range has long remained almost uncharted territory. This is now rapidly changing, following recent experiments by Lilly et al. and by Du et al. on extremely clean two-dimensional electron systems (2DES) for Landau level (LL) filling factor ν > 4. The central observation is that the resistivity becomes strongly anisotropic close to half filling of the topmost Landau level in this filling factor range. This is believed to be a signature of a novel Coulomb-induced charge density wave ground state whose existence had been predicted by Fogler et al. and by Moessner and Chalker. Unlike the Laughlin states, these states can be partially understood within the Hartree-Fock (HF) approximation. In fact, it was already suggested at the end of the ’70s by Fukuyama et al. that the HF ground state of the lowest Landau level is a charge density wave (CDW). While in the lowest Landau level, the CDW ultimately turned out to be preempted by the Laughlin states, it seems to be more favorable in higher Landau levels. Different ground states have been predicted depending on filling factor. Near half filling of higher Landau levels (ν ≃ N + 1/2), the HF ground state should be a unidirectional charge density wave (UCDW). In this state, the filling factor alternates between stripes of filling factor N and N + 1. The period of the density modulation is of the order of the cyclotron radius Rc. Further away from half filling one expects a so-called bubble phase, in which clusters of the minority filling factor (N or N +1) order on a triangular lattice with characteristic length Rc. Very close to integer filling factors, a Wigner crystal phase should form. The strongly anisotropic transport properties near half filling of higher Landau levels are believed to be associated with the unidirectional charge density wave phase. In this paper we briefly review some of the recent work on these states. The experimental results are reviewed in Sec. 2. Sec. 3 focuses on theoretical devel-