Two-dimensional electron system in high magnetic fields: Wigner crystal vs. composite-fermion liquid

The two dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a parameter range where theory and many experiments had previously suggested the Wigner crystal phase, thus calling into question our current understanding. This Letter shows how very small quantitative corrections (< 1%) in the energy due to the weak interaction between composite fermions can cause a fundamental change in the nature of the ground state, thus providing insight into the puzzling experimental results.Comment: 4 pages, 2 figure

Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of lowest-Landau-level states in the neighborhood of nu=1/3

Motivated by recent experiments, and using the rotating-and-vibrating electron-molecule (RVEM) theory [Yannouleas and Landman, Phys. Rev. B 66, 115315 (2002); Phys. Rev. A 81, 023609 (2010)], in conjunction with exact diagonalization, we develop a unified microscopic approach for the interplay between liquid fractional-quantum-Hall-effect (FQHE) states and Wigner-solid states in the lowest Landau level (LLL) in the neighborhood of nu=1/3. Liquid characteristics of the FQHE states are associated with the symmetry-conserving rotations and vibrations of the electron molecule. Although the electron densities of the symmetry-conserving LLL states do not exhibit crystalline patterns, the intrinsic crystalline correlations are reflected in the conditional probability distributions and the emergence of cusp yrast states in the LLL spectra. It is shown that away from the exact fractional fillings, weak pinning perturbations (due to weak disorder) may overcome the energy gaps between adjacent global states and generate pinned broken symmetry ground states as a superposition of symmetry-conserving LLL states with different total angular momenta. The electron densities of such mixed states (without good angular momentum quantum numbers) exhibit oscillating patterns that correspond to molecular crystallites. These pinned Wigner crystallites represent finite-size precursors of the bulk Wigner-solid state. It is further shown that the emergence of these molecular crystallites is a consequence of the presence of RVEM components in the symmetry-conserving LLL states. In addition, it is shown that the RVEM approach accounts for the Wigner-solid state in the neighborhood of nu=1, which was also found in the experiments. We utilize results for sizes in a wide range from N=6 to N=29 electrons, and we address the extrapolation to the thermodynamic limit.Comment: 19 pages, 17 figures, 4 tables. For related papers, see http://www.prism.gatech.edu/~ph274cy

Fractional statistics in the fractional quantum Hall effect

A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $\nu=1/3$ and $\nu=2/5$ by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discussed.Comment: Phys. Rev. Lett., in pres

Relevance of inter-composite fermion interaction to the edge Tomonaga-Luttinger liquid

It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of non-interacting composite fermions. However, the weak residual interaction between composite fermions appears to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one dimensional theory.Comment: 5 pages; accepted in Phys. Rev. Let

Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness

The activation gaps for fractional quantum Hall states at filling fractions $\nu=n/(2n+1)$ are computed for heterojunction, square quantum well, as well as parabolic quantum well geometries, using an interaction potential calculated from a self-consistent electronic structure calculation in the local density approximation. The finite thickness is estimated to make $\sim$30% correction to the gap in the heterojunction geometry for typical parameters, which accounts for roughly half of the discrepancy between the experiment and theoretical gaps computed for a pure two dimensional system. Certain model interactions are also considered. It is found that the activation energies behave qualitatively differently depending on whether the interaction is of longer or shorter range than the Coulomb interaction; there are indications that fractional Hall states close to the Fermi sea are destabilized for the latter.Comment: 32 pages, 13 figure

Fractional Quantum Hall Hierarchy and the Second Landau Level

We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.Comment: 10 pages; v2: many additional details and discussion included to help clarify the original results, including a composite fermion type formulation of some of the states; v3: minor correction

Band Structure of the Fractional Quantum Hall Effect

The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. Thus, somewhat like in Landau's fermi liquid theory, there is a one-to-one correspondence between the low energy Hilbert space of strongly interacting electrons in the fractinal quantum Hall regime and that of weakly interacting electrons in the integer quantum Hall regime.Comment: 10 page