50,944 research outputs found
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
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
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
and 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
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