Analytical Theory of Strongly Correlated Wigner Crystals in the Lowest Landau Level

Abstract

In this work, we present an analytical theory of strongly correlated Wigner crystals (WCs) in the lowest Landau level (LLL) by constructing an approximate, but accurate effective two-body interaction for composite fermions (CFs) participating in the WCs. This requires integrating out the degrees of freedom of all surrounding CFs, which we accomplish analytically by approximating their wave functions by delta functions. This method produces energies of various strongly correlated WCs that are in excellent agreement with those obtained from the Monte Carlo simulation of the full CF crystal wave functions. We compute the compressibility of the strongly correlated WCs in the LLL and predict discontinuous changes at the phase boundaries separating different crystal phases.

9 pages, 6 figures

References in corpus (8)

• Interaction phenomena in graphene seen through quantum capacitance
• Density of states and zero Landau level probed through capacitance of graphene
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Melting of a 2D Quantum Electron Solid in High Magnetic Field
• Evidence for Two Different Solid Phases of Two Dimensional Electrons in High Magnetic Fields
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Cited by in corpus (7)

• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Sharp Tunneling Resonance from the Vibrations of an Electronic Wigner Crystal
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Dynamics of the Wigner Crystal of Composite Particles
• Wigner solid pinning modes tuned by fractional quantum Hall states of a nearby layer
• Wigner solids of wide quantum wells near Landau filling $\nu =1$