We show that the solid phase between the 1/5 and 2/9 fractional quantum Hall states arises from an extremely delicate interplay between type-1 and type-2 composite fermion crystals, clearly demonstrating its nontrivial, strongly correlated character. We also compute the phase diagram of various crystals occurring over a wide range of filling factors and demonstrate that the elastic constants exhibit nonmonotonic behavior as a function of the filling factor, possibly leading to distinctive experimental signatures that can help mark the phase boundaries separating different kinds of crystals.

The Wigner crystal of composite fermions is a strongly correlated state of complex emergent particles in two dimensions, and therefore its unambiguous detection would be of significant importance. Recent observation of optical resonances in the vicinity of filling factor ν = 1/3 has been interpreted as evidence for a pinned Wigner crystal of composite fermions [Zhu et al., Phys. Rev. Lett. 105, 126803 (2010)]. We evaluate in a microscopic theory the shear modulus and the magnetophonon and magnetoplasmon dispersions of the composite fermion Wigner crystal in the vicinity of filling factors 1/3, 2/5, and 3/7. We determine the region of stability of the crystal phase, and also relate the frequency of its pinning mode to that of the corresponding electron crystal near integer fillings. These results are in good semiquantitative agreement with experiment, and therefore support the identification of the optical resonance as the pinning mode of the composite fermions Wigner crystal. Our calculations also bring out certain puzzling features, such as a relatively small melting temperature for the composite fermion Wigner crystal, and also suggest a higher asymmetry between Wigner crystals of composite fermion particles and holes than that observed experimentally.

We calculate the phase diagram of the two-component fractional quantum Hall effect as a function of the spin or valley Zeeman energy and the filling factor, which reveals new phase transitions and phase boundaries spanning many fractional plateaus. This phase diagram is relevant to the fractional quantum Hall effect in graphene and in GaAs and AlAs quantum wells, when either the spin or the valley degree of freedom is active.PACS numbers: 73.43. Cd, 71.10.Pm The interplay between the Coulomb interaction and the electron spin degree of freedom has led to an impressive amount of physics in the fractional quantum Hall effect (FQHE). Phase transitions have been observed as a function of the Zeeman splitting, E Z , in transport, 1-6 optical 7-10 and NMR experiments. 11-15 Recent years have witnessed a remarkable resurgence of interest in multicomponent FQHE due to the experimental observation of FQHE in systems with both spin and valley degrees of freedom, such as AlAs quantum wells, 16-18 graphene, 19-21 and H-terminated Si(111) surface. 22 These enable new and more powerful methods of controlling the relative strengths of the (spin or valley) "Zeeman" splitting and the interaction, thus opening the door into investigations of the physics of multicomponent FQHE states over a broad range of parameters.We consider FQHE for SU(2) electrons, applicable to parameter regimes in which either the valley or the spin degree of freedom is active. For simplicity, we will refer to the two-components generically as "spins." Phase transitions at the isolated filling factors ν = n/(2pn±1), n and p integers, were studied theoretically previously. [23][24][25][26][27] We obtain in this Letter the more complete E Z −ν phase diagram, which reveals many phase boundaries arising from a competition between the Zeeman and the Coulomb energies.

A longstanding puzzle for the lowest-Landau-level crystal phase has been an order of magnitude discrepancy between the theoretically calculated energy of the defects and the measured activation gap. We perform an extensive study of various kinds of defects in the correlated composite fermion crystal and find that the lowest energy defect is a sixfold symmetric "hypercorrelated bubble interstitial," in which an interstitial particle forms a strongly correlated bound state with a particle of the crystal. The energy of the bubble defect is a factor of ∼3 smaller than that of the lowest energy defect in a Hartree-Fock crystal. The anomalously low activation energies measured in transport experiments are thus a signature of the unusual quantum nature of the crystal and its defects.