Static and Dynamic Properties of Type-II Composite Fermion Wigner Crystals

TL;DR

This paper provides a microscopic theoretical analysis of the properties and stability of the composite fermion Wigner crystal near certain filling factors, supporting experimental identification of its pinning mode and revealing new insights into its melting temperature and particle-hole asymmetry.

Contribution

It offers the first detailed microscopic calculations of the shear modulus and collective mode dispersions of the composite fermion Wigner crystal near fractional fillings.

Findings

Good agreement with experimental pinning mode frequencies

Relatively low melting temperature of the crystal

Higher asymmetry between particle and hole Wigner crystals than observed experimentally

Abstract

The Wigner crystal of composite fermions is a strongly correlated state of complex emergent particles, and therefore its unambiguous detection would be of significant importance. Recent observation of optical resonances in the vicinity of filling factor {\nu} = 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.