4 research outputs found
Electromagnetic absorption of a pinned Wigner crystal at finite temperatures
We investigate the microwave absorption of a pinned, two-dimensional Wigner
crystal in a strong magnetic field at finite temperatures. Using a model of a
uniform commensurate pinning potential, we analyze thermal broadening of the
electromagnetic absorption resonance. Surprisingly, we find that the pinning
resonance peak should remain sharp even when the temperature is comparable or
greater than the peak frequency. This result agrees qualitatively with recent
experimental observations of the ac conductivity in two-dimensional hole
systems in a magnetically induced insulating state. It is shown, in analogy
with Kohn's theorem, that the electron-electron interaction does not affect the
response of a harmonically pinned Wigner crystal to a spatially uniform
external field at any temperature. We thus focus on anharmonicity in the
pinning potential as a source of broadening. Using a 1/N expansion technique,
we show that the broadening is introduced through the self-energy corrections
to the magnetophonon Green's functions.Comment: 21 pages, 9 eps figure
Hamiltonian Theory of the Composite Fermion Wigner Crystal
Experimental results indicating the existence of the high magnetic field
Wigner Crystal have been available for a number of years. While variational
wavefunctions have demonstrated the instability of the Laughlin liquid to a
Wigner Crystal at sufficiently small filling, calculations of the excitation
gaps have been hampered by the strong correlations. Recently a new Hamiltonian
formulation of the fractional quantum Hall problem has been developed. In this
work we extend the Hamiltonian approach to include states of nonuniform
density, and use it to compute the excitation gaps of the Wigner Crystal
states. We find that the Wigner Crystal states near are
quantitatively well described as crystals of Composite Fermions with four
vortices attached. Predictions for gaps and the shear modulus of the crystal
are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table
Nonlinear conductivity of a two-dimensional pinned charge-density wave in a strong magnetic field
We present the theory of the dynamics of a two-dimensional Wigner crystal in a high magnetic field, assuming charge-density-wave correlations extend over a distance large compared to the interelectronic spacing. We consider the effects of both weak disorder and screening by uncondensed carriers. In an electric field large compared to the threshold field for sliding, a perturbative theory is used to calculate the nonlinear conductivity and correlation functions of the elastic strain. We compare our results to the behavior of conventional charge-density-wave systems, and stress the role of the large magnetic field, soft shear modulus, and screening by the background linear conductivity