Abstract
``Two dimensional electron system`` (2DES) here refers to electrons whose dynamics is free in 2 dimensions but blocked in the third. Experiments have been performed in two limiting situations: the classical, low density, limit realised by electrons deposited on a liquid helium surface and the quantum, high density, limit realised by electrons at an interface between two epitaxially matched semiconductors. In the classical system, where T{sub Q} << V{sub c} so that the thermodynamic state is determined by the competition between the temperature and the Coulomb interaction, melting is induced either by raising the temperature at constant density or by lowering the density at finite temperature. In the quantum system, it is not possible to lower the density below about 100n{sub W} without the Coulomb interaction losing out to the random field representing the extrinsic disorder imposed by the semiconductor host. Instead one has to induce crystallisation with the help of the Lorentz force, by applying a perpendicular magnetic field B{sup [2]}. As the quantum magnetic length l{sub c} = (Planck constant c/eB){sup 1/2} is reduced with respect to the interelectronic spacing a, expressed by the filling factor {nu} 2l{sub c}{sup 2}/a{sup 2}, the system exhibits the quantum Hall effect
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Citation Formats
Williams, F I.B.
Experiments on melting in classical and quantum two dimensional electron systems.
France: N. p.,
1991.
Web.
Williams, F I.B.
Experiments on melting in classical and quantum two dimensional electron systems.
France.
Williams, F I.B.
1991.
"Experiments on melting in classical and quantum two dimensional electron systems."
France.
@misc{etde_10137962,
title = {Experiments on melting in classical and quantum two dimensional electron systems}
author = {Williams, F I.B.}
abstractNote = {``Two dimensional electron system`` (2DES) here refers to electrons whose dynamics is free in 2 dimensions but blocked in the third. Experiments have been performed in two limiting situations: the classical, low density, limit realised by electrons deposited on a liquid helium surface and the quantum, high density, limit realised by electrons at an interface between two epitaxially matched semiconductors. In the classical system, where T{sub Q} << V{sub c} so that the thermodynamic state is determined by the competition between the temperature and the Coulomb interaction, melting is induced either by raising the temperature at constant density or by lowering the density at finite temperature. In the quantum system, it is not possible to lower the density below about 100n{sub W} without the Coulomb interaction losing out to the random field representing the extrinsic disorder imposed by the semiconductor host. Instead one has to induce crystallisation with the help of the Lorentz force, by applying a perpendicular magnetic field B{sup [2]}. As the quantum magnetic length l{sub c} = (Planck constant c/eB){sup 1/2} is reduced with respect to the interelectronic spacing a, expressed by the filling factor {nu} 2l{sub c}{sup 2}/a{sup 2}, the system exhibits the quantum Hall effect (QHE), first for integer then for fractional values of {nu}. The fractional quantum Hall effect (FQHE) is a result of Coulomb induced correlation in the quantum liquid, but as {nu} is decreased still further the correlations are expected to take on long-range crystal-like periodicity accompanied by elastic shear rigidity. Such a state can nonetheless be destroyed by the disordering effect of temperature, giving rise to a phase boundary in a (T, B) plane. The aim of experiment is first to determine the phase diagram and then to help elucidate the mechanism of the melting. (author).}
place = {France}
year = {1991}
month = {Dec}
}
title = {Experiments on melting in classical and quantum two dimensional electron systems}
author = {Williams, F I.B.}
abstractNote = {``Two dimensional electron system`` (2DES) here refers to electrons whose dynamics is free in 2 dimensions but blocked in the third. Experiments have been performed in two limiting situations: the classical, low density, limit realised by electrons deposited on a liquid helium surface and the quantum, high density, limit realised by electrons at an interface between two epitaxially matched semiconductors. In the classical system, where T{sub Q} << V{sub c} so that the thermodynamic state is determined by the competition between the temperature and the Coulomb interaction, melting is induced either by raising the temperature at constant density or by lowering the density at finite temperature. In the quantum system, it is not possible to lower the density below about 100n{sub W} without the Coulomb interaction losing out to the random field representing the extrinsic disorder imposed by the semiconductor host. Instead one has to induce crystallisation with the help of the Lorentz force, by applying a perpendicular magnetic field B{sup [2]}. As the quantum magnetic length l{sub c} = (Planck constant c/eB){sup 1/2} is reduced with respect to the interelectronic spacing a, expressed by the filling factor {nu} 2l{sub c}{sup 2}/a{sup 2}, the system exhibits the quantum Hall effect (QHE), first for integer then for fractional values of {nu}. The fractional quantum Hall effect (FQHE) is a result of Coulomb induced correlation in the quantum liquid, but as {nu} is decreased still further the correlations are expected to take on long-range crystal-like periodicity accompanied by elastic shear rigidity. Such a state can nonetheless be destroyed by the disordering effect of temperature, giving rise to a phase boundary in a (T, B) plane. The aim of experiment is first to determine the phase diagram and then to help elucidate the mechanism of the melting. (author).}
place = {France}
year = {1991}
month = {Dec}
}