Crystal states in two-dimensional quantum Hall systems

Miscellaneous · Wed Jan 01 00:00:00 EST 1992

OSTI ID:7014292

Kahng, Jonghyun

Since high quality two-dimensional electron systems (2DES) became available in the inversion layer in GaAs-AlGaAs heterojunctions, there have been experimental observations of highly insulating phases at many filling factors ([nu]) including these above and below [nu] = 1/5. If these phases are crystals, the implied phase diagram of the 2DES is much different from the conventional belief that there is a single phase transition from the quantum Hall state to the Wigner crystal at some critical filling factor. The author has studied crystallization of quasiparticles created on top of quantum Hall states. It is deduced that every stable quantum Hallstate is surrounded by pairs of quasihole and quasielectron crystals on either side of its filling factor. The wavefunctions of arbitrary quantum Hall states as well as quasiparticle crystals are derived largely based on their symmetry properties. By Monte Carlo simulations, the author determined the range of filling factors where quasihole crystals derived from Laughlin's incompressible quantum fluid states (parent states) are more stable than the Wigner crystal. This range is wider for higher parent filling factor. The Wigner crystal is expected to be found only at low filling factors while crystals at higher filling factors such as those near 1/5 and above are more likely to be quasiparticle crystals. The density variation in crystal states of the 2DES produces an array of circular currents and induced magnetic fields, which are different for different crystals. To estimate the magnitude of these magnetic fields, the density profile in quasihole crystals was evaluated by Monte Carlo calculations. For Wigner crystals, it was possible to obtain essentially exact results from the simplified expression that were derived for the density. For typical experimental environments, the induced magnetic field in Wigner crystals near [nu] = 1/5 is on the order of one Gauss while that of quasihole crystals is much smaller.

• Research Organization: The Ohio State Univ., Columbus, OH (United States)
• OSTI ID: 7014292
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
HETEROJUNCTIONS
CRYSTAL MODELS
HALL EFFECT
WIGNER THEORY
ALUMINIUM ARSENIDES
GALLIUM ARSENIDES
MONTE CARLO METHOD
QUANTUM CRYSTALS
ALUMINIUM COMPOUNDS
ARSENIC COMPOUNDS
ARSENIDES
CALCULATION METHODS
CRYSTALS
GALLIUM COMPOUNDS
JUNCTIONS
MATHEMATICAL MODELS
PNICTIDES
SEMICONDUCTOR JUNCTIONS
665430* - Other Topics in Quantum Fluids & Solids- (1992-)