Strongly Magnetized two Dimensional Electron Gas with Account of Confinement and Pair Interaction of Electrons
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Date
2011-06
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Addis Ababa University
Abstract
During the past decade two-dimensional electron systems at low temperatuer and high
magnetic eld have repeatedly surprised with exotic electron correlation phenomena. The
quantum liquids of the fractional quantum Hall e ect (FQHE), the still enigmatic electron
crystal at very low lling factors, and vanishing and reappearance of certain quantum
Hall states in double layer electron systems all re
ect the dominance of electron-electron
interaction at very high magnetic elds. Recently the nature of the electronic interaction
at the half- lled Landau levels has received much attention. The magnetization of twodimensional
electron gases at low temperatures and in a strong magnetic eld B oriented
normal to the plane of the electron motion was calculated along the same lines as in the
work of Landau. With in two-dimensional electron system new surprises arise year after
year, exotic states of electronic matter, new materials with fascinating quantum Hall
properties keep triggering an intense activity in the eld. Two-dimensional electron gases
with crossing energy levels can be realized in a variety of systems with di erent relative
sizes of orbital and spin e ects, Coulomb energy, and di erent coupling between the components.
Their study has lead to the discovery of many correlated Quantum Hall states
and much e ort is put into unravelling the energy-level structure of these systems. In this
work we have four parts. The rst part contens Two-Dimensional Electron gas, Quantum
Con nement and Density of States, Potential wells in Semiconductors, Con nement of
Electrons, E ect of Quantum Con nement on Electrons, Semiconductors Nanostructures
with Con ned Electrons and Properties and Applications of Con ned Electron Gases.
The second part includes Landau Levels and Landau Level degeneracy. The third part
is about Classical and Quantum Hall e ect. Finally the forth part presents two charged
particles in a magnetic eld and Parabolic con nement in strong magnetic eld. Here we
see charged particle in weak magnetic eld and how the particle is confi ned
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Keywords
Strongly Magnetized two Dimensional Electron