Abstract
It is well known that in condensed matter physics no single-particle theory can provide us with an exact description of the real experiment due to a huge number of interacting particles involved in the process. However, the main goal for the theory is to catch the basic unusual idea, which would give a clear physical picture and explain essential experimental results. One famous successful example of a many-body theory is the Bardeen-Cooper-Schrieffer model, explaining superconductivity in terms of new composite particles—pairs of electrons which experience a Bose-Einstein condensation. Another successful example is a new theory of Composite Fermions (CFs) [1], explaining the Fractional Quantum Hall Effect [2] in terms of novel composite particles, each consisting of an electron and a number of magnetic flux quanta. The properties of these composite particles are governed by the number of the fluxes attached to the electron—they are bosons for odd numbers of fluxes and fermions for even numbers. The CFs are electrons dressed with two magnetic flux quanta. An attachment of the flux quanta to an electron is a rather natural way to minimize the energy of the system, since these vortices would expel other electrons resulting in a decrease of the repulsion interaction between 2D-electrons. The main consequence of the theory of CFs is that at half filling of the lowest Landau level (υ = 1/2) an external magnetic field is effectively compensated by two flux quanta and a metallic state of these composite particles is formed. This state can be characterized by a Fermi wave-vector and a Fermi-energy [3] and a deviation of the magnetic field from exact half filling results in the appearance of a non-zero effective magnetic field which quantizes the CF motion and discretizes their energy spectrum into Landau levels. In this model, the FQHE is a manifestation of the Landau quantization of CFs and a rich variety of experimental observations can be understood straightforwardly in terms
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