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The fractional quantum Hall (FQHE) effect states in the lowest Landau level for the sequence of filling factors n/(2n+1) [n is an integer] are well understood by composite fermion (CF) theory. A CF is a bound state of an electron and two quantized vortices. CFs form their own kinetic energy levels called effective Landau levels. The integer quantum Hall effect of CFs with effective filling factor n can be translated into the FQHE of electrons at the filling factor n/(2n+1). However, there is no FQHE at half-filling as the CFs form Fermi surface and give rise to gapless excitations.
Although some of the FQHE states such as 4/11, 5/13, 6/17, and 3/8 which are between the fundamental filling factors 1/3 and 2/5 have been observed more than a decade ago, the origin of these states were never understood. In this talk, I will describe how these states can be understood through novel mechanisms. |