Study of correlations in fractional quantum Hall effect

Bulk two-dimensional electron systems in a strong perpendicular magnetic field exhibit the fascinating phenomenon of fractional quantum Hall effect. Composite fermion theory was developed in the process of understanding the fractional quantum Hall effect and was proven to work successfully for the FQHE and even beyond. In this dissertation, we explore the effect of the strong correlation between electrons in several cases. All of them belong to the category of 2DES in strong perpendicular magnetic field and they are listed below: (i)A fractional quantum Hall island surrounded by a bulk fractional quantum Hall state with a different filling factor. Specifically, we study the resonant tunneling composite fermions through their quasibound states around the island. A rich set of possible transitions are found and the possible relevance to an interesting experiment is discussed. Also, we discuss the subtlety of separating the effect of fractional braiding statistics from other factors. (ii) Correlated states of a quantum dot, at high magnetic fields, assuming four electrons with two components. Such a dot can be realized by reducing the two lateral dimensions of a 2DES tremendously. Both the liquid states and crystallites (the latter occurring at large angular momenta) of four electrons in terms of composite fermions are considered. Residual interaction between composite fermions is shown to leads to complex spin correlations. (iii) Bilayer quantum Hall effect at total filling $ u_T=5$. This can accommodate an excitonic superfluid state at small layer separations just like at $ u_T=1$. At large layer separations, however, $ u_T=5$ state evolves into uncorrelated $ u=5/2$ fractional quantum Hall states in both layers, in contrast to uncorrelated composite Fermi sea in $ u_T=1$ case. We focus on finding the critical layer separation at which the correlation between electrons on different layers are destroyed. Effects due to the finite width of the layers are also considered.