Interacting composite fermions

by Chang, Chia-Chen.

Systems containing a collection of strongly interacting particles are at the frontier of physics. Many-particle physics is challenging in that many of the usual tools for quantitative calculation are not applicable, and new concepts and techniques are usually required. Theoretical breakthrough in many-body physics is usually accompanied by the identification an emergent particle derived from the original interacting system. A good illustration is provided by the composite fermion (CF) theory of the fractional quantum Hall effect (FQHE). The composite fermion theory of FQHE transcends any other theory in the field of FQHE. It provides a mapping between the strongly interacting electrons and a system of weakly interacting composite fermions. The CF theory unifies the FQHE with the well understood integral quantum Hall effect, allowing a single particle description to be utilized. The non-interacting CF theory has successfully explained the physics of FHQE at the fillings ? = n/(2pn ± 1) where p and n are integers. However, new physics can occur due to the weak interaction between CFs, which is the primary concern of this thesis. (i) Recently, experiments show signatures of new FQHE states, for example 4/11 and 5/13, which cannot be understood in a model of non-interacting composite fermions. By including the residual interaction of CFs, these new fractions are understood as the fractional quantum Hall effect of composite fermions. (ii) An extremely accurate description of few electrons in a semiconductor quantum dot at high magnetic field is developed based on correlated basis of the CF theory. (iii) At low filling factors, we show, by directly comparing with exact eigenstates, that the crystal state, resulting from the interacting between particles, is a topological quantum crystal of composite fermions. (iv) Motivated by the CF theory for electrons, we study the mapping of interacting bosons in a rapidly rotating trap at filling factors n/(n+1) onto non-interacting fermions at fillings n. This mapping provides a good account of the behavior of bosons for small n. (v) The competition iii between the CF-crystal and CF-liquid orders at filling factor 1/5 is investigated. In the thermodynamic limit, the liquid state prevails. A variational combination of the crystal and liquid states provides an extremely accurate description for small systems. iv