# Interacting composite fermions

Abstract (Summary)

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.
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Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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