When a two-dimensional electron system is exposed to a strong
transverse magnetic field, electrons minimize their interaction energy
by capturing
an even number of quantized vortices to transform into composite
fermions.
The complex, strongly correlated liquid of interacting electrons
transforms into
a simple, weakly interacting gas of composite fermions. (An artistic depiction by Kwon Park.)
Composite fermions were originally predicted theoretically to
explain the remarkable phenomenon of the "fractional quantum Hall
effect" (FQHE), but are now known to describe a superstructure
that encompasses other phenomena as well. Since its inception,
the composite
fermion concept has been critically examined through a large number of
tests,
within and beyond the FQHE, which have established a close
correspondence
between the reality and the composite fermion theory.
It is experimentally established that composite fermions:
- fill a fermi sea (the composite-fermion fermi sea)
- execute semiclassical cyclotron orbits
- form Landau levels (called CF-Landau levels)
- exhibit Shubnikov-de Haas oscillations
- show integral QHE (FQHE of electrons)
- show fractional QHE (more FQHE of electrons)
- can be seen in mesoscopic experiments
- form a BCS like paired state
Many quantum numbers and parameters of the composite fermion have been
measured. These are:
- charge
- spin
- statistics
- magnetic moment
- Fermi wave vector
- mass
Also, its many excitations have been observed:
- charged excitations
- excitons
- rotons
- bi-rotons
- skyrmions (?)
- spin reversed excitations
- cyclotron resonance
The composite fermion theory possesses many qualities we desire in
a theory.
- Unification. Unification is one of the strongest driving
forces in physics. The composite fermion theory unifies the mysterious
phenomenon of the fractional quantum Hall effect with the well understood
phenomenon of the integral quantum Hall effect. This
provides an explanation for the former: the fractional quantum Hall
effect is the integral quantum Hall effect of composite fermions.
All fractional quantum Hall states and their excitations are
understood in a single stroke. Like all successful unifications, the
FQHE-IQHE unification has unanticipated consequences that
have subsequently been verified. The dramatic predictions that follow
from it include the existence of
composite fermions, composite fermion Fermi sea, spin polarizations
of the fractional quantum Hall states, pairing of composite fermions,
filling factor dependence of gaps, etc.
- Uniqueness. Another goal of theoretical physics
is to reduce the number
of parameters. The fewer parameters a theory has, the more
fundamental it is. Amazingly, the composite fermion theory provides a
detailed and accurate microscopic description of the strongly correlated
FQHE state with no adjustable parameters.
- Simplicity. Composite fermion theory
produces a simple intuitive explanation for
the phenomenology of the fractional quantum Hall effect,
e.g., for the appearance of certain sequences of
odd-denominator fractions and the lack
of FQHE at certain even-denominator fractions.
- Falsifiability. The composite fermion theory makes
numerous definite and non-trivial predictions, qualitative as well as
quantitative, which have been confirmed over the years in experimental
and exact numerical studies. Through parameter-free wave
functions, the theory has been verified beautifully in
rigorous, unbiased and detailed tests against exact "computer experiments."
- Accuracy.
Extensive studies have shown that the composite fermion theory gives
a faithful counting of the low-energy eigenstates, and wave functions
and energies that are essentially exact. That is particularly striking
in view of its lack of adjustable parameters.
- New particle. Strongly interacting particles
of one
kind often reorganize to form new particles that are weakly
interacting. These weakly interacting particles form the basis
for describing the physics, and phenomena that looked mysterious
earlier become simply explicable as properties
of nearly free particles. Composite fermions are the weakly
interacting objects of the FQHE liquid. They embody the
profound reorganization that takes place when a collection of
two-dimensional electrons is subjected to a strong magnetic field.
Further reading: A huge number of scientists have made
significant contributions to the field of composite fermion. The
interested reader may find it useful to consult the following books
and review articles, and the original
articles referenced therein.
