Text: THE COMPOSITE FERMION The composite fermion is a new particle in condensed matter physics. It is the bound state of an electron and an even number of quantized vortices, often thought of as an electron carrying an even number of magnetic flux quanta. 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 becomes a simple, weakly interacting gas of composite fermions. (An artistic depiction by Kwon Park.) The composite fermion was originally envisioned to explain the remarkable phenomenon of the "fractional quantum Hall effect" (FQHE), but is now known to describe a superstructure that encompasses other phenomena as well, with the FQHE being only one of its many manifestations. Since its inception, the composite fermion 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. One reason why the tests are clean and non-trivial is because the composite fermion theory makes definite statements with little room for any ad hoc, case by case adjustments. In addition, the validity of the composite fermion description has also been shown rigorously in detailed tests against computer experiments. Predictions play a more decisive role in the validation of a new concept than explanations of existing facts. Numerous predictions of the composite fermion theory have been confirmed, e.g., the effective magnetic field, the composite-fermion Fermi sea at the half filled Landau level, the phase diagram as a function of the Zeeman energy, and of course, the very existence of the composite fermion itself. It is experimentally established that composite fermions: * fill a fermi sea (the composite fermi sea) * execute semiclassical cyclotron orbits * form Landau levels (called CF-Landau levels) * exhibit Shubnikov-de Haas oscillations * show integral QHE (FQHE of electrons) * can be seen in mesoscopic experiments * perhaps even 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 * rotons * bi-rotons * skyrmions (?) * spin reversed excitations * cyclotron resonance The composite fermion theory possesses many qualities we desire in a theory. o Unification. The quest for unification is one of the most basic driving forces in physics, taking us to ever deeper intellectual structure. An important accomplishment of the composite fermion theory is the unification of phenomena that were earlier thought to be distinct. It not only explains all fractions in an equivalent manner, but also unifies the fractional and the integral quantum Hall effects. It shows that the they are are both integral quantum Hall effects, only for different particles. Furthermore, the theory also describes states where no FQHE is seen, for example, the compressible states at even denominator fractions. o Uniqueness. Another central goal in physics is the search for a theory with fewer and fewer parameters.The fewer the parameters, the more fundamental the theory. The concept of composite fermion is so powerful that it provides a detailed microscopic description of a strongly correlated many body state with no adjustable parameters. Specifically, it produces parameter-free microscopic wave functions for the ground and low energy excited states at certain special filling factors. o Simplicity. The composite fermions provide a simple intuitive explanation for the basic phenomenology of the fractional quantum Hall effect, e.g., for the appearance of certain sequences of odd-denominator fractions (where a gap opens up because the composite fermions occupy an integral number of levels) and the lack of FQHE at even-denominator fractions (where the composite fermions form a Fermi sea which has no gap). Such simplicity is not only satisfying but is to be demanded on physical grounds -- it would be inconceivable for a phenomenon as simple and universal as the FQHE to have a complex physical origin. o Falsifiability. The composite fermion theory makes numerous definite and non-trivial predictions, which have been confirmed over the years in experimental as well as theoretical studies. o Accuracy. Through parameter-free wave functions, the theory lends itself to rigorous, unbiased and detailed tests against exact "computer experiments" on finite systems. Extensive studies have shown that the composite fermion theory gives a faithful counting of the low-energy eigenstates, and the wave functions are essentially exact: They have close to 100% overlap with the exact eigenstates, and their energies are accurate to better than 0.1%. [To see comparisons of the exact eigenspectrum and the low-energy spectrum predicted by the composite fermion theory (dashes and dots, respectively) for systems of 8-12 particles at sevaral filling factors, click here .] Such accuracy is rare in condensed matter physics, let alone for a theory without parameters. The comparison with laboratory experiments is less accurate because many features extraneous to the composite fermion physics (for example, corrections due to finite thickness or the ever-present disorder) are quantitatively not as well understood. o New particle. Strongly interacting particles of one kind often reorganize to form new particles that are weakly interacting. These weakly interacting particles are truely the "particles" of the system in question, because the title "particle," which carries with it the fundamental notion of individuality, ought to be reserved for nearly independent objects. If a mapping into weakly interacting particles can be accomplished, the problem is solved, because one can switch off the interaction altogether to explain the qualitative phenomenology, and treat the interaction perturbatively to obtain a quantitative understanding. These new particles therefore form the basis for describing the physics, and phenomena that looked mysterious earlier become simply explicable as properties of nearly free particles. Some examples of weakly interacting particles (in approprite situations) are quarks, nucleons, atoms, phonons, magnons, Cooper pairs, or stars. The composite fermions are the weakly interacting objects in the lowest Landau level liquid, therefore the particles of this new state of matter; they embody the profound reorganization that takes place when a collection of two-dimensional electrons is subjected to a strong magnetic field. The following observations are also worth noting. A quantum particle. Even though it behaves as an ordinary fermion to a great extent, the composite fermion is an unusual particle. First of all, it is a collective, many body entity, because one of its constituents, namely the vortex, is made up of all particles in the system. Moreover, the composite fermion is a quantum particle. Of course, quantum mechanics describes all particles, but it participates in the very definition of the composite fermion, whose creation is the union of an electron and quantum mechanical phases (vortices). The composite fermion could not exist in a purely classical world. It is interesting to note that the semiclassical cyclotron orbits of the quantum composite fermion particles themselves become quantized to produce Landau levels, which manifests most dramatically through fractional quantum Hall effect. Macroscopic quantum phenomenon. The composite fermion theory clarifies that the quantization of Hall resistance is a direct consequence of certain fundamental principles of quantum mechanics. The exact quantization of the vorticity of the composite fermion, which must be an integer, with no correction, as required by the principle of single-valuedness of the quantum mechanical wave function, lies at the root of the exact quantization of the macroscopic Hall resistance. The antisymmetry of the wave function requires that the integer be even, which results in the odd-denominator rule. Emergent phenomenon. ("More Is Different" - P.W. Anderson, 1972.) The composite fermion state provides a dramatic example of emergent behavior. The behavior of many interacting electrons in the lowest Landau level cannot be anticipated from what we know of a single electron. The fundamentally new and beautiful structures that emerge in this system are described in terms of composite fermions. The composite fermion is an emergent particle. An "impossible" problem? The only relevant energy for electrons confined to the lowest Landau level is their Coulomb interaction. If the interaction is switched off, all eigenstates (configurations of electrons) are degenerate. The interaction picks out one of these states as the ground state, the identification of which lies at the heart of the problem. For a typical 1mm X 1mm sample containing 10^9 electrons, for a filling of say 0.4, there are 10^(7 X 10^8) distinct configurations. Even for a much smaller system containing only 100 electrons, the number of states is 10^72. On purely theoretical grounds, we have no idea where to start (A priori, a crystalline state might appear to be a good starting point, but experiments clearly rule it out in the region of interest.) and the situation looks hopeless. Dramatic clues from experiment, enormous luck, and the power of analogy have led us to the solution to this problem. It is awe-inspiring that so much about this system can be explained from the single principle of composite fermion. 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 two books, which also contain references to the original articles. * "Composite Fermions", edited by O. Heinonen, World Scientific, 1998. * "Perspectives in Quantum Hall Effects", edited by S. Das Sarma and A. Pinczuk, Wiley, 1997. * "The Composite Fermion: A Quantum Particle and Its Quantum Fluids," J.K. Jain, Physics Today 53(4), 39-45 (2000). (Reprinted by Michael Marder)

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