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| {{other uses|Fermions#Composite fermions}}
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| A '''composite fermion''' is the bound state of an electron and an even number of quantized [[Quantum vortex|vortices]], sometimes visually pictured as the bound state of an electron and, attached, an even number of magnetic flux quanta.<ref name=CFbook>{{cite book |title=Composite Fermions |author=J.K. Jain |year=2007 |publisher=Cambridge University Press |location=New York |isbn=978-0-521-86232-5 |url=http://www.amazon.com/dp/0521862329}}</ref><ref name=Heinonenbook>{{cite book|title=Composite Fermions |author=O. Heinonen (ed.)|year=1998|publisher=World Scientific |location=Singapore|isbn=981-02-3592-5|url=http://www.amazon.com/dp/9810235925 }}</ref><ref name=DPbook>{{cite book |title=Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low Dimensional Semiconductor Structures |author=S. Das Sarma and A. Pinczuk (eds.) |year=1996 |publisher=Wiley-VCH |location=New York |isbn=978-0-471-11216-7 |url= http://www.amazon.com/dp/047111216X }}</ref> Composite fermions were originally envisioned in the context of the [[fractional quantum Hall effect]],<ref name="Tsui82">{{cite journal |title=Two-dimensional magnetotransport in the extreme quantum limit |author=D.C. Tsui, H.L. Stormer, and A.C. Gossard |year=1982 |journal=[[Physical Review Letters]] |volume=48 |issue=22 |page=1559 |doi= 10.1103/PhysRevLett.48.1559 |bibcode = 1982PhRvL..48.1559T }}</ref> but subsequently took on a life of their own, exhibiting many other consequences and phenomena.
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| Vortices are an example of [[topological defect]], and also occur in other situations. Quantized vortices are found in type II superconductors, called [[Abrikosov vortex|Abrikosov vortices]]. Classical vortices are relevant to the [[Kosterlitz–Thouless transition|Berezenskii–Kosterlitz–Thouless]] transition in two-dimensional [[XY model]].
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| == Description ==
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| When electrons are confined to two dimensions, cooled to very low temperatures, and subjected to a strong magnetic field, their kinetic energy is quenched due to [[Landau quantization|Landau level quantization]]. Their behavior under such conditions is governed by the Coulomb repulsion alone, and they produce a strongly correlated quantum liquid. Experiments have shown<ref name=CFbook/><ref name=Heinonenbook/><ref name=DPbook/> that electrons minimize their interaction by capturing quantized vortices to become composite fermions.<ref name=Jaincf>{{cite journal |author=J.K. Jain |title=Composite fermion approach for fractional quantum Hall effect |year=1989 |journal= [[Physical Review Letters]] |volume= 63 |issue= 2 |page= 199 |doi= 10.1103/PhysRevLett.63.199|bibcode = 1989PhRvL..63..199J }}</ref> The interaction between composite fermions themselves is often negligible to a good approximation, which makes them the physical [[quasiparticle]]s of this quantum liquid.
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| The signature quality of composite fermions, which is responsible for the otherwise unexpected behavior of this system, is that they experience a much smaller magnetic field than electrons. The magnetic field seen by composite fermions is given by
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| :<math> B^*=B-2p \rho \phi_0,</math>
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| where <math> B </math> is the external magnetic field, <math> 2p </math> is the number of vortices bound to composite fermion (also called the vorticity or the vortex charge of the composite fermion), <math>\rho</math> is the particle density in two dimensions, and <math>\phi_0=hc/e</math> is called the “flux quantum” (which differs from the [[Magnetic flux quantum|superconducting flux quantum]] by a factor of two). The effective magnetic field is a direct manifestation of the existence of composite fermions, and also embodies a fundamental distinction between electrons and composite fermions.
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| Sometimes it is said that electrons "swallow" <math> 2p </math> flux quanta each to transform into composite fermions, and the composite fermions then experience the residual magnetic field <math>B^*.</math> More accurately, the vortices bound to electrons produce their own [[geometric phase]]s which partly cancel the [[Aharonov–Bohm effect|Aharonov–Bohm phase]] due to the external magnetic field to generate a net geometric phase that can be modeled as an Aharonov–Bohm phase in an effective magnetic field <math> B^*.</math>
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| The behavior of composite fermions is similar to that of electrons in an effective magnetic field <math>B^*.</math> Electrons form Landau levels in a magnetic field, and the number of filled Landau levels is called the filling factor, given by the expression <math> \nu=\rho \phi_0/B.</math> Composite fermions form Landau-like levels in the effective magnetic field <math>B^*,</math> which are called composite fermion Landau levels or <math>\Lambda</math> levels. One defines the filling factor for composite fermions as <math> \nu=\rho \phi_0/|B^*|.</math> This gives the following relation between the electron and composite fermion filling factors
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| :<math> \nu=\frac{\nu^*}{2p\nu^*\pm 1}.</math>
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| The minus sign occurs when the effective magnetic field is antiparallel to the applied magnetic field, which happens when the geometric phase from the vortices overcompensate the Aharonov–Bohm phase.
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| == Experimental manifestations ==
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| The main statement of composite fermion theory is that the strongly correlated electrons at a magnetic field <math>B</math> (or filling factor <math>\nu</math>) turn into weakly interacting composite fermions at a magnetic field <math>B^*</math> (or composite fermion filling factor <math>\nu^*</math>). This allows an effectively single-particle explanation of the otherwise complex many-body behavior, with the interaction between electrons manifesting as an effective kinetic energy of composite fermions. Here are some of the phenomena arising from composite fermions:<ref name=CFbook/><ref name=Heinonenbook/><ref name=DPbook/>
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| === Fermi sea ===
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| The effective magnetic field for composite fermions vanishes for <math>B=2p\rho\phi_0</math>, where the filling factor for composite fermions is <math>\nu=1/2p</math>. Here, composite fermions make a Fermi sea.<ref name=HLR>{{cite journal |author = B. I. Halperin, P.A. Lee and N. Read |title = Theory of the half-filled Landau level |year = 1993 |journal = [[Physical Review B]] |volume = 47 |issue = 12 |page = 7312 |doi = 10.1103/PhysRevB.47.7312|bibcode = 1993PhRvB..47.7312H }}</ref> This Fermi sea has been observed in a number of experiments, which also measure the Fermi wave vector.<ref name=SAW>{{cite journal |author=R.L. Willett, R.R. Ruel, K.W. West, and L.N. Pfeiffer|title=Experimental demonstration of a Fermi surface at one-half filling of the lowest Landau level |year=1993 |journal=[[Physical Review Letters]] |volume=71 |issue=23 |page=3846 |doi= 10.1103/PhysRevLett.71.3846|bibcode = 1993PhRvL..71.3846W }}</ref><ref name=antidot/><ref name=Goldmanfocus/><ref name=Smetfocus/>
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| === Cyclotron orbits ===
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| As the magnetic field is moved slightly away from <math>B^*=0</math>, composite fermions execute semiclassical cyclotron orbits. These have been observed by coupling to surface acoustic waves,<ref name=SAW /> resonance peaks in antidot superlattice,<ref name=antidot>{{cite journal
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| |author=W. Kang, H. L. Stormer, L. N. Pfeiffer, K. W. Baldwin, and K. W. West
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| |title=How Real are composite fermions?
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| |year=1993
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| |journal=[[Physical Review Letters]]
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| |volume=71
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| |issue=23
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| |page=3850
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| |doi= 10.1103/PhysRevLett.71.3850
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| |bibcode = 1993PhRvL..71.3850K }}</ref> and magnetic focusing.<ref name=Goldmanfocus>{{cite journal |title=Detection of composite fermions by magnetic focusing |author=V.J. Goldman, B. Su, and J.K. Jain |year=1994 |journal=[[Physical Review Letters]] |volume=72 |issue=13 |page=2065 |doi= 10.1103/PhysRevLett.72.2065 |bibcode = 1994PhRvL..72.2065G }}</ref><ref name=Smetfocus>
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| {{cite journal
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| |author=J. H. Smet, D. Weiss, R. H. Blick, G. Lütjering, K. von Klitzing, R. Fleischmann, R. Ketzmerick, T. Geisel, and G. Weimann
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| |title=Magnetic focusing of composite fermions through arrays of cavities
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| |year=1996
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| |journal=[[Physical Review Letters]]
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| |volume=77
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| |issue=11
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| |page=2272
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| |doi= 10.1103/PhysRevLett.77.2272
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| |bibcode = 1996PhRvL..77.2272S }}</ref><ref name="Smet99">
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| {{cite journal
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| |author=J. H. Smet, S. Jobst, K. von Klitzing, D. Weiss, W. Wegscheider, and V. Umansky
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| |title=Commensurate composite fermions in weak periodic electrostatic potentials: Direct evidence of a periodic effective magnetic field
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| |year=1999
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| |journal=[[Physical Review Letters]]
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| |volume=83
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| |issue=13
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| |page=2620
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| |doi= 10.1103/PhysRevLett.83.2620
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| |bibcode = 1999PhRvL..83.2620S }}</ref> The radius of the cyclotron orbits is consistent with the effective magnetic field <math>B^*=0</math> and is sometimes an order of magnitude or more larger than the radius of the cyclotron orbit of an electron at the externally applied magnetic field <math>B</math>. Also, the observed direction of trajectory is opposite to that of electrons when <math>B^*</math> is anti-parallel to <math>B</math>.
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| === Cyclotron resonance ===
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| In addition to the cyclotron orbits, cyclotron resonance of composite fermions has also been observed by photoluminescence.<ref name=cfresonance>
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| {{cite journal
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| |author=I. V. Kukushkin, J. H. Smet, D. Schuh, W. Wegscheider, and K. von Klitzing
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| |title=Dispersion of the composite-fermion cyclotron resonance mode
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| |year=2007
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| |journal=[[Physical Review Letters]]
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| |volume=98
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| |issue=6
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| |page=066403
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| |doi= 10.1103/PhysRevLett.98.066403
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| |bibcode = 2007PhRvL..98f6403K }}</ref>
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| === Shubnikov de Haas oscillations ===
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| As the magnetic field is moved further away from <math>B^*=0</math>, [[quantum oscillations (experimental technique)|quantum oscillations]] are observed that are periodic in <math>1/B^*.</math> These are Shubnikov–de Haas oscillations of composite fermions.<ref name=Leadley>{{cite journal |author=D.R. Leadley, R.J. Nicholas, C.T. Foxon, and J.J. Harris |title=Measurement of the effective mass and scattering times of composite fermions from magnetotransport analysis |year=1994|journal= [[Physical Review Letters]]|volume= 72|issue= 12|page= 1906|doi= 10.1103/PhysRevLett.72.1906 |bibcode = 1994PhRvL..72.1906L }}</ref><ref name=DuSdH>{{cite journal |author=R.R. Du, H.L. Stormer, D.C. Tsui, L.N. Pfeiffer, and K.W. West |title=Shubnikov–de Haas oscillations around <math>\nu=1/2 </math> Landaulevel filling |journal=Solid State Communications |volume=90 |page=71 |year=1994 |url= http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVW-46SW4KB-2&_user=10&_coverDate=04%2F30%2F1994&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1539483388&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=edb79eb0a2ec00028f9812100006574d&searchtype=a |doi=10.1016/0038-1098(94)90934-2|bibcode = 1994SSCom..90...71D }}</ref> These oscillations arise from the quantization of the semiclassical cyclotron orbits of composite fermions into composite fermion Landau levels. From the analysis of the Shubnikov–de Haas experiments, one can deduce the effective mass and the quantum lifetime of composite fermions.
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| === Integer quantum Hall effect ===
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| With further increase in <math>|B^*|</math> or decrease in temperature and disorder, composite fermions exhibit integer quantum Hall effect.<ref name=Jaincf/> The integer fillings of composite fermions, <math>\nu^*=n</math>, correspond to the electrons fillings
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| :<math> \nu=\frac{n}{2pn\pm 1}.</math>
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| Combined with
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| :<math> \nu=1-\frac{n}{2pn\pm 1},</math>
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| which are obtained by attaching vortices to holes in the lowest Landau level, these constitute the prominently observed sequences of fractions. Examples are
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| :<math>{n\over 2n+1}={1\over 3},\, {2\over 5},\, {3\over 7},\, {4\over 9},\,{5\over 11},\cdots </math>
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| :<math>{n\over 2n-1}={2\over 3},\, {3\over 5},\, {4\over 7},\, {5\over 9},\,{6\over 11},\cdots </math>
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| :<math>{n\over 4n+1}={1\over 5},\, {2\over 9},\, {3\over 13},\, {4\over 17},\cdots </math>
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| The [[fractional quantum Hall effect]] of electrons is thus explained as the integer quantum Hall effect of composite fermions.<ref name=Jaincf/> It results in fractionally quantized Hall plateaus at
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| :<math> R_H={h\over \nu e^2}, </math>
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| with <math>\nu </math> given by above quantized values. These sequences terminate at the composite fermion Fermi sea. Note that the fractions have odd denominators, which follows from the even vorticity of composite fermions.
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| === Fractional quantum Hall effect ===
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| The above sequences exhaust most, but not all, observed fractions. Other fractions have been observed, which arise from a weak residual interaction between composite fermions, and are thus more delicate.<ref name =cffqhe>{{cite journal |title= Fractional quantum Hall effect of composite fermions |author=W. Pan, H.L. Stormer, D.C. Tsui, L.N. Pfeiffer, K.W. Baldwin, and K.W. West |year=2003 |journal=[[Physical Review Letters]] |volume=90 |issue=1 |page=016801 |doi= 10.1103/PhysRevLett.90.016801|arxiv = cond-mat/0303429 |bibcode = 2003PhRvL..90a6801P }}</ref> A number of these are understood as fractional quantum Hall effect of composite fermions. For example, the fractional quantum Hall effect of composite fermions at <math>\nu^*=4/3</math> produces the fraction 4/11, which does not belong to the primary sequences.<ref>{{cite journal |author=C.-C. Chang and J.K. Jain |title=Microscopic origin of the next generation fractional quantum Hall effect |year=2004|journal=[[Physical Review Letters]]|volume=92|issue=19|page=196806|doi= 10.1103/PhysRevLett.92.196806|arxiv = cond-mat/0404079 |bibcode = 2004PhRvL..92s6806C }}</ref>
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| === Superconductivity ===
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| An even denominators fraction, <math>\nu=5/2,</math> has been observed.<ref name=willetteven>{{cite journal |title=Observation of an even-denominator quantum number in the fractional quantum Hall effect |author=R. Willett, J.P. Eisenstein, H.L. Stormer, D.C. Tsui, A.C. Gossard, and J.H. England|year=1987 |journal=[[Physical Review Letters]] |volume=59 |issue=15 |page=1776 |doi= 10.1103/PhysRevLett.59.1776 |bibcode = 1987PhRvL..59.1776W }}</ref> Here the second Landau level is half full, but the state cannot be a Fermi sea of composite fermions, because the Fermi sea is gapless and does not show quantum Hall effect. This state is viewed as a “superconductor “ of composite fermion,<ref name=Moore>{{cite journal |title=Nonabelions in the fractional quantum Hall effect |author=G. Moore and N. Read |journal=Nuclear Physics B |volume=360 |page=362 |year=1991 |url=http://www.physics.rutgers.edu/~gmoore/MooreReadNonabelions.pdf |bibcode = 1991NuPhB.360..362M |doi = 10.1016/0550-3213(91)90407-O }}</ref><ref name=ReadGreen>{{cite journal |title=Paired states of fermions in two dimensions with breaking of parity and time reversal symmetries and the fractional quantum Hall effect |author=N. Read and D. Green |year=2000 |journal=[[Physical Review B]] |volume=61 |issue=15 |page=10267 |doi= 10.1103/PhysRevB.61.10267|arxiv = cond-mat/9906453 |bibcode = 2000PhRvB..6110267R }}</ref> arising from a weak attractive interaction between composite fermions at this filling factor. The pairing of composite fermions opens a gap and produces a fractional quantum Hall effect.
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| === Excitons ===
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| The neutral excitations of various fractional quantum Hall states are [[exciton]]s of composite fermions, that is, particle hole pairs of composite fermions.<ref>{{cite journal |title=Rotons of composite fermions: Comparison between theory and experiment |author=V.W. Scarola, K. Park, and J.K. Jain |year=2000 |journal=[[Physical Review B]] |volume=61 |issue=19 |page=13064 |doi= 10.1103/PhysRevB.61.13064 |bibcode = 2000PhRvB..6113064S }}</ref> The energy dispersion of these excitons has been measured by light scattering<ref>{{cite journal |title=Observation of multiple magnetorotons in the fractional quantum Hall effect |author=M. Kang, A. Pinczuk, B.S. Dennis, L.N. Pfeiffer, and K.W. West |journal=Physial Review Letters |year=2001 |journal=[[Physical Review Letters]] |volume=86 |issue=12 |page=2637 |doi= 10.1103/PhysRevLett.86.2637|bibcode = 2001PhRvL..86.2637K }}</ref><ref>{{cite journal |title=Composite-fermion spin excitations at <math>
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| u</math> approaches ½: Interactions in the Fermi sea |author=I. Dujovne, A. Pinczuk, M. Kang, B.S. Dennis, L.N. Pfeiffer, and K.W. West |year=2005 |journal=[[Physical Review Letters]] |volume=95 |issue=5 |page=056808 |doi= 10.1103/PhysRevLett.95.056808|bibcode = 2005PhRvL..95e6808D }}</ref> and phonon scattering.<ref>{{cite journal |title=Phonon excitations of composite fermion Landau levels |author=F. Schulze-Wischeler, F. Hohls, U. Zeitler, D. Reuter, A.D. Wieck, and R.J. Haug |year=2004 |journal=[[Physical Review Letters]] |volume=93 |issue=2 |page=026801 |doi= 10.1103/PhysRevLett.93.026801 |bibcode = 2004PhRvL..93b6801S }}</ref>
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| === Spin ===
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| At high magnetic fields the spin of composite fermions is frozen, but it is observable at relatively low magnetic fields. The fan diagram of the composite fermion Landau levels has been determined by transport, and shows both spin-up and spin-down composite fermion Landau levels.<ref name=cfspin>{{cite journal
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| |author=R. R. Du, A. S. Yeh, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, and K. W. West
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| |title=Fractional quantum Hall effect around <math>\nu=3/2</math>: Composite fermions with a spin
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| |year=1995
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| |journal=[[Physical Review Letters]]
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| |volume=75
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| |issue=21
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| |page=3926
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| |doi= 10.1103/PhysRevLett.75.3926
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| |bibcode = 1995PhRvL..75.3926D }}</ref> The fractional quantum Hall states as well as composite fermion Fermi sea are also partially spin polarized for relatively low magnetic fields.<ref name=cfspin/><ref name=kukushkinspin>{{cite journal |title=Spin polarization of composite fermions: Measurements of the Fermi energy |author=I.V. Kukushkin, K. v. Klitzing, and K. Eberl |year=1999 |journal= [[Physical Review Letters]] |volume= 82 |issue= 18 |page= 3665 |doi= 10.1103/PhysRevLett.82.3665 |bibcode = 1999PhRvL..82.3665K }}</ref><ref name=melinte>{{cite journal |title=NMR determination of 2D electron spin polarization at <math>\nu=1/2</math> |author=S. Melinte, N. Freytag, M. Horvatic, C. Berthier, L.P. Levy, V. Bayot, and M. Shayegan |year=2000 |journal= [[Physical Review Letters]] |volume= 84 |issue= 2 |page= 354 |doi= 10.1103/PhysRevLett.84.354 |arxiv = cond-mat/9908098 |bibcode = 2000PhRvL..84..354M }}</ref>
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| === Effective magnetic field ===
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| The effective magnetic field of composite fermions has been confirmed by the similarity of the fractional and the integer quantum Hall effects, observation of Fermi sea at half filled Landau level, and measurements of the cyclotron radius.
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| === Mass ===
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| The mass of composite fermions has been determined from the measurements of: the effective cyclotron energy of composite fermions;<ref name=cfmass>{{cite journal
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| |author=R.R. Du, H. L. Stormer, D.C. Tsui, L. N. Pfeiffer, K. W. Baldwin, and K. W. West
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| |title=Experimental evidence for new particles in the fractional quantum Hall effect
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| |year=1993
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| |journal=[[Physical Review Letters]]
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| |volume=70
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| |issue=19
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| |page=2944
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| |doi= 10.1103/PhysRevLett.70.2944|bibcode = 1993PhRvL..70.2944D }}</ref><ref>{{cite journal |title=Signatures of a novel Fermi liquid in a two-dimensional composite particle model |author=H.C. Manoharan, M. Shayegan, and S.J. Klepper |year=1994 |journal=[[Physical Review Letters]] |volume=73 |issue=24 |page=3270 |doi= 10.1103/PhysRevLett.73.3270|bibcode = 1994PhRvL..73.3270M }}</ref> the temperature dependence of Shubnikov–de Haas oscillations;<ref name=Leadley/><ref name=DuSdH/> energy of the cyclotron resonance;<ref name=cfresonance/> spin polarization of the Fermi sea;<ref name=melinte/> and quantum phase transitions between states with different spin polarizations.<ref name=cfspin/><ref name=kukushkinspin/> Its typical value in GaAs systems is on the order of the electron mass in vacuum. (It is unrelated to the electron band mass in GaAs, which is 0.07 of the electron mass in vacuum.)
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| == Theoretical formulations ==
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| Much of the experimental phenomenology can be understood from the qualitative picture of composite fermions in an effective magnetic field. In addition, composite fermions also lead to a detailed and accurate microscopic theory of this quantum liquid. Two approaches have proved useful.
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| === Trial wave functions ===
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| The following trial wave functions<ref name=Jaincf/> embody the composite fermion physics:
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| <math> \Psi^{\rm FQHE}_{\nu}=P\;\; \Psi^{\rm IQHE}_{\nu^*} \prod_{j<k=1}^N(z_j-z_k)^{2p} </math>
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| Here <math>\Psi^{\rm FQHE}_{\nu}</math> is the wave function of interacting electrons at filling factor <math>\nu</math>; <math>\Psi^{\rm IQHE}_{\nu^*}</math> is the wave function for weakly interacting electrons at <math>\nu^*</math>; <math>N</math> is the number of electrons or composite fermions; <math>z_j=x_j+iy_j</math> is the coordinate of the <math>j</math>th particle; and <math>P</math> is an operator that projects the wave function into the lowest Landau level. This provides an explicit mapping between the integer and the fractional quantum Hall effects. Multiplication by <math>\prod_{j<k=1}^N(z_j-z_k)^{2p} </math> attaches <math>2p</math> vortices to each electron to convert it into a composite fermion. The right hand side is thus interpreted as describing composite fermions at filling factor <math>\nu^*</math>. The above mapping gives wave functions for both the ground and excited states of the fractional quantum Hall states in terms of the corresponding known wave functions for the integral quantum Hall states. The latter do not contain any adjustable parameters for <math>\nu^*=n</math>, so the FQHE wave functions do not contain any adjustable parameters at <math>\nu=n/(2pn\pm 1) </math>.
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| Comparisons with exact results show that these wave functions are quantitatively accurate. They can be used to compute a number of measurable quantities, such as the excitation gaps and exciton dispersions, the phase diagram of composite fermions with spin, the composite fermion mass, etc. For <math>\nu^*=1</math> they reduce to the [[Laughlin wavefunction]] <ref>{{cite journal |title=Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations |author=R.B. Laughlin |year=1983 |journal=[[Physical Review Letters]] |volume=50 |issue=18 |page=1395 |doi= 10.1103/PhysRevLett.50.1395|bibcode = 1983PhRvL..50.1395L }}</ref> at fillings <math>\nu=1/(2p+1)</math>.
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| === Chern–Simons field theory ===
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| Another formulation of the composite fermion physics is through a Chern–Simons field theory, wherein flux quanta are attached to electrons by a singular gauge transformation.<ref name=HLR/><ref>{{cite journal |title=Fractional quantum Hall effect and Chern–Simons gauge theories |author=A. Lopez and E. Fradkin |year=1991 |journal=[[Physical Review B]] |volume=44 |issue=10 |page=5246 |doi= 10.1103/PhysRevB.44.5246 |bibcode = 1991PhRvB..44.5246L }}</ref> At the mean field approximation the physics of free fermions in an effective field is recovered. Perturbation theory at the level of the random phase approximation captures many of the properties of composite fermions.
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| == See also ==
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| *[[Quantum Hall effect|Integer quantum Hall effect]]
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| *[[Fractional quantum Hall effect]]
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| ==External links==
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| *[http://rmp.aps.org/pdf/RMP/v71/i4/p875_1 Nobel Lecture: The fractional quantum Hall effect] by [[Horst Ludwig Störmer|H.L. Stormer]]
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| *Composite Fermions: New particles in the fractional quantum Hall effect, by H. Störmer and D. Tsui, Physics News in 1994, American Institute of Physics 1995, p. 33.
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| *[http://www.phys.psu.edu/~jain/cf.html Composite Fermion] at the [[Pennsylvania State University]]
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| *[http://www.fkf.mpg.de/klitzing/research_topics/research_topics_single.php?topic=Composite%20fermions Composite Fermions - von Klitzing's department] at the [[Max Planck Institute]]
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| *[http://www.aip.org/pnu/1994/split/pnu205-1.htm Composite fermions are real] at the [Physics News Update, [[American Institute of Physics]]
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| *[http://ptonline.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTOAD000046000007000017000001&idtype=cvips Half filled Landau level yields intriguing data and theory] in [[Physics Today]]
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| *[http://ptonline.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTOAD000053000004000039000001&idtype=cvips The composite fermion: A quantum particle and its quantum fluids] in [[Physics Today]]
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| == References ==
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| {{Reflist|2}}
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| [[Category:Hall effect]]
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| [[Category:Condensed matter physics]]
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| [[Category:Quantum phases]]
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