A composite fermion is the topological bound state of an electron and an even number of quantized vortices, sometimes visually pictured as the bound state of an electron and, attached, an even number of magnetic flux quanta.
[1][2][3] Composite fermions were originally envisioned in the context of the fractional quantum Hall effect,[4] but subsequently took on a life of their own, exhibiting many other consequences and phenomena.
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 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[1][2][3] that electrons minimize their interaction by capturing quantized vortices to become composite fermions.
[5] The interaction between composite fermions themselves is often negligible to a good approximation, which makes them the physical quasiparticles of this quantum liquid.
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 behavior of composite fermions is similar to that of electrons in an effective magnetic field
Composite fermions form Landau-like levels in the effective magnetic field
This gives the following relation between the electron and composite fermion filling factors 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.
The central statement of composite fermion theory is that the strongly correlated electrons at a magnetic field
) turn into weakly interacting composite fermions at a magnetic field
These have been observed by coupling to surface acoustic waves,[7] resonance peaks in antidot superlattice,[8] and magnetic focusing.
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
From the analysis of the Shubnikov–de Haas experiments, one can deduce the effective mass and the quantum lifetime of composite fermions.
or decrease in temperature and disorder, composite fermions exhibit integer quantum Hall effect.
, correspond to the electrons fillings Combined with which are obtained by attaching vortices to holes in the lowest Landau level, these constitute the prominently observed sequences of fractions.
Other fractions have been observed, which arise from a weak residual interaction between composite fermions, and are thus more delicate.
[15] A number of these are understood as fractional quantum Hall effect of composite fermions.
The pairing of composite fermions opens a gap and produces a fractional quantum Hall effect.
[24] The fractional quantum Hall states as well as composite fermion Fermi sea are also partially spin polarized for relatively low magnetic fields.
[24][25][26] 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.
The mass of composite fermions has been determined from the measurements of: the effective cyclotron energy of composite fermions;[27][28] the temperature dependence of Shubnikov–de Haas oscillations;[13][14] energy of the cyclotron resonance;[12] spin polarization of the Fermi sea;[26] and quantum phase transitions between states with different spin polarizations.
[24][25] Its typical value in GaAs systems is on the order of the electron mass in vacuum.
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.
The right hand side is thus interpreted as describing composite fermions at filling factor
Comparisons with exact results show that these wave functions are quantitatively accurate.
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.
Perturbation theory at the level of the random phase approximation captures many of the properties of composite fermions.