Composite fermions

A composite fermion is the 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. Composite fermions were originally envisioned in the context of the fractional quantum Hall effect, but subsequently took on a life of their own, exhibiting many other consequences and phenomena.

Vortices are an example of topological defect, and also occur in other situations. Quantized vortices are found in type II superconductors, called Abrikosov vortices. Classical vortices are relevant to the Berezenskii–Kosterlitz–Thouless transition in two-dimensional XY model.

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 that electrons minimize their interaction by capturing quantized vortices to become composite fermions. 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 magnetic field seen by composite fermions is given by

where ${\displaystyle B}$ is the external magnetic field, ${\displaystyle 2p}$ is the number of vortices bound to composite fermion (also called the vorticity or the vortex charge of the composite fermion), ${\displaystyle \rho }$ is the particle density in two dimensions, and ${\displaystyle \phi _{0}=hc/e}$ is called the “flux quantum” (which differs from the 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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