number of filled Landau levels is called the filling factor, given by the expression Composite fermions form Landau-like levels in the effective magnetic field which are called composite fermion Landau levels or levels. One defines the filling factor for composite fermions as 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. Experimental manifestations The central statement of composite fermion theory is that the strongly correlated electrons at a magnetic field (or filling factor ) turn into weakly interacting composite fermions at a magnetic field (or composite fermion filling factor ). 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: Fermi sea The effective magnetic field for composite fermions vanishes for , where the filling factor for electrons is . Here, composite fermions make a Fermi sea. This Fermi sea has been observed at half filled Landau level in a number of experiments, which also measure the Fermi wave vector. Cyclotron orbits As the magnetic field is moved slightly away from , composite fermions execute semiclassical cyclotron orbits. These have been observed by coupling to surface acoustic waves, resonance peaks in antidot superlattice, and magnetic focusing. The radius of the cyclotron orbits is consistent with the effective magnetic field 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 . Also, the observed direction of trajectory is opposite to that of electrons when is anti-parallel to . Cyclotron resonance In addition to the cyclotron orbits, cyclotron resonance of composite fermions has also been observed by photoluminescence. Shubnikov de Haas oscillations As the magnetic field is moved further away from , quantum oscillations are observed that are periodic in These are Shubnikov–de Haas oscillations of composite fermions. 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. Integer quantum Hall effect With further increase in or