Quantum statistical theory of the fermionic quantum Hall effect

At the even-denominator filling factor nu=P/Q, even Q, a fermionic Quantum Hall (QH) state is normally developed in a pure heterojunction GaAs/AlGaAs at the lowest temperatures. The QH state at nu=5/2 is an exception, and it is known to be bosonic. The fermionic state is formed by the composite (c-) fermions, each with an electron and Q flux quanta (fluxons). The conductivity sigma=J/E, J= current density, E= applied field, becomes a universal constant (e(2)/h)Q(-1) as the temperature approaches zero while the Hall conductivity sigma(H)=J/E-H, E-H=Hall field, becomes approximately equal to (e(2)/h)P/Q. The widths in the resistivity rho=sigma(-1) are symmetric with respect to high and low fields. They are temperature dependent. The resistivity (rho) curve smoothly approaches a constant as the field is lowered toward zero.