Question

Dirac quantization relation says that the electric charge must be quantized if there is a magnetic monopole in our universe. But the fractional quasi-particles and quasi-holes in FQHE have fractional charge, while I haven't seen any argument on their contradiction with Dirac quantization, so do they violate this relation? Intuitively, I suppose no but I do not find a proper argument. I know that for a deconfined quark with e/3 electric charge, one can say that they gain an extra phase from the SU(3) gauge group when the monopole also carries a color magnetic charge, then by summing the contribution together we get the correct answer. But there seems no other gauge group here for FQHE, so is it the topological degeneracy that plays the role? Or will the monopole need to be put outside the FQHE material, and the boundary state will cancel the fractional phase?

Answer 1

The fractional quasi-particles and quasi-holes in FQHE do not violate the Dirac quantization relation. They are emergent phenomena that arise from the collective behavior of electrons in the presence of strong magnetic fields and are not isolated particles in free space. The topological properties of the FQHE system ensure that the total charge of the system remains quantized.

Step-by-step explanation:

The fractional quasi-particles and quasi-holes in FQHE (Fractional Quantum Hall Effect) do not violate the Dirac quantization relation. The Dirac quantization relation states that the electric charge must be quantized. However, in the case of FQHE, the fractional charges of the quasi-particles and quasi-holes do not exist as isolated particles in free space. Instead, they are emergent phenomena that arise from the collective behavior of electrons in the presence of strong magnetic fields.

These fractional charges are not fundamental particles, but rather, they are quasiparticles that have fractional charge due to the topological properties of the FQHE system. The topological degeneracy and the unique properties of the FQHE state ensure that the total charge of the system remains quantized, even though individual particles may carry fractional charges.

Therefore, the presence of fractional quasi-particles and quasi-holes in FQHE does not contradict the Dirac quantization relation.