The proof of 101 different fractions which occur in the quantum Hall effect is reported. One factor arises from the Bose-Einstein statistics for Landau levels so that the eigen values are proportional to (n+1/2). Another factor arises from the spin and the orbit. Some of the fractions arise because of a transition to zero-energy state while others arise from the transition's amongst levels. These transitions create quasiparticles in the system so that the moving quasiparticles can combine to make new two or three particle states. The energy spectrum has a variety of quasiparticles so that in a given cluster, the spin can be a fraction like 1/2, 3/2, … or an integer like, 0, 1, 2, …. The integer spin gives rise to even denominators such as 1/2, 5/2, 7/2, 3/2, 1/6, 5/6, 3/10, 7/10, etc. There is considerable clustering of electrons in the sample. The unit of flux quantum is φo = hc/e so that flux can quantize in units of n'φo (n' = integer). For n' = 2, the plateaus can occur at 3/8, 5/8 and 29/8. The state at 1/2 is four-fold degenerate and hence can not be described as a paired state. The factor of 8 in the denominator is a result of 1/2 from Bose-Einstein distribution, 1/2 from l and s and 1/2 from the flux quantum. But another 1/2 can arise from the cyclotron frequency. Hence there are four sources of 1/2 out of which only three are needed to obtain 1/8. Hence 3/8, 5/8 and 29/8 can not be described by a Pfaffian determinant which gives only a two particle state. However, some of the states are paired.
Frontiers in Physics: 3rd International Meeting
- Pub Date:
- July 2009
- Boson systems;
- Transition metals and alloys;
- Scattering by phonons magnons and other nonlocalized excitations;
- Oscillators pulse generators and function generators