Abstract
Fractional quantum Hall effect (FQHE) is investigated by employing normal electrons and the fundamental Hamiltonian without any quasi particle. There are various kinds of electron configurations in the Landau orbitals. Therein only one configuration has the minimum energy for the sum of the Landau energy, classical Coulomb energy and Zeeman energy at any fractional filling factor. When the strong magnetic field is applied to be upward, the Zeeman energy of down-spin is lower than that of up-spin for electrons. So, all the Landau orbitals in the lowest level are occupied by the electrons with down-spin in a strong magnetic field at 1 ν . On the other hand, the Landau orbitals are partially occupied by up-spins. Two electrons with up-spin placed in the nearest orbitals can transfer to all the empty orbitals of up-spin at the specific filling factors and so on. When the filling factor ν deviates from ν0, the number of allowed transitions decreases abruptly in comparison with that at ν0. This mechanism creates the energy gaps at ν0. These energy gaps yield the fractional quantum Hall effect. We compare the present theory with the composite fermion theory in the region of 2/3 ν .
Highlights
The composite fermion theory introduces a quasi-particle named composite fermion which is an electron bound by even number 2 p of flux quanta
On the other hand the Landau orbitals are partially occupied by up-spins
In this paper we investigate only the case of a strong magnetic field.) The up-spin electron pair placed in the nearest orbitals can transfer to all the empty orbitals of up-spin at ν0 =(4 j +1) (2 j +1), ν0 =(3 j −1) (2 j −1) and so on
Summary
The composite fermion theory introduces a quasi-particle named composite fermion which is an electron bound by even number 2 p of flux quanta. The direction of the effective field, the kind of particle (hole or electron) and the number of attached flux quanta are assumed to change with variation of the filling factor. (Note: In the previous papers [15]-[19] we have already examined the case of a weak magnetic field In the case both down- and up-spin-electrons partially occupy the lowest Landau orbitals. This special case appears in a weak magnetic field by adjusting the gate voltage. These energy gaps can explain the fractional quantum Hall effect in the region 1 2 in the previous articles [20]-[30].)
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