Abstract
We have investigated the Fractional Quantum Hall Effect (FQHE) on the fundamental Hamiltonian with the Coulomb interactions between normal electrons without any quasi particle. The electron pairs placed in the Landau orbitals can transfer to many empty orbitals. The number of the quantum transitions decreases discontinuously when the filling factor v deviates from the specific fractional number of v0. The discontinuous decreasing produces the energy valley at the specific filling factors v0 = 2/3, 4/5, 3/5, 4/7, 3/7, 2/5, 1/3 and so on. The diagonal elements of the total Hamiltonian and the number of the quantum transitions give the total energy of the FQH states. The energy per electron has the discontinuous spectrum depending on the filling factor v. We obtain the function form of the energy per electron in the quantum Hall system. Then the theoretical Hall resistance curve is calculated near several filling factors. Therein the quantum Hall plateaus are derived from the energy valleys. The depths of the energy valleys are compared with the widths of the quantum Hall plateaus appearing in the experimental data of the Hall resistance. Our theoretical results are in good agreement with the experimental results.
Highlights
The quantum Hall effect is derived by the total Hamiltonian HT of a many-electron system which is composed of the single electron Hamiltonian H0,i of the i-th electron and the Coulomb interaction between electrons as follows: How to cite this paper: Sasaki, S. (2015) Relation between Fractional Quantum Hall Effect (FQHE) Plateau Width and Valley Energy
The total energy of the quantum Hall system is the sum of W and all the pair energy of electrons, because the Coulomb interaction works between two electrons
The theoretical results are in good agreement with the experimental data
Summary
The quantum Hall effect is derived by the total Hamiltonian HT of a many-electron system which is composed of the single electron Hamiltonian H0,i of the i-th electron and the Coulomb interaction between electrons as follows: How to cite this paper: Sasaki, S. (2015) Relation between FQHE Plateau Width and Valley Energy. The classical Coulomb energy becomes a minimum for only one electron configuration in the Landau orbitals. This property has been proven in the previous paper [9]. All the electron pairs placed in the nearest Landau orbitals can transfer to all the empty orbitals at the specific filling factors ν 0. The total energy of the quantum Hall system is the sum of W (expectation value of HT ) and all the pair energy of electrons (placed in nearest orbital pairs and more distant orbital pairs), because the Coulomb interaction works between two electrons. The valley depth in the pair energy and the function form of W give the quantum Hall plateaus at the specific filling factors ν 0. The theoretical results are in good agreement with the experimental data
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
