1 The Unified Interpretation for Quantum Hall Effects Mengqi Wu1 and Wei Wu21 The 802nd Research Institute, Shanghai Academy of Spaceflight Technology, China 207 Li Ping Road, Shanghai, China, 200090 2Shanghai Office of STMicroelectronics (Shanghai) Co., Ltd. E-mail: mengqi.wu163.com Abstract: Based on the potential energy expression for carriers in magnetic field, and two stability conditions of circular harmonic oscillator and linear harmonic oscillator, a new energy levels formula of Hall effects was founded, and then the unified interpretation for quantum Hall effects of integer and fraction can be obtained. The “filling factors” of integer quantum Hall effect and “fraction charges” of fraction quantum Hall effect all have a corresponding energy level in new formula. The corresponding connection between the energy level with filling factors or fraction charges are showed by a table; the fundamental parameter of carriers on different energy level are figured out; three models of quantum Hall effects are differentiated; the interpretation of Hall resistance plateaus are obtained by use the velocity distributions of carriers; further, a new viewpoint that the samples of quantum Hall effect are the Quantum Superconductor at the same time was put forward. Based on the spin of electron, an inverse Hall effect shall be produced when the carrier is electron. Keywords: quantum Hall effects, energy level, filling factor, fraction charge, Hall resistance plateaus 1 Introduction As known, general Hall effects (GHE) can be analyzed according to Lorentz force; the integer quantum Hall effects (IQHE) must count Landau energy level 1-9; the fraction quantum Hall effects (FQHE) must count the strong interaction between the electrons, assuming existence of fraction electric charge 5-8, although different Hall effects (including GHE, IQHE and FQHE) are very harmonious on same experimental curves 6-8. All unified explanations so far are unsatisfactory 9-12 because there are no unified mechanism and calculation methods. A significant amount of experimental and theoretical researches are continuing today 13-19. Our new explanation preserves the traditional theory, overcomes the shortcoming in explaining http:/www.paper.edu.cn 2 quantum Hall effects, and proves that the assumptions on filling factor and fraction charge are no longer necessary. We conclude that Landau energy level formula (LELF) is not suitable to describe quantum Hall effects because it is only based on the model of linear harmonic oscillator (LHO). Only the LHO model is different from true motion of electrons in uniform magnetic field. This paper indicates that a moving electron in magnetic field can obtain additional momentum and energy, which depends only on magnetic potential Ar(section 2). In fact, true motion of electrons is a doublet of beeline and orbiting in Hall effects (see Fig. 1). Therefore, supplement of LELF must be based on the doublet of both LHO and Circular Harmonic Oscillator (CHO). Following analysis of doublet, we obtained a stability condition of the doublet and a new LELF for quantum Hall effects (section 3 and 4). Some basic parameters of moving electrons and formula of quantum Hall resistance are obtained for different energy levels (section 5 and 6). The relationship of quantum Hall resistance and superconductivity, relationship of energy levels and the filling factors or fraction charges, and three models of quantum Hall Effects are discussed (section 7-9). We indicate that every Hall sensor of quantum Hall effect also is also a superconductor; therefore the quantum Hall effect can also be called Quantum Superconductivity Effect. We proved that quantum Hall resistances are only dependent of energy level and stability condition, and are independent of the fraction charge and the filling factor. We find a new quantum Hall effect model that quantum Hall resistance can be in inverse proportion to the magnetic field. Further, quantum Hall resistance plateaus are explained by velocity distribution of orbiting electrons (section 10). We also present an inverse effect of Hall effects that is based on spin of electrons (section 11). In this paper, the electrons all can be replaced by any carriers in quantum Hall effects, with no effect on our analysis. The mechanism and calculation methods of quantum Hall effects are based on the doublet of the CHO and LHO on Hall surface. Unifying the explanations of quantum Hall effects is not only possible, but is also independent of the assumption on fraction charges and filling factors. Finally, the reason that people could not obtained a unified explanation of quantum Hall effects stems from the fact that some http:/www.paper.edu.cn 3 basic laws of moving electron in magnetic field were not well used in electromagnetic theory. 2 Obtained potential energy by orbiting electron in uniform magnetic field I