The fractional quantum Hall (FQH) states with higher Landau levels have new characters different from those with . The FQH states at are examined by developing the Tao-Thouless theory. We can find a unique configuration of electrons with the minimum Coulomb energy in the Landau orbitals. Therein the electron (or hole) pairs placed in the first and second nearest Landau orbitals can transfer to all the empty (or filled) orbitals at , 14/5, 7/3, 11/5, and 5/2 via the Coulomb interaction. More distant electron (or hole) pairs with the same centre position have the same total momentum. Therefore, these pairs can also transfer to all the empty (or filled) orbitals. The sum of the pair energies from these quantum transitions yields a minimum at . The spectrum of the pair energy takes the lowest value at and a higher value with a gap in the neighbourhood of because many transitions are forbidden at a deviated filling factor from . From the theoretical result, the FQH states with are stable and the plateaus appear at the specific filling factors . 1. Introduction The plateau at the filling factor attracts a great deal of attention because of a new fractional quantum Hall (FQH) character. The plateau in the filling factor has characters different from that at . For example, Pan et al. [1] have found a deep minimum of the diagonal resistance, and , at and . At and the diagonal resistance exhibits a strongly anisotropic behaviour, where has a sharp peak while has a minimum at [1–3]. (The definition of the coordinate axes, , , and , will be shown in Figure 5 of the next section.) Eisenstein et al. [4] have obtained the plateaus of Hall resistance at and with even denominator. Furthermore, the other plateaus have been discovered at , and with odd denominator as seen in Figure 1. Figure 1: Behavior of Hall resistance in the region of quoted from [ 4]. The plateaus have the precise Hall resistance value. For example, the plateau at has the Hall resistance value within 0.015% as measured in [4]. This accuracy of the Hall resistance indicates that the state has a lower energy than the one at . Further experimental data are shown in Figure 2 which have been observed by Dean et al. [5] and Xia et al. [6]. The Hall resistance-curve in the left panel of Figure 2 [5] is different from that in the right panel [6]. This difference means that the shape of the Hall resistance versus magnetic field curve depends on the samples and the experimental conditions (magnetic field strength, etc.). In particular, the difference is large at . Figure 2: Hall resistance curve in the region
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