Abstract
The fractional quantum Hall (FQH) states with higher Landau levels have new characters different from those with 0<ν<2. The FQH states at 2<ν<3 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 ν0=8/3, 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 ν=ν0. The spectrum of the pair energy takes the lowest value at ν0 and a higher value with a gap in the neighbourhood of ν0 because many transitions are forbidden at a deviated filling factor from ν0. From the theoretical result, the FQH states with ν=ν0 are stable and the plateaus appear at the specific filling factors ν0.
Highlights
The plateau at the filling factor ] = 5/2 attracts a great deal of attention because of a new fractional quantum Hall (FQH) character
As will be shown below, in the region of 2.5 < ] < 3, we find fractional filling factors where both first and second nearest electron pairs can transfer to all the empty Landau orbitals with L = 1
We examine the exact energy of any FQH state
Summary
These experimental findings at ] > 2 have stimulated theoretical studies. Morf argued the quantum Hall states at ] = 5/2 by a numerical diagonalization [21] He studied spin-polarized and -unpolarized states with N ≤ 18 electrons. Their results are based on numerical studies for up to 16 electrons in two geometries: sphere and torus They found a first order phase transition from a striped state to a strongly paired state. The fundamental properties will be shortly summarized for the quasi-2D electron system below
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