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We present an investigation into the manipulation of nuclear spins near the ν="1 quantum Hall state of GaAs/AlGaAs using optical pumping methods.
It is noted that the SdH formula is derived without considering quantum localization effects which give rise to formation of quantum Hall state.
Further considering the Rashba SOI, a valley-polarized quantum anomalous Hall state is predicted in silicene owing to the topological phase transition [31].
Most importantly, the onset of strong localization which gives rise to the formation of quantum Hall state does not correspond to the direct I-QH transition.
The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers.
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A letter from lawyers to City Hall states: "It is suspected that the decision to erect the fencing was made for the sole or primary purpose of preventing Occupy Democracy from holding any demonstration on PSG [Parliament Square Garden].
Moreover, the observed oscillations for B > B c do not always correspond to formation of quantum Hall states.
We find that interactions drive spontaneous breaking of the emergent SU 4) symmetry of the graphene Landau levels, leading to a variety of non-trivial integer and fractional quantum Hall states.
It is known that in the low disorder or high B limit, the filling factor of a resistivity (or conductivity) peak is given exactly by the average value of the filling factors of the two adjacent quantum Hall states [15].
Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a variational solution, known as the Laughlin wavefunction.
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