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In quantum mechanics, the energies of cyclotron orbits of charged particles in a uniform magnetic field are quantized to discrete values, thus known as Landau levels. These levels are degenerate , with the number of electrons per level directly proportional to the strength of the applied magnetic field.
The fractional quantum Hall effect is more complicated and still considered an open research problem. [2] Its existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was a quantum Hall effect without Landau levels. [3] This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect.
In a quantum oscillation experiment, the external magnetic field is varied, which causes the Landau levels to pass over the Fermi surface, which in turn results in oscillations of the electronic density of states at the Fermi level; this produces oscillations in the many material properties which depend on this, including resistance (the ...
That is, the distribution of energy levels for small-scale changes in the applied magnetic field recursively repeats patterns seen in the large-scale structure. [1] " Gplot", as Hofstadter called the figure, was described as a recursive structure in his 1976 article in Physical Review B , [ 1 ] written before Benoit Mandelbrot 's newly coined ...
In condensed matter physics, the Laughlin wavefunction [1] [2] is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas placed in a uniform background magnetic field in the presence of a uniform jellium background when the filling factor of the lowest Landau level is = / where is an odd positive integer.
Fractional Chern insulators (FCIs) are lattice generalizations of the fractional quantum Hall effect that have been studied theoretically since 1993 [1] and have been studied more intensely since early 2010. [2] [3] They were first predicted to exist in topological flat bands carrying Chern numbers. They can appear in topologically non-trivial ...
The fan diagram of the composite fermion Landau levels has been determined by transport, and shows both spin-up and spin-down composite fermion Landau levels. [24] The fractional quantum Hall states as well as composite fermion Fermi sea are also partially spin polarized for relatively low magnetic fields. [24] [25] [26]
Fig 1 shows the Fermi energy E F located in between [1] two Landau levels. Electrons become mobile as their energy levels cross the Fermi energy E F. With the Fermi energy E F in between two Landau levels, scattering of electrons will occur only at the edges of a sample where the levels are bent. The corresponding electron states are commonly ...