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Transport theory. (English) Zbl 1179.82029

Summary: The unusual quantum Hall effect (QHE) in graphene is often discussed in terms of Dirac fermions moving with a linear dispersion. A new theory describing the same phenomena is presented in terms of the more traditional composite bosons. The “electron” (wave packet) is shown to move easier in the direction [110] \(\equiv \) [110 \(c\)-axis] of the honeycomb lattice than perpendicular to it, while the “hole” moves easier in [001]. Since “electrons” and “holes” move in different channels, the number densities can be very high especially when the Fermi surface has “necks”. The strong QHE at filling factor \(\nu = 2\) arises from the “neck” Fermi surfaces.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
81V70 Many-body theory; quantum Hall effect
81V45 Atomic physics
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