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The anomalous Hall effect should be present in the Gapped case as well (Although I don't know if it has been experimentally observed in a gapped system). The reason is that for massive Dirac Fermions, the effective Bloch dynamics is also governed by a Berry gauge field, this time a non-Abelian gauge field. Please see Chen, Pang, Pu and Wang equations ...


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This is my favorite graphene reference. It's more concerned with the high magnetic field behavior of graphene (quantum Hall regime), but it's introduction is still very well done. A few points: -The wavefunction is the sum of two Bloch functions (one for each sublattice of graphene). The tight binding approximation assumes that the electronic wavefunction ...


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You can only distinguish the sublattices in this case because you've tagged them A,B. The process of inversion only exchanges identical carbon with carbon, leaving the crystal physically unchanged. If you gave me a crystal with one orientation and I then returned it to you without telling you whether or not it's been inverted, you'd have no way of knowing. ...



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