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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 ...


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. ...


In a 2deg this is straightforward to measure from the temperature dependence of the shubnikov de haas oscillations, which depends directly on vf.


According to @Bercioux answer, if we choose the basis: $$ \phi_1=(\Psi_{A+},\Psi_{B+},\Psi_{A-},\Psi_{B-},\Psi_{A+}^\dagger,\Psi_{B+}^\dagger,\Psi_{A-}^\dagger,\Psi_{B-}^\dagger) $$ The BdG Hamiltonian should be written like this: $$ H_{BdG}^1=\begin{pmatrix}H_+-E_F&0&0&\Delta_2\\0&H_--E_F&-\Delta_2&0\\ ...

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