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Using a general symmetry-based approach, we provide a classification of generic miniband structures for electrons in graphene placed on substrates with the hexagonal Bravais symmetry.
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The Hamiltonian in the vicinity of other two inequivalent points on the sBZ edge, 𝝁 ′ = R ^ 2 π / 3 𝝁 \bm{\mu}^{\prime}=\hat{R}_{2\pi/3}\bm{\mu} , 𝝁 ′′ = R ^ 4 π / 3 𝝁 \bm{\mu}^{\prime\prime}=\hat{R}_{4\pi/3}\bm{\mu} , can be obtained using H 𝝁 + 𝒒 = H 𝝁 ′ + R ^ 2 π / 3 𝒒 = H 𝝁 ′′ + R ^ 4 π / 3 𝒒 H_{\bm{\mu}+\bm{q}}=H_{\bm{\mu}^{\prime}+\hat{R}_{2\pi/3}\bm{q}}=H_{\bm{\mu}^{\prime\prime}+\hat{R}_{4\pi/3}\bm{q}}
Cited in the paper.
Note that the spectra derived from H ^ ζ ( 𝜿 + 𝒒 ) \hat{H}_{\zeta(\bm{\kappa}+\bm{q})} obey the three-fold rotational symmetry
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2012
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M. Kindermann, B. Uchoa, D. L. Miller, Phys. Rev. B 86
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J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, Phys. Rev. B 86
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