Graphene Band Structure

Physics: Graphene tight-binding: E(k) = ±t|f(k)| + t'·g(k) where f(k) = 1 + e^(ik·a₁) + e^(ik·a₂). Bands touch at K = (2π/3a, 2π/3√3a) and K' = −K (valley degeneracy g_v = 2). Near K: E ≈ ±ℏv_F|δk|, v_F = 3ta/2ℏ ≈ 10⁶ m/s with t ≈ 2.8 eV, a = 0.246 nm. Pseudospin conservation → chiral anomaly; Berry phase π around each Dirac point. Anomalous QHE: σ_xy = ±4(N+½)e²/h (factor 4 from spin × valley). Suspended graphene mobility > 200,000 cm²/Vs — highest among known materials. Bilayer graphene has parabolic touching (massive Dirac fermions).