Graphene Dirac Cone under Uniaxial Strain — DFT

Band structure evolution from 0% to 20% uniaxial strain
π and π* band evolution along Γ → M → K → Γ across 11 strain levels (0–20%)
Gap: 0 → 2.85 eV 11 strain levels QE · PBE/PAW · 2D k-scan

First-principles PBE study (Quantum ESPRESSO) of how the Dirac cone in graphene responds to uniaxial tensile strain along the zigzag direction, from 0% to 20% in 2% steps. The key methodological contribution: a 2D k-scan around the K point at selected strain levels revealed that the standard 1D band path overestimates the gap by 23× at 4% strain — the apparent 479 meV gap reduces to 21 meV once the actual (shifted) Dirac point is located. This makes the Fermi velocity asymmetry a practical diagnostic: the ratio of M→K to K→Γ band slopes tracks whether a gap is a geometric path artifact or a true topological transition. Three regimes emerge cleanly — cone survives (0–4%), cone deforming (6–10%), cone destroyed (>10%) — with the critical strain appearing lower than simple tight-binding predictions (~10% vs ~20%), attributed to DFT capturing bond-weakening and orbital rehybridization absent from the tight-binding model. Structural relaxation under each strained cell (BFGS, fixed cell) confirmed that sublattice shifts grow from ~0.001 to ~0.016 crystal units at 20%, making internal relaxation non-negligible at large deformation.

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Band gap at K and Fermi velocity vs. strain
Top: gap at K grows approximately linearly with strain. Bottom: Fermi velocity from M→K and K→Γ directions. Velocity divergence above ~6% marks the transition from shifted Dirac cone to true gap opening.
2D k-scan gap map around K at 4% and 10% strain
Band gap mapped on a 21×21 k-grid around K. At 4% (left), the Dirac point has shifted off the nominal K with a true gap of only 21 meV. At 10% (right), the 71 meV minimum gap and elongated gap valley confirm the cone is on the verge of destruction — a result invisible on the standard 1D path.