Twisted Bilayer Graphene: Magic Angle Simulator

Twist Angle

⚡ Magic angle — flat bands

Twist angle θ 2.50°

Moiré period

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Band flatness

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Effective mass

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Est. T꜀

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Electrons & Temperature

Filling ν (e⁻ / moiré cell) 0.0

Temperature T 4.0 K

R / R_N at T

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Regime

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How this works

Two honeycomb graphene sheets are stacked with a relative twist θ. Overlaying two periodic lattices at an angle produces a much larger-scale moiré beat pattern with period L = a / (2·sin(θ/2)), where a is graphene's atomic lattice constant — so a tiny twist yields a huge superlattice.

Near θ ≈ 1.1° (the "magic angle"), interlayer tunneling between the sheets nearly cancels the electrons' kinetic energy, crushing the conduction and valence bands into an almost flat band. Flat bands mean electron-electron interactions dominate over kinetic motion, which is what opens the door to correlated-insulator and unconventional-superconductor phases as the flat band is filled.

Twist angle — sets the moiré period and, via the model band-flatness curve below, how flat the low-energy bands become.
Filling ν — electrons packed into the moiré unit cell; the simulated superconducting dome only turns on near ν ≈ ±2 and near the magic angle.
Temperature — the resistance curve is a simplified model (sigmoid drop for correlated/SC-like regimes, linear-ish otherwise), not a first-principles transport calculation.

Layer 1 (bottom) Layer 2 (twisted)

moiré view — top down

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Electronic band structure (near Fermi level)

Resistance vs. temperature

Twisted Bilayer Graphene: Magic-Angle Simulator