Moiré Interference Pattern

Pattern Type

Spacing d₁ 20px Spacing d₂ 22px Angle θ 5° Animate 0°/s Line width 1.5

Math

k₁ = 2π/d₁
k₂ = 2π/d₂
Δk = k₁ - k₂
Beat Λ = 2π/|Δk|
——
Λ = ∞

About

Moiré patterns arise when two periodic grids overlap with a slight difference in spacing or angle. The interference creates a new pattern with wavelength Λ = d₁d₂/|d₁−d₂| (spacing beat) or Λ = d/(2sin(θ/2)) (angle beat). Graphene bilayers at the "magic angle" ~1.1° show superconductivity through Moiré flat bands.