K-Paths & Brillouin Zone

FCC Brillouin Zone

EmpiricalTightBinding.jl provides high-symmetry k-points for the FCC/zinc-blende Brillouin zone (in units of 2π/a):

PointCoordinates
Γ(0, 0, 0)
X(1, 0, 0)
L(1/2, 1/2, 1/2)
K(3/4, 3/4, 0)
U(1, 1/4, 1/4)
W(1, 1/2, 0)

Predefined Paths

  • vogl_kpath(; nk=100): L → Γ → X → U,K → Γ (Vogl Fig.1)
  • textbook_kpath(; nk=100): L → Γ → X

Custom Paths

Build custom paths with make_kpath:

# W → L → Γ → X → W → K
kp = make_kpath([:W => :L, :L => :Γ, :Γ => :X, :X => :W, :W => :K])

Discontinuities

Use nothing to indicate a jump (e.g., U,K point in the Vogl path):

kp = make_kpath([
    :L => :Γ, :Γ => :X, :X => :U,
    nothing,
    :K => :Γ
])