3D Dirac Semimetal — Linear Band Crossing

Parameters

Fermi velocity v_F: 1.0 Mass term m (breaks Dirac): 0.0 Chemical potential μ: 0.0 k_z (axial momentum): 0.0

H(k) = v_F(k·σ) + mσ_z
E±(k) = ±√(v_F²|k|² + m²)
Dirac point: m=0, |k|=0
Two Dirac nodes at ±k_D on k_z-axis

A 3D Dirac semimetal hosts 4-fold degenerate band crossings protected by crystal symmetry. Each Dirac point splits into two Weyl nodes upon breaking inversion or time-reversal symmetry.