A Dirac semimetal hosts a linear band crossing at isolated Dirac points in momentum space. The low-energy quasiparticles are massless Dirac fermions described by the 2D Dirac equation, carrying a Berry phase of π around the Dirac point.
Dirac dispersion: E±(k) = ±ℏv_F√(k² + m²). At m=0, the bands cross linearly — a protected Dirac point. The crossing is protected by combined time-reversal and inversion symmetry; breaking either gaps the cone (gives a Chern insulator). Left: band structure E(kₓ) along one direction. Right: 2D Fermi surface in (kₓ,kᵧ) plane at the selected Fermi energy — for |E_F| small, this is two Dirac points (dots); for larger |E_F| it expands into circular pockets. The Berry phase γ = π around each Dirac point leads to weak antilocalization.