Nodal Line Semimetal — Drumhead Surface States

Zero-Energy Surface Flat Band

A nodal-line semimetal has band crossings that form a closed loop (nodal ring) in the 3D Brillouin zone, rather than isolated Weyl points. The ring is protected by mirror or PT symmetry.

Projected onto a surface, the nodal ring becomes a region bounded by the projected loop. Inside this region, a drumhead surface state appears — a nearly flat band at zero energy (like the membrane of a drum).

Examples: Ca₃P₂, Cu₃PdN, ZrSiS. The flat band has enormous DOS, potentially leading to exotic magnetism or superconductivity.

H(k) = (k_x²+k_y²−k_0²)σ_z + k_z σ_x
Nodal ring: k_x²+k_y²=k_0², k_z=0
Surface state: E≈0 inside ring projection
DOS(E→0) → ∞ (flat band)