2D Nodal-Line Semimetal: Drumhead Surface States

Band Model Parameters

Nodal-ring radius k₀ 0.80

k_z dispersion m 1.00

Surface hybridization ε 0.00

Show bulk gap heatmap

Live Readouts

Nodal ring radius |k|

0.80

Berry phase around ring

180.0°

Drumhead bandwidth

0.000

How it works

2D companion to the 3D rendered scene: the identical minimal two-band model of a nodal-line semimetal (Weng-type), read off a top-down kx-ky heatmap instead of a rotatable 3D surface.

H(k) = (kx² + ky² + kz² − k0²) σx + m·kz σy

Eigenvalues: E±(k) = ± sqrt{ (kx²+ky²+kz²−k0²)² + (m·kz)² }

The main panel is the k_z=0 slice: the gap E+ vanishes only where kx²+ky²=k0², drawn as the glowing orange nodal ring. Everywhere else on the heatmap the color encodes the bulk gap magnitude — dark near the ring, brightening outward and inward. The drumhead disk (kx²+ky²<k0²) is the topologically protected, nearly dispersionless surface band that appears on a slab cut through the ring's interior; the ε slider domes it away from perfectly flat, as real finite-thickness slabs do, and orbiting dots represent its surface-state density.

The lower panel is a local cross-section near the ring in coordinates u = |k_∥| − k0 and v = k_z, where the Hamiltonian is H = (2k0u+u²+v²) σx + (m·v) σy — an ordinary Dirac-cone gap map. The green circle is the loop used for a discretized Wilson-loop calculation of the Berry phase; it stays pinned at exactly 180° regardless of k0 or m, which is the topological invariant guaranteeing the drumhead band survives smooth deformations — only closing the ring itself can remove it.

Nodal ring (bulk gap = 0) Bulk gap heatmap E+(kx,ky,0) Drumhead surface states

Local Dirac cone (u,v) & Berry loop