bandContact

Band contact is a term used in solid-state physics to describe a point in momentum space where two energy bands of a crystalline solid become degenerate, meaning their energies are equal and the band gap vanishes at that point. Such contacts are the opposite of a band gap, where a finite energy separation remains between the valence and conduction bands. Band contacts are central to the classification of materials as metals, semimetals, or insulators and to the study of electronic transport and optical properties.

Band contacts can occur for symmetry reasons, where crystal symmetries protect a crossing, or arise accidentally when system parameters (such as pressure, strain, or composition) bring bands into alignment. Spin-orbit coupling can lift or preserve degeneracy depending on the symmetry of the crystal and the involved bands. In three-dimensional systems, band contacts often appear as discrete points known as Dirac or Weyl nodes when the crossing is linear in momentum, forming Dirac or Weyl semimetals. In two dimensions, graphene’s Dirac points are a canonical example of band contacts with linear dispersion.

Examples and implications: graphene exhibits band contact points at the K and K' points, yielding massless Dirac fermions and high mobility. In three-dimensional materials, Dirac and Weyl semimetals host band-contact points that lead to unusual transport phenomena and nontrivial topology. Band contacts influence electron dynamics, optical responses, and can give rise to topological surface states.

Terminology: the expression “band contact” is less common than “band touching point” or “degenerate point,” and literature may vary in usage. Nonetheless, band contacts remain a key concept for understanding gapless electronic excitations in solids.