Excitonic insulator: In a narrow-gap semiconductor or semimetal, Coulomb attraction between conduction-band electrons and valence-band holes can spontaneously form exciton pairs, analogous to Cooper pairs in BCS. The order parameter Δ = U⟨c†_k v_k⟩ satisfies a gap equation identical to BCS: Δ = U Σ_k Δ/(2E_k), where E_k = √((ξ_k)²+Δ²). For E_g > 0 (semiconductor), this is BEC-like (preformed excitons condense). For E_g < 0 (semimetal), it is BCS-like (Fermi surface instability). The BCS-BEC crossover is tunable via pressure, strain, or electric field.