freeelectronlike

Freeelectronlike describes electronic states in a solid that behave similarly to free electrons. In practice, it refers to bands whose energy-versus-momentum dispersion is close to parabolic and whose effective mass is near the bare electron mass. This behavior emerges when the lattice potential is weak or when electrons are highly delocalized, so Bloch states resemble plane waves.

In the nearly free-electron model, conduction electrons move in a uniform positive background. The energy as a function of crystal momentum k can be approximated by E(k) = E0 + ħ^2 k^2 / (2m*), with m* the effective mass. For many simple metals, m* ≈ m_e and the Fermi surface is nearly spherical, supporting a free-electron gas description of metallic behavior.

Where observed: Alkali metals such as sodium and potassium are classic examples of free-electronlike conduction bands. Some noble metals also display free-electron-like behavior near the Fermi level, although contributions from d bands introduce deviations at higher binding energies.

Limitations and deviations: Real materials have a periodic lattice potential that produces band structure and gaps, leading to anisotropy and non-parabolic dispersion near Brillouin zone boundaries. Electron-electron interactions and spin-orbit coupling can further modify the dispersion. The freeelectronlike view is therefore a useful first-order approximation and is commonly employed in models of metallic conductivity and plasmon dispersion within the free-electron gas or jellium frameworks.

See also: nearly free electron model, free-electron model, effective mass, jellium, band structure.