Halfvulling

Halfvulling, translating to half filling in English, is a term used in condensed matter physics to denote the electron density in lattice models where the average number of electrons per lattice site equals one when two spin states are possible. For a lattice with a maximum occupancy of two electrons per site, half filling corresponds to n = 1. In non-interacting tight-binding models, half filling means the Fermi energy lies at the middle of the electronic band and the system exhibits particle–hole symmetry.

In systems with strong electron–electron interactions, such as the Hubbard model, half filling is special because the repulsion U can open a Mott gap, turning a would-be metal into a Mott insulator at low temperatures. The occurrence and nature of the transition depend on dimensionality, lattice geometry, and the ratio U/W. At half filling, many lattices also support antiferromagnetic order via superexchange between neighboring spins.

Doping away from half filling (adding or removing electrons) changes the electronic properties, often driving metal–insulator transitions, superconductivity, or other correlated phases depending on material and model. In ultracold-atom experiments with optical lattices, achieving half filling is a common target for realizing Mott insulating states with one particle per site.

Note that the term half filling is context-dependent and may also appear in other models where occupancy statistics yield an effective average of one per site.

See also: Hubbard model, Mott insulator, tight-binding model, antiferromagnetism, doping, optical lattice.