Mott, Slater, Band, and Charge-Transfer Insulators

Mott, Slater, band, charge-transfer, and Anderson insulators are mechanisms, not interchangeable names for large resistivity. They are distinguished by how the gap or localization arises, which symmetry is required, which orbitals carry addition/removal weight, whether the bulk is compressible, and how spectra evolve when interaction, order, or disorder is varied.

Required background. Use Hubbard bands and spectral transfer. Helpful background. Anderson localization scaling and Bloch/Wannier band theory develop the corresponding detailed mechanisms.

Insulator mechanisms in a diagnostic matrix

Mechanism	Controlled anchor	Gap or localization signature	Symmetry/order test	Strong falsifier
Band	Filled noninteracting bands in the actual unit cell	Single-particle gap adiabatic to $U=0$	No broken symmetry required	Gap cannot remain open along any symmetry-preserving path to the noninteracting limit
Slater	Weak-coupling density-wave mean field	Folded bands and gap tied to order parameter	Translation or spin symmetry breaks	Robust paramagnetic charge gap far above the order scale
Mott	Commensurate interacting atomic/strong-coupling limit	Addition gap, incompressibility, Hubbard-weight transfer	Conventional order not required	Gap disappears whenever order is removed and shows no interaction-driven weight transfer
Charge transfer	Correlated metal–ligand orbitals with transfer energy $\Delta$	Valence and conduction edges have different orbital character; often $\Delta<U_d$	No unique required order	One-band spectrum reproduces edges and response without ligand degrees of freedom
Anderson	Noninteracting or interacting disorder with localized eigenstates	Vanishing dc transport and finite localization length; spectral DOS need not vanish	No periodic symmetry breaking required	Extended-state scaling or a clean interaction gap explains the same regime

The charge-transfer distinction and its relation to Hubbard scales were formulated by Zaanen, Sawatzky, and Allen 1985, pp. 418–421. Mixed regimes are common: an antiferromagnetic Mott material can have both Slater reconstruction and correlation-driven spectral transfer.

Observable protocol

Resistivity alone cannot identify a mechanism. Combine charge compressibility or addition energies, momentum- and orbital-resolved spectra, optical spectral weight, order-parameter scaling, disorder dependence, and temperature evolution Imada, Fujimori, and Tokura 1998, §§ II–V, pp. 1047–1155. Use the actual crystallographic or spontaneously enlarged unit cell. Matrix-element suppression can imitate a spectral gap, while finite temperature turns a sharp gap into a crossover.

For a Mott claim, test whether a paramagnetic gap and transfer over energy $U$ persist. For a Slater claim, test whether the gap tracks the ordering amplitude and closes when the order is suppressed. For charge-transfer physics, establish ligand versus correlated-orbital character on the two sides of the gap. For Anderson localization, use size-dependent transport or localization observables rather than the density of states alone.

Exercises

A disordered system has finite single-particle density of states at the chemical potential but zero extrapolated dc conductivity. Which mechanism is immediately compatible, and what remains to test?

Solution

Anderson localization is compatible because localized states can give finite DOS without transport. One must still establish localization scaling, rule out finite-size or inelastic effects, and test interactions; the observation alone does not exclude an interacting Anderson–Mott regime.

References

• Masatoshi Imada, Atsushi Fujimori, and Yoshinori Tokura, “Metal–Insulator Transitions,” Reviews of Modern Physics 70 (1998) 1039–1263, doi:10.1103/RevModPhys.70.1039.
• Jan Zaanen, George A. Sawatzky, and John W. Allen, “Band Gaps and Electronic Structure of Transition-Metal Compounds,” Physical Review Letters 55 (1985) 418–421, doi:10.1103/PhysRevLett.55.418.