Mott insulator

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Mott insulators are a class of materials that are expected to conduct electricity under conventional band theories, but which in fact turn out to be insulators when measured (particularly at low temperatures). This effect is due to electron-electron interactions which are not considered in the formulation of conventional band theory.

1 History
2 Applications
3 See also
4 External links
5 References

History

Although the band theory of solids had been very successful in describing various electrical properties of materials, in 1937 Jan Hendrik de Boer and Evert Johannes Willem Verwey pointed out that a variety of transition metal oxides that are predicted to be conductors by band theory (because they have an odd number of electrons per unit cell) are in fact insulators.^[1] Nevill Mott and R. Peierls then (also in 1937) predicted that this anomaly can be explained by including interactions between electrons.^[2]

In 1949, in particular, Mott proposed a model for NiO as an insulator, in which conduction can be understood based on the formula^[3]

(Ni²⁺O²⁻)₂ $\rightarrow$ Ni³⁺O²⁻ + Ni¹⁺O²⁻.

In this situation, the formation of an energy gap preventing conduction can be understood as the competition between the Coulomb potential U between 3d electrons and the transfer integral t of 3d electrons between neighboring atoms (the transfer integral is a part of the tight-binding approximation). The total energy gap is then

E_gap = U − 2zt,

where z is the number of nearest-neighbor atoms.

In general, Mott insulators occur when the repulsive Coulomb potential U is large enough to create an energy gap. One of the simplest theories of Mott insulators is the 1963 Hubbard model.

Applications

Mott insulators are of growing interest in advanced physics research, and are not yet fully understood. They have applications in thin-film magnetic heterostructures and high-temperature superconductivity, for example.^[4]

External links

lecture slides

References

^ de Boer, J. H.; Verwey, E. J. W. (1937). "Semi-conductors with partially and with completely filled ₃d-lattice bands". Proceedings of the Physical Society of London 49: 59.
^ Mott, N. F.; Peierls, R. (1937). "Discussion of the paper by de Boer and Verwey". Proceedings of the Physical Society of London 49: 72.
^ Mott, N. F. (1949). "The basis of the electron theory of metals, with special reference to the transition metals". Proceedings of the Physical Society of London Series A 62: 416.
^ Kohsaka, Y.; Taylor, C.; Wahl, P.; et al. (August 28, 2008). "How Cooper pairs vanish approaching the Mott insulator in Bi₂Sr₂CaCu₂O_8+δ". Nature 454: 1072–1078. doi:10.1038/nature07243.