Mottness

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In condensed matter physics, mottness is a term which denotes the additional ingredient, aside from antiferromagnetic ordering, which is necessary to fully describe a Mott Insulator. In other words, we might write

antiferromagnetic order + mottness = Mott insulator

Thus, mottness accounts for all of the properties of Mott insulators that cannot be attributed simply to antiferromagnetism.

[edit] Properties

There are a number of properties of Mott insulators, derived from both experimental and theoretical observations, which cannot be attributed to antiferromagnetic ordering and thus constitute mottness. These properties include

Spectral weight transfer on the Mott scale [3,4]
Vanishing of the single particle Green function along a connected surface in momentum space in the first brillouin zone [5]
Two sign changes of the Hall coefficient as electron doping goes from $n = 0$ to $n = 2$ (band insulators have only one sign change at $n = 1$ )
The presence of a charge $2 e$ (with $e < 0$ the charge of an electron) boson at low energies [6,7]
A pseudogap away from half-filling ( $n = 1$ ) [8]

[edit] See also

[edit] References

[1] R.B. Laughlin, "A Critique of Two Metals," http://arxiv.org/abs/cond-mat/9709195

[2] Philip W. Anderson and G. Baskaran, "A Critique of 'A Critique of Two Metals,'" http://arxiv.org/abs/cond-mat/9711197

[3] Philip Phillips, "Mottness," http://arxiv.org/abs/cond-mat/0702348

[4] M.B.J. Meinders, H. Eskes, and G.A. Sawatzky, Phys. Rev. B 48 3916 (1993)

[5] Tudor D. Stanescu, Philip Phillips, and Ting-Pong Choy, "Theory of the Luttinger surface in doped Mott insulators," Phys. Rev. B 75 104503 (2007)

[6] Robert G. Leigh, Philip Phillips, and Ting-Pong Choy, "Hidden Charge 2e Boson in Doped Mott Insulators: Field Theory of Mottness," to be published in Phys. Rev. Lett., http://arxiv.org/abs/cond-mat/0612130v3 (2007)

[7] Ting-Pong Choy, Robert G. Leigh, Philip Phillips, and Philip D. Powell, "Exact Integration of the High Energy Scale in Doped Mott Insulators," http://arxiv.org/abs/0707.1554

[8] Tudor D. Stanescu and Philip Phillips, "Pseudogap in Doped Mott Insulators is the Near-neighbour Analogue of the Mott Gap," Phys. Rev. Lett. 91, 017002 (2003), http://arxiv.org/abs/cond-mat/0209118

Of possible interest for this material is a recent generalization of the T.D. Lee-Friedberg BEC theory of cuprate superconductors that does NOT exclude hole-pairs, see. e.g. Physica C 453, 37-45 (2007) (S.K. Adhikari, M. de Llano, F.J. Sevilla, M.A. Solís & J.J. Valencia) The BCS-Bose crossover theory. Also of interest might be a generalization of Cooper pairing that, similarly, does not exclude hole-pairs, by use of the Bethe-Salpeter equation in 3D [Physica C 364-365, 95 (2001) (M. Fortes, M.A. Solís, M. de Llano & V.V.Tolmachev) Cooper pairs as resonances] and in 2D [Sol. State Comm. 129, 577-581 (2004) (V.C. Aguilera-Navarro, M. Fortes & M. de Llano) Stable and resonant Cooper pairs]. Manuel de Llano, UNAM, Mexico City [dellano@servidor.unam.mx]