Mottness

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.

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 $2e$ (with the charge of an electron) boson at low energies [6,7]
*A pseudogap away from half-filling ($n=1$) [8]

See also

*Mott insulator
*Hubbard model
*Antiferromagnetism
*Green's function (many-body theory)

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 [[e-mail]]