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.

Contents

Properties

Related Topics

References

Properties

Stating the above definition of mottness slightly differently, mottness can be thought of as the "residue" which is left over when we try to attribue a Mott insulator's behavior to its antiferromagnetic ordering. For example, if we attribute a truant school boy's behavior to his boring course work we are left with a residue, namely, the boy's attitude. Similarly, if we attribute the Sahara Desert to global warming we are left with a residue, what the Sahara desert is in the first place.
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]

Related Topics

★ 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