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Atomistic calculations give t=- (0.08-0.14) eV, U=2.5-2.8 eV, and Δ=0.03-0.16 eV (Refs.). Further, CoO2, which is described by model 1 at half filling with Δ=0, is a strongly correlated metal rather than a Mott insulator. This suggests U/ |t| 12-15, the critical value for a Mott insulator on the triangular lattice (Refs.)
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33
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66249117914
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The tight-binding band structure of model 1 consists of two bands due to hybridization between A and B sites. At 3/4 filling, for t>0 and any non-zero Δ, the lower band is filled and the upper band is half filled, while for t<0 the lower band is filled for |Δ| 0.64t.
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The tight-binding band structure of model 1 consists of two bands due to hybridization between A and B sites. At 3/4 filling, for t>0 and any non-zero Δ, the lower band is filled and the upper band is half filled, while for t<0 the lower band is filled for |Δ| 0.64t.
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34
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In the strong-coupling limit we find, from degenerate perturbation theory that, for either sign of t, nB - nA =1-8 (t/Δ) 2 +16 (t/Δ) 3 +O [(t/Δ) 4]. For t=0 the ground state of model 1 is a charge ordered insulator consisting of rows of doubly occupied B sites alternating with rows of singly occupied A sites. In the strong-coupling limit, U Δ |t|, virtual hopping processes lead to magnetic interactions between electrons in A sites. Equation 1 reduces to a Heisenberg model on an rectangular lattice: H=J { ij } [Si Sj - 1 4] + J [ij] [Si Sj - 1 4], where J= 4 t2 U - 8 t3 Δ2 and J = 16 t4 Δ2 [1 U + 1 2Δ+U + 1 2Δ]. J results from the usual superexchange antiferromagnetic coupling and "ring" exchange process around a three-site plaquette. In our previous paper, the O (t3) term was neglected. J becomes negative for t>0 and Δ 2Ut leading to a ferromagnetic interaction. In contrast J is always antiferromagnetic.
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In the strong-coupling limit we find, from degenerate perturbation theory that, for either sign of t, nB - nA =1-8 (t/Δ) 2 +16 (t/Δ) 3 +O [(t/Δ) 4]. For t=0 the ground state of model 1 is a charge ordered insulator consisting of rows of doubly occupied B sites alternating with rows of singly occupied A sites. In the strong-coupling limit, U Δ |t|, virtual hopping processes lead to magnetic interactions between electrons in A sites. Equation 1 reduces to a Heisenberg model on an rectangular lattice: H=J { ij } [Si Sj - 1 4] + J [ij] [Si Sj - 1 4], where J= 4 t2 U - 8 t3 Δ2 and J = 16 t4 Δ2 [1 U + 1 2Δ+U + 1 2Δ]. J results from the usual superexchange antiferromagnetic coupling and "ring" exchange process around a three-site plaquette. In our previous paper, the O (t3) term was neglected. J becomes negative for t>0 and Δ 2Ut leading to a ferromagnetic interaction. In contrast J is always antiferromagnetic.
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The lowest-order correction to the charge gap, in the strong-coupling limit, comes from the kinetic energy of a hole (doublon) propagating along the B (A) chains when extracting (adding) an electron to the zeroth-order ground-state configuration. Using degenerate perturbation theory we find that the gap is given, to O (t3), by Δc =Δ-2 |t| +4 t2 /Δ-8 t3 / Δ2 + E 1D t-J, where E 1D t-J is the energy of a hole in a half-filled t-J chain with J given by the expression in Ref.. E 1D t-J is given by the Bethe ansatz expression for J>0, while E 1D t-J =-2 |t| -J/2 for J<0.
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The lowest-order correction to the charge gap, in the strong-coupling limit, comes from the kinetic energy of a hole (doublon) propagating along the B (A) chains when extracting (adding) an electron to the zeroth-order ground-state configuration. Using degenerate perturbation theory we find that the gap is given, to O (t3), by Δc =Δ-2 |t| +4 t2 /Δ-8 t3 / Δ2 + E 1D t-J, where E 1D t-J is the energy of a hole in a half-filled t-J chain with J given by the expression in Ref.. E 1D t-J is given by the Bethe ansatz expression for J>0, while E 1D t-J =-2 |t| -J/2 for J<0.
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-
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