PmWikiFisica | Superconductivity / ChargeTransferInsulators browse

< Superconductivity.Resistivity | Index | Superconductivity.ResistivityVsTemperature >

Notes from Rep.Prog Phys 71 (2008) 036501

Ionic Picture, e.g. {$ \mbox{La}_{\mbox{2}}\mbox{CuO}_{\mbox{4}} $}

Octahedra are tetragonally distorted (more precisely orthorhombically), with Cu-O distences

0f 1.9 and 2.4 Å, respectively for the in-plane and apical oxygen ions.

Electrons, among the two the {$e_g$} levels, favour occupation of {$d_{3z^2-r^2}$} over {$d_{x^2-y^2}$}
Hence the hole-band is composed of {$d_{x^2-y^2}$} orbitals and oxygen {$p$}

Undoped: only Cu²⁺ spins obeying the Heisenberg model, with J derived from hopping, {$t_{dp}$}, U repulsion and charge transfer energy. The result is roughly equal to 120 meV, equivalent to around 1400 K.

Note concepts of Charge Transfer and Mott insulator do not coincide and the first applies here, not the second (see Zaanen et al. PRL 55 418 (1985)). A Mott insulator is insulator because U, the energy of a double occupancy on {$d$}, as well as the separation between Upper and lower Hubbard bands, is large, hence the electron hopping between neighbor cells

{$ d_i^nd_{i+1}^n \rightarrow d_i^{n-1}d_{i+1}^{n+1} $}

is prohibited and electrons (holes) become localised. A CT mechanism exists however

{$ d_i^n \rightarrow d_i^{n+1}L^{-1} $}

where {$L^{-1}$} is a hole in the anion valence (Ligand) band and the energy cost of this process is {$\Delta$}, (equal to {$U_d-\Delta_p$} of the figure), not U.

(a) and (c ): ground states of CT and Mott, respectively; the two Cu levels are the lower and upper Hubbard bands

(b) and (d): their lowest energy excitations

When U {$< \Delta$} (in the figure, {$\Delta_p<0$}) the former determines the gap (Mott insulator). When U{$> \Delta$} (in the figure, {$\Delta_p>0$}) it is the latter that determines the gap (CT insulator) and this is the actual case for cuprates. Incipient transport then involves the simultaneous excitation of d electrons into the upper Hubbard band in the final cell and the creation of a hole in the ligand band in the starting cell, although true transport is further hindered by the distortion of the Neel ground state. This predicts heavy electrons with relatively light holes (see Figure)

In simple words in the insulator the first charge to move would be a hole in the Ligand band, not the Cu d hole in the lower Hubbard band,

< Superconductivity.Resistivity | Index | Superconductivity.ResistivityVsTemperature >