| |||
|
| The mechanism of negative-U center formation. |
|
According to this model negative-U centers (NUC) are formed under doping on pairs of neighboring copper ions in the CuO2-plane.
(a) Electron spectrum of undoped cuprate HTSC. U_H is the repulsive energy for two electrons on Cu ion. The charge-transfer gap Delta_ct corresponds to the transition of electron from oxygen to nearest Cu ion with the origin of hole extended over 4 surrounding oxygen ions (Fig. 1b). (c) The energy of two such excitations can be lowered if two side-by-side hydrogen pseudo-atoms form hydrogen pseudo-molecule (Fig. 1d). Delta_E_U is the binding energy. It is possible due to formation of a bound state (of the Heitler-London type) from two electrons and two holes that emerge in the immediate vicinity of this pair of cations. The analogy with H_2 molecule is justified because the distance a between cations in all HTSC amounts to about 4 and is close to R_0 x epsilon, where R_0~0,8 is the distance between the nuclei in an H_2 molecule, and epsilon is the high-frequency dielectric constant, with epsilon~4,5-5 for all HTSC. That is, HTSC has an inborn ability to form an intracrystalline H_2 molecule. Lowering of the energy is possible, as it takes place in the H_2 molecule, only for the bonding orbital of a singlet hole pair. |
| Doping |
|
If we now decrease Delta_ct to the point where the gap disappears for two-electron transitions but remains for one-electron transitions, we arrive at a system in which some of the electrons belonging to the oxygen valence band effectively interact with pair states of NUC. We believe that NUC activation in HTSC is realized by the doping that changes locally the Madelung volume energy in appropriate way. Further, by a NUC we will mean just such activated NUC.
It is well known that HTSC reveal nonhomogeneous properties down to the nanoscopical scale. In our opinion the reason for such behavior is the strong localization of doped charges in the near vicinity of doped ions (dopants). This localization results in local variations of electronic structure of the parent charge-transfer-insulator. Thus, the local electronic structure depends on the local mutual arrangement of doped charges. |
| Percolation |
|
At a random distribution of doped charges the simultaneous coexistence of the different types of doped charge arrangement is possible. Therefore it is difficult to expect the existence of large clusters whose properties are determined by one of a number of possible doped charge arrangements.
However, as we wish to show, in La(2-x)Sr(x)CuO4 at any concentration x the dopants fill the sites of the certain square lattices with different lattice constants depending on x, which are sub-lattices of CuO_2 lattice. |
| References: |
Хостинг от uCoz