Anderson localization insulator can be induced by defect disorder, such as impurity atoms, atom vacancies and so on.
Does anyone know the limited concentration value of defect disorder (such as oxygen vacancies in Pr0.7Ca0.3MnO3) to make Anderson localization, or is there have some papers have studied this question?
I don't have a direct answer for you, unfortunately. But my faint memories to lectures on the topic seem to tell me, than Anderson localization was a weak effect, observable at small temperatures in metals. (I may be misled, though) My question would therefor be whether the manganates such as the one you mention are good enough metals such that Anderson localization may take a leading role?
Anderson's model is tight binding electronic model where the disorder is introduced by a continuous distribution of site energies. This is not simple to associate to a concentration of defect potentials as you can seem to suggest in your question. I am afraid that you cannot know the answer just using Anderson's model alone.
Let me to give you two references:
1. Kramer and MacKinnon, Localization: theory and experiment, Rep.Prog. Phys.56, 1469 (1993)
2. Ishii, Progr.Theor.Phys.53,77(1973)
More important than the concentration, for Anderson's model, is the density of states (DOS) calculated by ab initio methods as DFT. It is true that the doping that you have is too expensive to calculate it with these methods and the use of the spectral theorem needs to have a good Green function. In any case, very difficult to find an answer for your question.
Look up papers by the group of A. Loidl on manganites about 10-15 years ago. I recollect that they looked at "universal dielectric response" of disordered solids, including manganites, in a Phys Rev Lett.
Dear Kai Fauth, Daniel Baldomir and M. S. Laad
Very thanks for your answers. It expand my ideas and I will read these recommended papers.
My question is: we have found the resistive switching phenomenon in Pr0.7Ca0.3MnO3 is based on Mott transition (Scientific Reports, 3: 1704 (2013)). It can transition from initial state of LHS into HRS with increase of oxygen vacancies induced by the redox reaction at the surface of PCMO, the electrons released from oxygen vacancies can change the occupation condition of Mn 3d orbit and result in Mott transition. Here, the increased oxygen vacancies can make PCMO has a Mott insulator state (the concentration of oxygen vacancies in PCMO with Mott insulator state is about or a little bigger than 5%). However, the increased oxygen vacancies also have the scattering effect for the electron transport, if the scattering effect is big enough, it can lead to the Anderson localization state (Here, I am not sure). If so, the HRS of PCMO was contributed by Mott transition and Anderson transition, however, we want to prepare ReRAM based on Mott transition rather than Anderson transition.
Therefore, how to prove whether there has Anderson localization state when PCMO transition from LRS to HRS based on the driving force of oxygen ion migration? Or to prove the HRS of PCMO mainly contributed by Mott transition.
One more thing, there are some papers have proves ZnO and BaPb1-xBiO3 can forming Anderson localization state with the increase concentration of oxygen vacancies, without the critical concentration.
"EFFECT OF OXYGEN VACANCIES ON CARRIER LOCALIZATION IN BaPb1-xBixO3 Solid State Communications, Vol. 53, No. 8, _pp.691-694, 1985."
"Electrical transport in ZnO films: Transition from band-gap insulator to Anderson
localized insulator Journal of Applied Physics 96, 3827 (2004)"
The physics of Anderson localisation is a one body problem (quantum interference of the one particle wave functions) , The Mott transition is completely different it is a many body problem. Regarding the Anderson localisation, disorder can induce indeed a localisation phenomenon, by giving rise to a mobility edge that separate localised sates from extended states , however the nature of the band structure and the type of the disorder (on site, potential, extended, uncorrelated), play an important role. The physical order parameter is the Drude weight, that is finite in metallic phase and zero in the insulating phase.
Here in your case Ca substitue Pr, 30% is a large amount of substitution, and each Ca atom is surrounded by 8 Mn that "feel" in a correlated manner the effect of Ca , thus in my view you can not view this problem as a fully uncorrelated description of random on site potential the you substitute Pr by Ca, but the disorder should include on the d orbitals of Mn this effect, this is very different from the standard Anderson problem.
For instance I suggest you to have a look to
"Effect of correlated disorder on the magnetism of double exchange systems"
Physical Review B 76 (2), 020401 (2007)
Model for Vacancy-Induced d0 Ferromagnetism in Oxide CompoundsPhys. Rev. Lett. 96, 207602
Hope that may help...
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