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1.3 Metal-insulator transitions transition is strictly connected with thermal fluctuations that destroy magnetic ordering. In the ground state, a Slater insulator consists of two sublattices with single-band described by Hubbard model - one s-electron per site. The atoms in sublattices ararranged in ABABABA... mode and are antiferromagnetically (AF) coupled. This and the repelling interaction of electrons lead to spins are arrange- ment of ↑, ↓, ↑, ↓, ↑, ↓, ↑... Such self-stabilizing spin density wave leads to doubling of the unit cell and halving of Brillouin zone, formation of energy gap and the system being an insulator. As the thermal fluctuations increase with temperature the local arrangement of electrons becomes destroyed and at the critical point of N ́eel temperature a simultaneous magnetic and MI transitions occur because the thermal energy is comparable to the coupling energy. Dynamical mean field theory (DMFT), as opposed to presented model, takes into account quantum effects, but neglects spatial fluctuations. The solid state is described as an effective medium, a self-consistent bath which contains all in- formation on the interactions between atoms with a single atom, an impurity, embedded into it. The information is described by a single-particle spectral func- tion ∆(ω). A single-impurity Anderson model is built (detail found in (32)): HSIAM = [εka†kσakσ + Vk(a†kσc0σ + h.c.)] − μ(n0↑ + n0↓) + Un0↑n0↓ (1.9) k,σ The Hamiltonian contains, reading from left, non-correlated electronic levels of medium, coupling of the impurity with the medium, electron-electron interactions. The hybridization parameters are the DMFT model parameters εk and Vk. The single-particle spectral function should represent all ways than electron can travel (tunnel) from site to the medium and back. In an insulating state the function has a gap that closes at the MIT so it is taken as a order parameter for the Mott transition. Advantages of DMFT include a correct description of Fermi liquid, high-temperature behaviour of materials where spatial fluctuations are not important and correct position of quasi-particle peak in experimental spectra though the width is underestimated. The model has ability to describe very well certain materials close to Mott transition - clean systems, some TM oxides, heavy fermion materials and Kondo insulators. However for materials where spatial fluctuations are strong and important, and for explaining some physical quantities near critical point the model is not suitable. 17PDF Image | Investigation of metal-insulator transition in magnetron sputtered samarium nickelate thin films
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