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Concept
Charge ordering
Summary
Charge ordering (CO) is a (first- or second-order) phase transition occurring mostly in strongly correlated materials such as transition metal oxides or organic conductors. Due to the strong interaction between electrons, charges are localized on different sites leading to a disproportionation and an ordered superlattice. It appears in different patterns ranging from vertical to horizontal stripes to a checkerboard–like pattern
and it is not limited to the two-dimensional case. The charge order transition is accompanied by symmetry breaking and may lead to ferroelectricity. It is often found in close proximity to superconductivity and colossal magnetoresistance.
This long range order phenomena was first discovered in magnetite (Fe3O4) by Verwey in 1939.
He observed an increase of the electrical resistivity by two orders of magnitude at TCO=120K, suggesting a phase transition which is now well known as the Verwey transition. He was the first to propose the idea of an ordering process in this context. The charge ordered structure of magnetite was solved in 2011 by a group led by Paul Attfield with the results published in Nature. Periodic lattice distortions associated with charge order were later mapped in the manganite lattice to reveal striped domains containing topological disorder.
The extended one-dimensional Hubbard model delivers a good description of the charge order transition with the on-site and nearest neighbor Coulomb repulsion U and V. It emerged that V is a crucial parameter and important for developing the charge order state. Further model calculations try to take the temperature and an interchain interaction into account.
The extended Hubbard model for a single chain including inter-site and on-site interaction V and U as well as the parameter for a small dimerization which can be typically found in the (TMTTF)2X compounds is presented as follows:
where t describes the transfer integral or the kinetic energy of the electron and and are the creation and annihilation operator, respectively, for an electron with the spin at the th or th site.
Official source
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