@MISC{Hwang_basicnotions, author = {H. Y. Hwang and Y. Iwasa and M. Kawasaki and B. Keimer and N. Nagaosa and Y. Tokura}, title = {BASIC NOTIONS}, year = {} }

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Abstract

Transition metal oxides (TMOs) are an ideal arena for the study of electronic correlations because the s-electrons of the transition metal ions are removed and transferred to oxygen ions, and hence the strongly correlated d-electrons determine their physical properties such as electrical transport, magnetism, optical response, thermal conductivity, and superconductivity. These electron correlations prohibit the double occupancy of metal sites and induce a local entanglement of charge, spin, and orbital degrees of freedom. This gives rise to a variety of phenomena, e.g., Mott insulators, various charge/spin/orbital orderings, metal-insulator transitions, multiferroics, and superconductivity. 1 In recent years, there has been a burst of activity to manipulate these phenomena, as well as create new ones, using oxide heterostructures. 2 Most fundamental to understanding the physical properties of TMOs is the concept of symmetry of the order parameter. As Landau recognized, the essence of phase transitions is the change of the symmetry. For example, ferromagnetic ordering breaks the rotational symmetry in spin space, i.e., the ordered phase has lower symmetry than the Hamiltonian of the system. There are three most important symmetries to be considered here. (i) Spatial inversion (I), defined as r