Mott insulating systems

Abstract In a solid with orbital degree of freedom, an orbital configuration does not minimize simultaneously bond energies in equivalent directions. This is a kind of frustration effect which exists intrinsically in orbital degenerate system. We review in this paper the intrinsic orbital frustration effects in Mott insulating systems. We introduce recent our theoretical studies in three orbital models, i.e. the cubic lattice orbital model, the two-dimensional orbital compass model and the honeycomb lattice orbital model. We show numerical results obtained by the Monte-Carlo simulations in finite size systems, and introduce some non-trivial orbital states due to the orbital frustration effect. 

The fully ionic solids (region I) afforded band insulators, 1 1 Mott insulators with ground states of antiferromagnets (E b(21) and F b(22) in Fig. 1) or spin-Peierls systems, ferroelectrics, ferromagnets, spin-ladders, and nonlinear transport materials (switching and memory). 

The switching or memory phenomena induced by electric field application or photo irradiation have been studied on Mott insulators, charge ordered insulators, and N-I transition systems and were found to be fast phase transitions in general. For the former two systems, the phase transitions caused a pronounced change in reflectance and conductivity from insulating to metallic features. The third system also exhibited a change in conductivity and dielectric response connected with the transports of solitons and/or domain walls, dynamic dimerization, and... 

These experimental facts indicate that this system can be an excellent model of band-filling control, and will be a good candidate for making a superlattice composed of Mott insulator/superconductor hetero-junctions. It should be emphasized that their lattice parameters are nearly kept constant through such an anion modification, which is the most essential feature for achieving the successful tuning of Tc in an organic superconductor. 

The possibility to vary the parameters governing the physical properties of (TM>2X compounds (nature of cation or anion, pressure and application of a magnetic field) allows an exploration moving continuously from half-filled band 1-D Mott insulators in sulfur based compounds to conducting systems in selenium or strongly pressurized sulfur based compounds (Fig. 4). 

It should be added that the expansion of the tr-conjugating system and/or the introduction of Se atoms with greater polarizability (as shown in BETS or TTPs) reduce the effective on-site Coulomb energy U. For example, the V values for the TTP-type donors estimated from electrochemical and optical measurements are considerably small. (TTM-TTP)l3 is a 1 1 salt with a highly one-dimensional half-filled band. Although 1 1 salts were believed to be non-metal due to the Coulomb interaction (Mott-insulator), this salt shows metallic behavior down to about 160 K. This system is regarded as a small-f/ case of a one-dimensional conductor with an inherently half-filled band [27]. 

M(dmit)2 molecule is 1/2-, frequently observed value, the conduction band is the half-filled (anti-bonding) HOMO band. This two-dimensional HOMO band has narrow width as a result of the strong dimerization (the effective band width is correlated to the interdimer transfer integrals). Therefore, the system tends to become a Mott insulator. 

We start from the model Hamiltonian to describe the strongly correlated electron system with the eg orbital degree of freedom. A system of the present interest is a Mott insulator where one electron occupies one of the doubly degenerate orbitals at each site in a simple cubic lattice. The doubly degenerate orbital degree of freedom is represented by the pseudo-spin operator with an amplitude of 1/2 defined by... 

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