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Electronic Properties of Perovskite Oxides
Published in Gibin George, Sivasankara Rao Ede, Zhiping Luo, Fundamentals of Perovskite Oxides, 2020
Gibin George, Sivasankara Rao Ede, Zhiping Luo
The Hubbard model is widely used to describe two opposing tendencies: the first one is to explain the metallic behavior due to electron hopping, which delocalizes the electrons into itinerant states, and latter is to explain the Mott insulators, which is the localization of electrons (electrons adherent to individual atoms). The interatomic Coulombic repulsion is determined by the degrees of freedom surrounding the d-electrons, i.e. charge, orbital, spin, lattice, etc. (Tsuda et al. 2000). Additionally, the transition metals occupying the B-site in a perovskite lattice have 3d (e.g. Fe, Co, Ni), 4d (e.g. Mo, Ru, Rh), or 5d (e.g. W, Re, Ir) electronic configuration. 3d-Orbitals are well localized and thus form a narrow band (W) with a large on-site Coulomb interaction (U). 5d-Orbitals are spatially more extended than 4d and 3d counterparts; as a result, nearest-neighbor orbitals overlap significantly, and therefore W is wider in 5d-orbitals than in 3d or 4d orbitals, i.e. W3d < W4d < W5d (Biswas et al. 2016). Therefore, perovskite structures with 5d and 4d transition elements behave like insulators at all the temperatures.
The Hubbard model: exact constraints on spectral moments in the strong coupling limit
Published in Philosophical Magazine, 2023
This is a mathematical presentation, generating rigorous and demanding benchmarks for any solution to the Hubbard model that purports to be accurate in the strong coupling region. The analysis here is based on extremely simple, if tedious, mathematics – in sharp contrast to the specialized techniques employed elsewhere, especially for 1D solutions. DMFT and its cluster extensions have been used to explain several experiments ([7,8, 10, 40,41] and references therein). But, as noted earlier, the Hubbard model is an extreme simplification of actual material behaviour. This model simplicity while still including physically significant effects may well drive some of the agreement with experiment. The real issue is whether any proposed solution is faithful to the essential physics of the model itself, without conflating actual material complexity. The spectral moment test offers just such a rigorous, unbiased test that includes some basic physical quantities (quasiparticle energy and width or scattering) applicable to the important strong coupling region.
Temperature-dependent electronic structure of bixbyite α-Mn2O3 and the importance of a subtle structural change on oxygen electrocatalysis
Published in Science and Technology of Advanced Materials, 2021
Junais Habeeb Mokkath, Maryam Jahan, Masahiko Tanaka, Satoshi Tominaka, Joel Henzie
The DFT results indicate that the transformation from orthorhombic to cubic phase relieved Jahn–Teller distortions that un-tilted the Mn3+O6 octahedra and leads to improved Mn 3d and O 2p covalent bonding and bandwidth. The observed semiconductor-to-semimetal transition can be explained using the well-known Hubbard model [30] considering the fact that PBE0 functional contains 25% of full range Hartree-Fock exchange. In the Hubbard model, electron motion among the atomic sites is controlled by the ratio of intra-atomic Coulomb repulsion strength (U) and 3d bandwidth (W). A large U/W ratio yields electron localization and hence a semiconductor or insulating state, while a small value enhances electron delocalization and a metallic nature. Figure 3 shows that the W value in the cubic phase is nearly 0.5 eV greater compared to the orthorhombic phase, thus interpreting the results using a simplified Hubbard model is relatively convincing.
Molecular Physics Longuet-Higgins Early Career Researcher Prize 2017 winner profile
Published in Molecular Physics, 2018
When it comes to describing strongly correlated materials or molecules, the standard low cost methods, such as density functional theory (DFT), usually fail. While more involved wavefunction-based approaches could in principle be applied, they remain out of reach due to the computational cost. A natural and intuitive idea is to merge the two methods to build a new one that gathers all advantages: a low computational cost and good accuracy. From a mathematical point of view, such a combination is very similar to the so-called ‘embedding approaches’ which are becoming increasingly popular in quantum chemistry. Providing an exact formulation of the hybrid theory is far from trivial since the methods to be merged are written in completely different formalisms. My paper deals with the development and practical implementation of a novel and in-principle-exact embedding approach which is referred to as site-occupation embedding theory (SOET). We first tested it on the Hubbard model, which is mostly used in condensed matter physics for describing strongly correlated materials. We currently work on the extension of SOET to quantum chemistry, thus making the approach truly at the interface between physics and chemistry.