Towards the Realization of Systematic, Self-Consistent Typical Medium Theory for Interacting Disordered Systems

This work is devoted to the development of a systematic method for studying electron localization. The developed method is Typical Medium Dynamical Cluster Approximation (TMDCA) using the Anderson-Hubbard model. The TMDCA incorporates non-local correlations beyond the local typical environment in a self-consistent way utilizing the momentum resolved typical-density-of-states and the non-local hybridization function to characterize the localization transition. For the (non-interacting) Anderson model, I show that the TMDCA provides a proper description of the Anderson localization transition in one, two, and three dimensions. In three-dimensions, as a function of cluster size, the TMDCA systematically recovers the re-entrance behavior of the mobility edge and obtains the correct critical disorder strength for the various disorder configurations and the associated \textit{universal order-parameter-critical-exponent} $\beta$ and in lower-dimensions, the well-knowing scaling relations are reproduced in agreement with numerical exact results. The TMDCA is also extended to treat diagonal and off-diagonal disorder by generalizing the local Blackman-Esterling-Berk and the importance of finite cluster is demonstrated. It was further generalized for multiband systems. Applying the TMDCA to weakly interaction electronic systems, I show that incorporating Coulomb interactions into disordered electron system result in two competing tendencies: the suppression of the current due to correlations and the screening of the disorder leading to the homogenizing of the system. It is shown that the critical disorder strength ($W_c^U$), required to localize all states, increases with increasing interactions ($U$); implying that the metallic phase is stabilized by interactions. Using the results, a soft pseudogap at the intermediate $W$ close to $W_c^U$ is predicted independent of filling and dimension, and I demonstrate in three-dimensions that the mobility edge is preserved as long as the chemical potential, $\mu$, is at or beyond the mobility edge energy ($\omega_\epsilon$). A two-particle formalism of electron localization is also developed within the TMDCA and used to calculate the direct-current conductivity, enabling direct comparison with experiments. Note significantly, the TMDCA benchmarks well with numerical exact results with a dramatic reduction in computational cost, enabling the incorporation of material\u27s specific details as such provide an avenue for the possibility of studying electron localization in real materials

First-Principle Wannier function analysis of the electronic structure of PdTe: Weaker magnetism and superconductivity

We report a first-principles Wannier function study of the electronic structure of PdTe. Its electronic structure is found to be a broad three-dimensional Fermi surface with highly reduced correlations effects. In addition, the higher filling of the Pd $d$-shell, its stronger covalency resulting from the closer energy of the Pd-$d$ and Te-$p$ shells, and the larger crystal field effects of the Pd ion due to its near octahedral coordination all serve to weaken significantly electronic correlations in the particle-hole (spin, charge, and orbital) channel. In comparison to the Fe Chalcogenide e.g., FeSe, we highlight the essential features (quasi-two-dimensionality, proximity to half-filling, weaker covalency, and higher orbital degeneracy) of Fe-based high-temperature superconductors.Comment: 5 Pages, 3 Figure

Electronic, structural, and elastic properties of metal nitrides XN (X = Sc, Y): A first principle study

We utilized a simple, robust, first principle method, based on basis set optimization with the BZW-EF method, to study the electronic and related properties of transition metal mono-nitrides: ScN and YN. We solved the KS system of equations self-consistently within the linear combination of atomic orbitals (LCAO) formalism. It is shown that the band gap and low energy conduction bands, as well as elastic and structural properties, can be calculated with a reasonable accuracy when the LCAO formalism is used to obtain an optimal basis. Our calculated, indirect electronic band gap (E gΓ-X) is 0.79 (LDA) and 0.88 eV (GGA) for ScN. In the case of YN, we predict an indirect band gap (EgΓ-X) of 1.09 (LDA) and 1.15 eV (GGA). We also calculated the equilibrium lattice constants, the bulk moduli (Bo), effective masses, and elastic constants for both systems. Our calculated values are in excellent agreement with experimental ones where the latter are available. Copyright 2012 Author(s)

Effective Cluster Typical Medium Theory for Diagonal Anderson Disorder Model in One- and Two-Dimensions

We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical medium theory utilizes the momentum resolved typical density of states and hybridization function to characterize the localization transition. We apply the formalism to the Anderson model of localization in one- and two-dimensions. In one dimension, we find that the critical disorder strength scales inversely with the linear cluster size with a power-law, $W_c \sim (1/L_c)^{1/\nu}$; whereas in two dimensions, the critical disorder strength decreases logarithmically with the linear cluster size. Our results are consistent with previous numerical work and in agreement with the one-parameter scaling theory.Comment: 8 Pages and 8 Figure

Study of multiband disordered systems using the typical medium dynamical cluster approximation

We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include inter-band and intra-band hopping and an intra-band disorder potential. Our results are consistent with the ones obtained by the transfer matrix and the kernel polynomial methods. We apply the method to K$_x$Fe$_{2-y}$Se$_2$ with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator. Our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.Comment: 10 pages, 8 figure

Electronic, transport, optical, and structural properties of rocksalt CdO

We report electronic, optical, and structural properties of rocksalt CdO as obtained from first-principle calculations with both the Tran-Blaha modified Becke-Johnson potential using linearized augmented planewave method in WIEN2k and local density approximation (LDA) potential using the LDA Bagayoko-Zhao-Williams-Ekuma-Franklin (BZW-EF) method in implementing the linear combination of Gaussian orbitals. The results are discussed in relation to existing experimental data, particularly to the Burstein-Moss effect. © 2013 AIP Publishing LLC

The study of the optical properties of copper based chalcopyrite semiconductors

Click on the link to view the abstract.Journal of the Nigerian Association of Mathematical Physics, Volume 15 (November, 2009), pp 345 - 34