26 research outputs found
Study of off-diagonal disorder using the typical medium dynamical cluster approximation
We generalize the typical medium dynamical cluster approximation (TMDCA) and
the local Blackman, Esterling, and Berk (BEB) method for systems with
off-diagonal disorder. Using our extended formalism we perform a systematic
study of the effects of non-local disorder-induced correlations and of
off-diagonal disorder on the density of states and the mobility edge of the
Anderson localized states. We apply our method to the three-dimensional
Anderson model with configuration dependent hopping and find fast convergence
with modest cluster sizes. Our results are in good agreement with the data
obtained using exact diagonalization, and the transfer matrix and kernel
polynomial methods.Comment: 10 pages, 8 figure
A Typical Medium Dynamical Cluster Approximation for the Study of Anderson Localization in Three Dimensions
We develop a systematic typical medium dynamical cluster approximation that
provides a proper description of the Anderson localization transition in three
dimensions (3D). Our method successfully captures the localization phenomenon
both in the low and large disorder regimes, and allows us to study the
localization in different momenta cells, which renders the discovery that the
Anderson localization transition occurs in a cell-selective fashion. As a
function of cluster size, our method systematically recovers the re-entrance
behavior of the mobility edge and obtains the correct critical disorder
strength for Anderson localization in 3D.Comment: 5 Pages, 4 Figures and Supplementary Material include
Finite Cluster Typical Medium Theory for Disordered Electronic Systems
We use the recently developed typical medium dynamical cluster (TMDCA)
approach~[Ekuma \etal,~\textit{Phys. Rev. B \textbf{89}, 081107 (2014)}] to
perform a detailed study of the Anderson localization transition in three
dimensions for the Box, Gaussian, Lorentzian, and Binary disorder
distributions, and benchmark them with exact numerical results. Utilizing the
nonlocal hybridization function and the momentum resolved typical spectra to
characterize the localization transition in three dimensions, we demonstrate
the importance of both spatial correlations and a typical environment for the
proper characterization of the localization transition in all the disorder
distributions studied. As a function of increasing cluster size, the TMDCA
systematically recovers the re-entrance behavior of the mobility edge for
disorder distributions with finite variance, obtaining the correct critical
disorder strengths, and shows that the order parameter critical exponent for
the Anderson localization transition is universal. The TMDCA is computationally
efficient, requiring only a small cluster to obtain qualitative and
quantitative data in good agreement with numerical exact results at a fraction
of the computational cost. Our results demonstrate that the TMDCA provides a
consistent and systematic description of the Anderson localization transition.Comment: 20 Pages, 19 Figures, 3 Table
Metal-Insulator-Transition in a Weakly interacting Disordered Electron System
The interplay of interactions and disorder is studied using the
Anderson-Hubbard model within the typical medium dynamical cluster
approximation. Treating the interacting, non-local cluster self-energy
() up to second order in the
perturbation expansion of interactions, , with a systematic incorporation
of non-local spatial correlations and diagonal disorder, we explore the initial
effects of electron interactions () in three dimensions. We find that the
critical disorder strength (), required to localize all states,
increases with increasing ; implying that the metallic phase is stabilized
by interactions. Using our results, we predict a soft pseudogap at the
intermediate close to and demonstrate that the mobility edge
() is preserved as long as the chemical potential, , is
at or beyond the mobility edge energy.Comment: 10 Pages, 8 Figures with Supplementary materials include