21 research outputs found
Locally self-consistent embedding approach for disordered electronic systems
We present a new embedding scheme for the locally self-consistent method to
study disordered electron systems. We test this method in a tight-binding basis
and apply it to the single band Anderson model. The local interaction zone is
used to efficiently compute the local Green's function of a supercell embeded
into a local typical medium. We find a quick convergence as the size of the
local interaction zone which reduces the computational costs as expected. This
method captures the Anderson localization transition and accurately predicts
the critical disorder strength. The present work opens the path towards the
development of a typical medium embedding scheme for the multiple
scattering methods.Comment: 7 pages, 5 figure
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, ; 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
Local theory for Mott-Anderson localization
The paramagnetic metallic phase of the Anderson-Hubbard model (AHM) is investigated using a nonperturbative local moment approach within the framework of dynamical mean-field theory with a typical medium. Our focus is on the breakdown of the metallic phase near the metal-insulators transition as seen in the single-particle spectra, scattering rates, and the associated distribution of Kondo scales. We demonstrate the emergence of a universal, underlying low-energy scale, TKpeak. This lies close to the peak of the distribution of Kondo scales obtained within the metallic phase of the paramagnetic AHM. Spectral dynamics for energies ωTKpeak display Fermi liquid universality crossing over to an incoherent universal dynamics for ωTKpeak in the scaling regime. Such universal dynamics indicate that within a local theory the low to moderately low-energy physics is governed by an effective, disorder renormalized Kondo screening
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
KFeSe 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
Systematic quantum cluster typical medium method for the study of localization in strongly disordered electronic systems
Great progress has been made in the last several years towards understanding
the properties of disordered electronic systems. In part, this is made possible
by recent advances in quantum effective medium methods which enable the study
of disorder and electron-electronic interactions on equal footing. They include
dynamical mean field theory and the coherent potential approximation, and their
cluster extension, the dynamical cluster approximation. Despite their
successes, these methods do not enable the first-principles study of the
strongly disordered regime, including the effects of electronic localization.
The main focus of this review is the recently developed typical medium
dynamical cluster approximation for disordered electronic systems. This method
has been constructed to capture disorder-induced localization, and is based on
a mapping of a lattice onto a quantum cluster embedded in an effective typical
medium, which is determined self-consistently. Here we provide an overview of
various recent applications of the typical medium dynamical cluster
approximation to a variety of models and systems, including single and
multi-band Anderson model, and models with local and off-diagonal disorder. We
then present the application of the method to realistic systems in the
framework of the density functional theory.Comment: 58 pages, 46 figure