An official website of the United States government
Great progress has been made in recent 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. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband 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 DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.
more »
« less
Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization
We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.
more »
« less
- PAR ID:
- 10323351
- Date Published:
- Journal Name:
- Crystals
- Volume:
- 11
- Issue:
- 11
- ISSN:
- 2073-4352
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This study was performed to investigate the validity of a real world version of the Trail Making Test (TMT) across age strata, compared to the current standard TMT which is delivered using a pen-paper protocol. We developed a real world version of the TMT, the Can-TMT, that involves the retrieval of food cans, with numeric or alphanumerical labels, from a shelf in ascending order. Eye tracking data was acquired during the Can-TMT to calculate task completion time and compared to that of the Paper-TMT. Results indicated a strong significant correlation between the real world and paper tasks for both TMTA and TMTB versions of the tasks, indicative of the validity of the real world task. Moreover, the two age groups exhibited significant differences on the TMTA and TMTB versions of both task modalities (paper and can), further supporting the validity of the real world task. This work will have a significant impact on our ability to infer skill or impairment with visual search, spatial reasoning, working memory, and motor proficiency during complex real-world tasks. Thus, we hope to fill a critical need for an exam with the resolution capable of determining deficits which subjective or reductionist assessments may otherwise miss.more » « less
-
Abstract Disorder is an essential parameter in photonic systems and devices, influencing phenomena such as the robustness of topological photonic states and the Anderson localization of modes in waveguides. We develop and demonstrate a method for both analyzing and visualizing positional, size, and shape disorder in periodic structures such as photonic crystals. This analysis method shows selectivity for disorder type and sensitivity to disorder down to less than 1%. We show that the method can be applied to more complex shapes such as those used in topological photonics. The method provides a powerful tool for process development and quality control, including analyzing the precision of E-Beam Lithography before patterns are transferred; quantifying the precision limits of lithography, deposition, or etch processes; and studying the intentional displacement of individual objects within otherwise periodic arrays.more » « less
-
Abstract From quasicrystalline alloys to twisted bilayer graphene, the study of material properties arising from quasiperiodic structure has driven advances in theory and applied science. Here we introduce a class of two-phase composites, structured by deterministic Moiré patterns, and we find that these composites display exotic behavior in their bulk electrical, magnetic, diffusive, thermal, and optical properties. With a slight change in the twist angle, the microstructure goes from periodic to quasiperiodic, and the transport properties switch from those of ordered to randomly disordered materials. This transition is apparent when we distill the relationship between classical transport coefficients and microgeometry into the spectral properties of an operator analogous to the Hamiltonian in quantum physics. We observe this order to disorder transition in terms of band gaps, field localization, and mobility edges analogous to Anderson transitions — even though there are no wave scattering or interference effects at play here.more » « less
-
We study mode localization in a quasi-one-dimensional disordered array of titanium dioxide waveguides above a silver film embedded inside a fused silica matrix. Disorder is introduced by randomly offsetting waveguides from their periodic positions by up to 20% of the array period. Using a perturbative coupled mode theory with nearest-neighbor coupling, we study how mode localization changes with increasing disorder and array size. Our results show mode localization, as measured by both the average effective mode area and variance for all modes, intensifies with increasing disorder, especially for the fundamental modes with tighter plasmonic confinement. Remarkably, we find the average variance scales with the array size, resulting in a universal dependence of normalized variance on disorder for arrays of any size. These findings may have implications for designing photonic devices and developing efficient photodetectors.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/cryst11111282
