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NMR Spin Diffusion Measurements in Disordered Systems: Insights and Limits.
Abstract not provided.
Relaxation time in disordered molecular systems
Relaxation time is the typical time it takes for a closed physical system to attain thermal equilibrium. The equilibrium is brought about by the action of a thermal reservoir inducing changes in the system micro-states. The relaxation time is intuitively expected to increase with system disorder. We derive a simple analytical expression for this dependence in the context of electronic equilibration in an amorphous molecular system model. We find that the disorder dramatically enhances the relaxation time but does not affect its independence of the nature of the initial state.
Approaches for handling high-dimensional cluster expansions of ionic systems
Disordered multicomponent systems attract great interest due to their engineering design flexibility and subsequent rich space of properties. However, detailed characterization of the structure and atomic correlations remains challenging and hinders full navigation of these complex spaces. A lattice cluster expansion is one tool to obtain configurational and energetic resolution. While in theory a cluster expansion can be applied to any system of any dimensionality, the method has primarily been used in binary systems or ternary alloys. Here we apply cluster expansions in high-component ionic systems, setting up the largest cluster expansion ever attempted to our knowledge. In doing so, we address and discuss challenges specific to high-component ionic systems, namely charge state assignments, structural relaxations, and rank-deficient systems. We introduce practical procedures to make the fitting and analysis of complex systems tractable, providing guidance for future computational studies of disordered ionic systems.
Many-body localization in disorder-free systems: The importance of finite-size constraints
Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.
Electronic glasses from a broken gauge symmetry in disorder-free systems
Glass phases can be stabilized by quenched disorders, as in most spin-glass materials, or self-generated through kinetic freezing in disorder-free systems. A canonical example of the latter is structural glasses, which have been extensively studied for many decades. Yet, how the rugged energy landscape of a glass phase is spontaneously generated in disorder-free systems remains one of the key questions in glass physics. Here, in this work, we present a general electronic mechanism for the emergence of glassy phase using the example of itinerant electrons coupled to XY spins on a lattice. This model can also be viewed as the mean-field theory of a superconducting system with attractive density-density interactions. Intriguingly, the electron gauge symmetry in the strong pairing limit gives rise to a macroscopic degeneracy of XY spins. In the presence of electron hopping that breaks the gauge symmetry, the lifting of the extensive degeneracy leads to a glass phase with disordered pairings. Our findings highlight a scenario in which a glassy state originates from the breaking of quantum gauge symmetry without quenched disorders.
Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems
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.
Response of a quantum disordered spin system to a local periodic drive
We consider a one-dimensional spin chain system with quenched disorder and in the presence of a local periodic drive. We study the time evolution of the system in the Floquet basis and evaluate the fidelity susceptibility, which is a measure of how a given state changes under a small perturbation, of states to a weak periodic drive. In this work, we demonstrate that the statistical properties of the fidelity susceptibility over different disorder realizations can be used to identify two phases of the system: (1) the many-body localized phase, in which the susceptibility exhibits long tails while its average value decreases rapidly as disorder increases, and (2) the ergodic phase, in which the susceptibility distribution is narrow and its average value weakly depends on disorder. This distinction in the average value of the susceptibility between the two phases develops readily for systems with ten or more spins. Therefore, recently built networks of qubits subject to a local drive can simulate dynamics of a system in the many-body localization regime. We also show that the spin accumulation speed is correlated with the fidelity susceptibility and can also be used to distinguish the two phases.
Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices
Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.
Exciton Condensation in a Two-Dimensional System with Disorder
The Bose–Einstein condensation of excitons in two-dimensional (2D) systems has been studied theoretically, taking into account both the random potential associated with imperfections of the structure and the finite exciton lifetime. It is shown that the disorder existing in the system makes condensation possible. The finite exciton lifetime limits the thermalization of excitons in the disordered system and sets an additional limit on the critical temperature of the transition. The effects of interparticle interaction and pump fluctuations have been analyzed. The phase correlator has been calculated and the failure of the condensate due to the effects of interaction and fluctuations has been analyzed. The propagation of perturbations in the condensate has been investigated.
Thermal and Thermoelectric Phenomena in Novel Naterials and Systems of Disordered and Interacting Electrons
The major goals of this project were: 1. To study thermal transport in systems of disordered electrons in the presence of the long-range Coulomb interaction, 2. To combine the Quantum Kinetic Equation approach with the Renormalization Group analysis of disordered interacting electrons for studying thermal transport near the Metal Insulator Transition, 3. To study thermal transport and thermopower in systems of disordered electrons in the presence of strong electron-electron collisions at intermediate temperatures, and 4. To study the effects of out of plane vibrations on the thermal transport in graphene.
The disorder-induced Raman scattering in Au/MoS{sub 2} heterostructures
The Raman scattering has been studied in heterostructures composed of a thin MoS{sub 2} flake and a 1-1.5 nm layer of thermally evaporated gold (Au). There have been Au nanoislands detected in the heterostructure. It has been found that their surface density and the average size depend on the MoS{sub 2} thickness. The Raman scattering spectrum in the heterostructure with a few monolayer MoS{sub 2} only weakly depends on the excitation (resonant vs. non-resonant) mode. The overall Raman spectrum corresponds to the total density of phonon states, which is characteristic for disordered systems. The disorder in the MoS{sub 2} layer is related to the mechanical strain induced in the MoS{sub 2} layer by the Au nanoislands. The strain results in the localization of phonon modes, which leads to the relaxation of the momentum conservation rule in the scattering process. The relaxation allows phonons from the whole MoS{sub 2} Brillouin zone to interact with electronic excitations. Our results show that the Au nanoislands resulted from thermal evaporation of a thin metal layer introduce substantial disorder into the crystalline structure of the thin MoS{sub 2} layers.
Locally self-consistent embedding approach for disordered electronic systems
We introduce an embedding scheme for the locally self-consistent method to study disordered electron systems. We test this approach 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 embedded 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 current work opens the path towards the development of a typical medium embedding scheme for the O(N) multiple scattering methods.
Spin-lattice Relaxation Time in Disordered Graphene Systems
We analyzed the spin-lattice relaxation time of graphene systems in the presence of disorder. We consider the case of strong scatterers (unitary limit). The effect of the impurity concentration on the spin-lattice relaxation time is analyzed. We find different behaviors of the spin-lattice relaxation time for different impurity concentrations.
The Nonuniversality of the Frequency Dependence of the Conductivity in Disordered Nanogranulated Systems
The real part of the high-frequency phononless conductivity is calculated in the pair approximation for a disordered array of densely packed spherical nanogranules. The generalization of the theory of phononless conductivity for systems with point impurities to systems with localized finite sizes (arrays of nanogranules or quantum dots) reveals that the high-frequency conductivity depends on the distribution function of the distances between the surfaces of granules P(w). This is expected to cause the discrepancy of the real part of the conductivity σ{sub 1}(ω) from the linear frequency dependence. In the vicinity of the frequency ω ~ ω{sub c} = 2I{sub 0}/ℏ (here I{sub 0} is a preexponential factor of the resonance integral) for disordered granulated systems is likely to deviate from the universality σ{sub 1}(ω) ~ ω{sup s} (s ≈ 1) due to the attenuation of the frequency dependence σ{sub 1}(ω) of the conductivity and its nonmonotonicity. The nonmonotonicity of σ{sub 1}(ω) must arise at lower frequencies as a result of decreased preexponential factor I{sub 0} of the resonance integral with increasing granule size.
Finite-temperature calculations of the Compton profile of Be, Li, and Si
High resolution inelastic x-ray scattering experiments are widely used to study the electronic and chemical properties of materials under a range of conditions, from ambient temperature to the warm dense matter regime. Here, we use the real-space multiple scattering (RSMS) Green's function formalism coupled with density functional theory molecular dynamics (DFT-MD) to study thermal effects on the Compton profile (CP) of disordered systems. The RSMS method is advantageous for calculations of highly disordered, aperiodic systems because it places no restriction on symmetry. As a test, we apply our approach to thermally disordered Be, Li, and Si in both liquid and solid phases. We find good agreement with experimental and other theoretical results, showing that the real-space multiple scattering approach coupled with DFT-MD is an efficient and reliable method for calculating the CP of disordered systems at finite temperatures.
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