Disorder screening in strongly correlated systems

Mooij Law Violation from Nanoscale Disorder

Nanoscale inhomogeneity can profoundly impact properties of two-dimensional van der Waals materials. Here, we reveal how sulfur substitution on the selenium atomic sites in Fe_1-ySe_1-xS_x (0 ≤ x ≤ 1, y ≤ 0.1) causes Fe-Ch (Ch = Se, S) bond length differences and strong disorder for 0.4 ≤ x ≤ 0.8. There, the superconducting transition temperature T_c is suppressed and disorder-related scattering is enhanced. The high-temperature metallic resistivity in the presence of strong disorder exceeds the Mott limit and provides an example of the violation of Matthiessen's rule and the Mooij law, a dominant effect when adding moderate disorder past the Drude/Matthiessen's regime in all materials. The scattering mechanism responsible for the resistivity above the Mott limit is unrelated to phonons and arises for strong Se/S atom disorder in the tetrahedral surrounding of Fe. Our findings shed light on the intricate connection between the nanostructural details and the unconventional scattering mechanism, which is possibly related to charge-nematic or magnetic spin fluctuations.

Local Spectroscopies Reveal Percolative Metal in Disordered Mott Insulators

We elucidate the mechanism by which a Mott insulator transforms into a non-Fermi liquid metal upon increasing disorder at half filling. By correlating maps of the local density of states, the local magnetization, and the local bond conductivity, we find a collapse of the Mott gap toward a V-shaped pseudogapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites but an increase of bond conductivity. These metallic regions percolate to form an emergent non-Fermi liquid phase with a conductivity that increases with temperature. Bond conductivity measured via local microwave impedance combined with charge and spin local spectroscopies are ideal tools to corroborate our predictions.

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.

Non-Fermi Liquid Behavior and Continuously Tunable Resistivity Exponents in the Anderson-Hubbard Model at Finite Temperature

We employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation U and disorder V strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling T^{α} for this metal reveals non-Fermi liquid characteristics. Moreover, a continuous dependence of α on U and V from linear to nearly quadratic is observed. We argue that these exotic results arise from a systematic change with U and V of the "effective" disorder, a combination of quenched disorder and intrinsic localized spins.

First-Principles-Based Method for Electron Localization: Application to Monolayer Hexagonal Boron Nitride

We present a first-principles-based many-body typical medium dynamical cluster approximation and density function theory method for characterizing electron localization in disordered structures. This method applied to monolayer hexagonal boron nitride shows that the presence of boron vacancies could turn this wide-gap insulator into a correlated metal. Depending on the strength of the electron interactions, these calculations suggest that conduction could be obtained at a boron vacancy concentration as low as 1.0%. We also explore the distribution of the local density of states, a fingerprint of spatial variations, which allows localized and delocalized states to be distinguished. The presented method enables the study of disorder-driven insulator-metal transitions not only in h-BN but also in other physical materials.

Non-Gaussian spatial correlations dramatically weaken localization

We perform variational studies of the interaction-localization problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size scaling studies for the conductance of disordered Hubbard chains at half-filling and zero temperature. While our results indicate that quasiparticle wave functions remain exponentially localized even in the presence of moderate to strong repulsive interactions, we show that interactions produce a strong decrease of the characteristic conductance scale g^{*} signaling the crossover to strong localization. This effect, which cannot be captured by a simple renormalization of the disorder strength, instead reflects a peculiar non-Gaussian form of the spatial correlations of the screened disordered potential, a hitherto neglected mechanism to dramatically reduce the impact of Anderson localization (interference) effects.

Universal quantum criticality at the Mott-Anderson transition

We present a large N solution of a microscopic model describing the Mott-Anderson transition on a finite-coordination Bethe lattice. Our results demonstrate that strong spatial fluctuations, due to Anderson localization effects, dramatically modify the quantum critical behavior near disordered Mott transitions. The leading critical behavior of quasiparticle wave functions is shown to assume a universal form in the full range from weak to strong disorder, in contrast to disorder-driven non-Fermi liquid ("electronic Griffiths phase") behavior, which is found only in the strongly correlated regime.

Quantum ripples in strongly correlated metals

We study how well-known effects of the long-ranged Friedel oscillations are affected by strong electronic correlations. We first show that their range and amplitude are significantly suppressed in strongly renormalized Fermi liquids. We then investigate the interplay of elastic and inelastic scattering in the presence of these oscillations. In the singular case of two-dimensional systems, we show how the anomalous ballistic scattering rate is confined to a very restricted temperature range even for moderate correlations. In general, our analytical results indicate that a prominent role of Friedel oscillations is relegated to weakly interacting systems.

Electronic Griffiths phase of the d = 2 Mott transition

We investigate the effects of disorder within the T = 0 Brinkman-Rice scenario for the Mott metal-insulator transition in two dimensions. For sufficiently weak disorder the transition retains the Mott character, as signaled by the vanishing of the local quasiparticle weights Z_{i} and strong screening of the renormalized site energies at criticality. In contrast to the behavior in high dimensions, here the local spatial fluctuations of quasiparticle parameters are strongly enhanced in the critical regime, with a distribution function P(Z) approximately Z;{alpha-1} and alpha --> 0 at the transition. This behavior indicates a robust emergence of an electronic Griffiths phase preceding the metal-insulator transition, in a fashion surprisingly reminiscent of the "infinite randomness fixed point" scenario for disordered quantum magnets.

Critical behavior at the mott-anderson transition: a typical-medium theory perspective

We present a detailed analysis of the critical behavior close to the Mott-Anderson transition. Our findings are based on a combination of numerical and analytical results obtained within the framework of typical-medium theory-the simplest extension of dynamical mean field theory capable of incorporating Anderson localization effects. By making use of previous scaling studies of Anderson impurity models close to the metal-insulator transition, we solve this problem analytically and reveal the dependence of the critical behavior on the particle-hole symmetry. Our main result is that, for sufficiently strong disorder, the Mott-Anderson transition is characterized by a precisely defined two-fluid behavior, in which only a fraction of the electrons undergo a "site selective" Mott localization; the rest become Anderson-localized quasiparticles.

Competition between Anderson localization and antiferromagnetism in correlated lattice fermion systems with disorder

The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.

Inhomogeneous metallic phase in a disordered Mott insulator in two dimensions

We show that, with increasing randomness, the spectral gap in a 2D Mott-Hubbard insulator is destroyed first at a disorder V(c1), while antiferromagnetism persists up to a higher V(c2). Most unexpectedly, between V(c1) and V(c2) the system is metallic and is sandwiched between the Mott insulator below V(c1) and the Anderson insulator above V(c2). The metal is formed when the spectral gap gets destroyed locally in regions where the disorder potential is high enough to overcome the interelectron repulsion. This generates puddles with enhanced charge fluctuations that percolate with increasing disorder, resulting in a spatially inhomogeneous metallic phase.