In the supplemental materials we justify our choice of the number of Chebychev moments used within the kernel polynomial method, show some preliminary results for the large coupling behavior, discuss possible correlation effects in the local density of states, estimate the spin relaxation length and introduce the goodness of fit probability that is used to assess the quality of the fits.
We study effects of classical magnetic impurities on the Anderson metal-insulator transition numerically. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude $W_{\rm c}$ with increasing exchange coupling strength $J$. The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $ν$ and enhances the multifractality parameter $α_…
It is well-known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo scre…
The localization length, $ξ$, in a 2--dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, $τ_s^{-1}$. For antiferromagnetic sign of the exchange, %constant, the time $τ_s$ is {\em itself a function of $ξ$}, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, $n_{\tiny M}$, is smaller than a critical value, $n_c$. For $n_{\tiny M}>n_c$, the dependence of $ξ$ on the dimensionless conductance, $g$, is {\em reentrant}, crossing over to unitary, and back to …
We present results on the Anderson localization in a quasi one-dimensional metallic wire in the presence of magnetic impurities. We focus within the same numerical analysis on both the universal localized and metallic regimes, and we study the evolution of these universal properties as the strength of the magnetic disorder is varied. For this purpose, we use a numerical Landauer approach, and derive the scattering matrix of the wire from electron's Green's function obtained from a recursive algorithm.
It is shown that if impurities in superfluid 3He have form of infinitely long non-magnetic strands, which are straight, parallel to each other and reflect quasi-particles specularly, the temperature of transition of liquid 3He from the normal into the polar phase coincides with that for the bulk liquid without impurities. Magnetic scattering lowers transition temperature for the polar phase in analogy with the conventional superconductors. These results are discussed in connection with the recent experimental findings.
By merging single-site typical medium theory with density functional theory we introduce a self-consistent framework for electronic structure calculations of materials with substitutional disorder which takes into account Anderson localization. The scheme and details of the implementation are presented and applied to the hypothetical alloy Li$_{c}$Be$_{1-c}$, and the results are compared with those obtained with the coherent potential approximation. Furthermore we demonstrate that Anderson localization suppresses ferromagnetic order for a very low concentration of (i) carbon impurities substit…
A conducting 1D line or 2D plane inside (or on the surface of) an insulator is considered.Impurities displace the charges inside the insulator. This results in a long-range fluctuating electric field acting on the conducting line (plane). This field can be modeled by that of randomly distributed electric dipoles. This model provides a random correlated potential with <U(r)U(r+k)> decaying as 1/k . In the 1D case such correlations give essential corrections to the localization length but do not destroy Anderson localization.
A perturbation theory and a diagram technique for a disordered metal are proposed when scattering of quasiparticles by nonmagnetic impurities is caused with a retarded interaction. The perturbation theory generalizes a case of the elastic scattering in a disordered metal. Eliashberg equations for s-wave superconductivity are generalized for such a disordered superconductor. Anderson's theorem is found to be violated in the sense that embedding of the impurities into a s-wave superconductor increases its critical temperature. We showed the amplification of superconducting properties is a result…
We consider chiral electrons moving along the 1D helical edge of a 2D topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.
Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal insulator transition and the integral and fractional quantum Hall effects. In this paper, we investigate the role of disorder in the context of the recently discovered topological insulator, which possesses a pair of helical edge states with opposing spins moving in opposite directions and exhibits the phenomenon of quantum spin Hall effect. We predict an unexpected and nontrivial quantum phase termed "topological Anderson insulator," which is obtained by introducing impurities in a two-…
According to the Anderson theorem, the critical temperature T_c of a disordered superconductor is determined by the average density of states and does not change at the localization threshold. This statement is valid under assumption of a self-averaging order parameter, which can be violated in the strong localization region. Stimulating by statements on the essential increase of T_c near the Anderson transition, we carried out the systematic investigation of possible violations of self-averaging. Strong deviations from the Anderson theorem are possible due to resonances at the quasi-discrete …
We study the transport properties of a finite three dimensional disordered conductor, for both weak and strong scattering on impurities, employing the real-space Green function technique and related Landauer-type formula. The dirty metal is described by a nearest neighbor tight-binding Hamiltonian with a single s-orbital per site and random on-site potential (Anderson model). We compute exactly the zero-temperature conductance of a finite size sample placed between two semi-infinite disorder-free leads. The resistivity is found from the coefficient of linear scaling of the disorder averaged re…
We present a quantum inspired image augmentation protocol which is applicable to classical images and, in principle, due to its known quantum formulation applicable to quantum systems and quantum machine learning in the future. The augmentation technique relies on the phenomenon Anderson localization. As we will illustrate by numerical examples the technique changes classical wave properties by interference effects resulting from scatterings at impurities in the material. We explain that the augmentation can be understood as multiplicative noise, which counter-intuitively averages out, by samp…
A metal can be driven to an insulating phase through distinct mechanisms. A possible way is via the Coulomb interaction, which then defines the Mott metal-insulator transition (MIT). Another possibility is the MIT driven by disorder, the so-called Anderson MIT. Here we analyze interacting particles in disordered Hubbard chains $-$ thus comprising the Mott-Anderson physics $-$ by investigating the ground-state entanglement with density functional theory. The localization signature on entanglement is found to be a local minimum at a certain critical density. Individually, the Mott (Anderson) MIT…
We report a numerical analysis of Anderson localization in a model of a doped semiconductor. The model incorporates the disorder arising from the random spatial distribution of the donor impurities and takes account of the electron-electron interactions between the carriers using density functional theory in the local density approximation. Preliminary results suggest that the model exhibits a metal-insulator transition.
