The crossover between a free magnetic moment phase and a Kondo phase in low dimensional disordered metals with dilute magnetic impurities is studied. We perform a finite size scaling analysis of the distribution of the Kondo temperature as obtained from a numerical renormalization group calculation of the local magnetic susceptibility and from the solution of the self-consistent Nagaoka-Suhl equation. We find a sizable fraction of free (unscreened) magnetic moments when the exchange coupling falls below a disorder-dependent critical value Jc. Our numerical results show that between the free moment phase due to Anderson localization and the Kondo screened phase there is a phase where free moments occur due to the appearance of random local pseudogaps at the Fermi energy whose width and power scale with the elastic scattering rate 1/τ .The Kondo problem is of central importance for understanding low-temperature anomalies in low-dimensional disordered metals [1,2,3,4,5,6,7,8,9,10,11,12], such as the saturation of the dephasing rate [13] and the non-Fermi-liquid behavior of certain magnetic alloys [1,14]. For a clean metal, the screening of a spin-1/2 magnetic impurity is governed by a single energy scale, the Kondo temperature T K . Thermodynamic observables and transport properties obey universal functions which scale with T K . Thus, in a metal where nonmagnetic disorder is also present, two fundamental questions naturally arise: (i) Is the Kondo temperature modified by nonmagnetic disorder? (ii) Is the one-parameter scaling behavior still valid? It is well known [1,2,5,7,11] that magnetic moments remain unscreened when conduction electrons are localized due to disorder. However, in weakly disordered two-dimensional electron systems, the localization length is macroscopically large, and so is the number N c of eigenstates with a finite amplitude at the position of the magnetic impurity. In this case, one does not expect to find unscreened magnetic moments for experimentally relevant values of the exchange coupling J.Another situation where magnetic moments remain free in metals at low temperatures occurs when the density of states has a global pseudogap at the Fermi energy E F , namely,. In clean metals, the pseudogap quenches the Kondo screening when J falls below a critical value J c (α). So far, only a few values of α have been realized experimentally: α = 1 in graphene and in d-wave superconductors and α = 2 in p-wave superconductors. In this Letter we examine the quantum phase diagram of magnetic moments diluted in two-dimensional disordered metals using a modified version of the numerical renormalization group (NRG) method. We find a free moment phase which we attribute to the random occurrence of local pseudogaps. The existence of free moments is confirmed directly with NRG by the Curie-like behavior of the the local magnetic susceptibility at low temperatures. Finite-size scaling is performed to demonstrate the robustness of our finding. Furthermore, the distribution of Kondo temperatures obtained numeric...

An accurate numerical consideration is carried out of the ground state for the simplified model which is traditionally used for the description of Verwey transition and related phenomena. In the framework of 1D spinless fermion model, the effects of next-nearest neighbour (NNN) interaction on the metal-insulator transition are investigated for electron concentrations 1/2 and 2/3. It is shown that for large enough NNN transfer integrals the electronic topological transition of metal-metal type is also possible. The corresponding phase diagrams are presented.

A numerical renormalization group (NRG) investigation of the one-centre t − t ′ Kondo problem is performed for the square lattice with account of logarithmic Van Hove singularities (VHS) in the electron density of states. The magnetic susceptibility, entropy and specific heat are calculated. The temperature dependences of the thermodynamic properties in the presence of VHS turn out to be non-trivial. For finite t ′ inverse logarithm of the corresponding Kondo temperature TK demonstrates a crossover from the square-root to standard linear dependence on the s − d exchange coupling. The low-temperature behavior of magnetic susceptibility and linear specific heat are investigated, and the Wilson ratio is obtained. For t ′ → 0 the Fermi-liquid behavior is broken.

We present a theory for spin-polarized scanning tunneling microscopy (SP-STM) of a Kondo impurity on an unpolarized metallic substrate. The spin polarization of the SP-STM breaks the spin symmetry of the Kondo system, similar to an applied magnetic field, leading to a splitting of the Abrikosov-Suhl-Kondo resonance. The amount of splitting is controlled by the strength of the coupling between the impurity and the SP-STM tip and also the overall spin polarization of the SP-STM.Comment: 4 pages, 4 figure