Typical-Medium Theory of Mott-Anderson Localization

The Mott and the Anderson routes to localization have long been recognized as the two basic processes that can drive the metal-insulator transition (MIT). Theories separately describing each of these mechanisms were discussed long ago, but an accepted approach that can include both has remained elusive. The lack of any obvious static symmetry distinguishing the metal from the insulator poses another fundamental problem, since an appropriate static order parameter cannot be easily found. More recent work, however, has revisited the original arguments of Anderson and Mott, which stressed that the key diference between the metal end the insulator lies in the dynamics of the electron. This physical picture has suggested that the "typical" (geometrically averaged) escape rate from a given lattice site should be regarded as the proper dynamical order parameter for the MIT, one that can naturally describe both the Anderson and the Mott mechanism for localization. This article provides an overview of the recent results obtained from the corresponding Typical-Medium Theory, which provided new insight into the the two-fluid character of the Mott-Anderson transition.Comment: to be published in "Fifty Years of Anderson localization", edited by E. Abrahams (World Scientific, Singapore, 2010); 29 pages, 22 figures

Anderson-Mott transition as a quantum glass problem

We combine a recent mapping of the Anderson-Mott metal-insulator transition on a random-field problem with scaling concepts for random-field magnets to argue that disordered electrons near an Anderson-Mott transition show glass-like behavior. We first discuss attempts to interpret experimental results in terms of a conventional scaling picture, and argue that some of the difficulties encountered point towards a glassy nature of the electrons. We then develop a general scaling theory for a quantum glass, and discuss critical properties of both thermodynamic and transport variables in terms of it. Our most important conclusions are that for a correct interpretation of experiments one must distinguish between self-averaging and non-self averaging observables, and that dynamical or temperature scaling is not of power-law type but rather activated, i.e. given by a generalized Vogel-Fulcher law. Recent mutually contradicting experimental results on Si:P are discussed in the light of this, and new experiments are proposed to test the predictions of our quantum glass scaling theory.Comment: 25pp, REVTeX, 5 ps figs, final version as publishe

Scaling of the Conductivity with Temperature and Uniaxial Stress in Si:B at the Metal-Insulator Transition

Using uniaxial stress to tune Si:B through the metal-insulator transition we find the conductivity at low temperatures shows an excellent fit to scaling with temperature and stress on both sides of the transition. The scaling functions yield the conductivity in the metallic and insulating phases, and allow a reliable determination of the temperature dependence in the critical regions on both sides of the transition

The RKKY interactions and the Mott Transition

A two-site cluster generalization of the Hubbard model in large dimensions is examined in order to study the role of short-range spin correlations near the metal-insulator transition (MIT). The model is mapped to a two-impurity Kondo-Anderson model in a self-consistently determined bath, making it possible to directly address the competition between the Kondo effect and RKKY interactions in a lattice context. Our results indicate that the RKKY interactions lead to qualitative modifications of the MIT scenario even in the absence of long range antiferromagnetic ordering.Comment: 10 pages, 10 figures; to appear in Phys. Rev. B (1999

Mean field theory of the Mott-Anderson transition

We present a theory for disordered interacting electrons that can describe both the Mott and the Anderson transition in the respective limits of zero disorder and zero interaction. We use it to investigate the T=0 Mott-Anderson transition at a fixed electron density, as a the disorder strength is increased. Surprisingly, we find two critical values of disorder W_{nfl} and W_c. For W > W_{nfl}, the system enters a ``Griffiths'' phase, displaying metallic non-Fermi liquid behavior. At even stronger disorder, W=W_c > W_{nfl} the system undergoes a metal insulator transition, characterized by the linear vanishing of both the typical density of states and the typical quasiparticle weight.Comment: 4 pages, 2 figures, REVTEX, eps

Electron propagation in crossed magnetic and electric fields

Laser-atom interaction can be an efficient mechanism for the production of coherent electrons. We analyze the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field--induced quantum mechanical drift motion of i) single electrons and ii) a dilute Fermi gas of electrons. The method yields the drift current and, at the same time it allows us to quantitatively establish the broadening of the (magnetic) Landau levels due to the electric field: Level number k is split into k+1 sublevels that render the $k$th oscillator eigenstate in energy space. Adjacent Landau levels will overlap if the electric field exceeds a critical strength. Our observations are relevant for quantum Hall configurations whenever electric field effects should be taken into account.Comment: 11 pages, 2 figures, submitte

Anisotropic Magnetoconductance in Quench-Condensed Ultrathin Beryllium Films

Near the superconductor-insulator (S-I) transition, quench-condensed ultrathin Be films show a large magnetoconductance which is highly anisotropic in the direction of the applied field. Film conductance can drop as much as seven orders of magnitude in a weak perpendicular field (< 1 T), but is insensitive to a parallel field in the same field range. We believe that this negative magnetoconductance is due to the field de-phasing of the superconducting pair wavefunction. This idea enables us to extract the finite superconducting phase coherence length in nearly superconducting films. Our data indicate that this local phase coherence persists even in highly insulating films in the vicinity of the S-I transition.Comment: 4 pages, 4 figure RevTex, Typos Correcte

Conductivity of Metallic Si:B near the Metal-Insulator Transition: Comparison between Unstressed and Uniaxially Stressed Samples

The low-temperature dc conductivities of barely metallic samples of p-type Si:B are compared for a series of samples with different dopant concentrations, n, in the absence of stress (cubic symmetry), and for a single sample driven from the metallic into the insulating phase by uniaxial compression, S. For all values of temperature and stress, the conductivity of the stressed sample collapses onto a single universal scaling curve. The scaling fit indicates that the conductivity of si:B is proportional to the square-root of T in the critical range. Our data yield a critical conductivity exponent of 1.6, considerably larger than the value reported in earlier experiments where the transition was crossed by varying the dopant concentration. The larger exponent is based on data in a narrow range of stress near the critical value within which scaling holds. We show explicitly that the temperature dependences of the conductivity of stressed and unstressed Si:B are different, suggesting that a direct comparison of the critical behavior and critical exponents for stress- tuned and concentration-tuned transitions may not be warranted

Evolution of the Density of States Gap in a Disordered Superconductor

It has only recently been possible to study the superconducting state in the attractive Hubbard Hamiltonian via a direct observation of the formation of a gap in the density of states N(w). Here we determine the effect of random chemical potentials on N(w) and show that at weak coupling, disorder closes the gap concurrently with the destruction of superconductivity. At larger, but still intermediate coupling, a pseudo-gap in N(w) remains even well beyond the point at which off-diagonal long range order vanishes. This change in the elementary excitations of the insulating phase corresponds to a crossover between Fermi- and Bose-Insulators. These calculations represent the first computation of the density of states in a finite dimensional disordered fermion model via the Quantum Monte Carlo and maximum entropy methods.Comment: 4 pages, 4 figure

The Field-Tuned Superconductor-Insulator Transition with and without Current Bias

The magnetic-field-tuned superconductor-insulator transition has been studied in ultrathin Beryllium films quench-condensed near 20 K. In the zero-current limit, a finite-size scaling analysis yields the scaling exponent product vz = 1.35 +/- 0.10 and a critical sheet resistance R_{c} of about 1.2R_{Q}, with R_{Q} = h/4e^{2}. However, in the presence of dc bias currents that are smaller than the zero-field critical currents, vz becomes 0.75 +/- 0.10. This new set of exponents suggests that the field-tuned transitions with and without dc bias currents belong to different universality classes.Comment: RevTex 4 pages, 4 figures, and 1 table minor change