53 research outputs found
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 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
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