85 research outputs found
Kondo-Anderson Transitions
Dilute magnetic impurities in a disordered Fermi liquid are considered close
to the Anderson metal-insulator transition (AMIT). Critical Power law
correlations between electron wave functions at different energies in the
vicinity of the AMIT result in the formation of pseudogaps of the local density
of states. Magnetic impurities can remain unscreened at such sites. We
determine the density of the resulting free magnetic moments in the zero
temperature limit. While it is finite on the insulating side of the AMIT, it
vanishes at the AMIT, and decays with a power law as function of the distance
to the AMIT. Since the fluctuating spins of these free magnetic moments break
the time reversal symmetry of the conduction electrons, we find a shift of the
AMIT, and the appearance of a semimetal phase. The distribution function of the
Kondo temperature is derived at the AMIT, in the metallic phase and in
the insulator phase. This allows us to find the quantum phase diagram in an
external magnetic field and at finite temperature . We calculate the
resulting magnetic susceptibility, the specific heat, and the spin relaxation
rate as function of temperature. We find a phase diagram with finite
temperature transitions between insulator, critical semimetal, and metal
phases. These new types of phase transitions are caused by the interplay
between Kondo screening and Anderson localization, with the latter being
shifted by the appearance of the temperature-dependent spin-flip scattering
rate. Accordingly, we name them Kondo-Anderson transitions (KATs).Comment: 18 pages, 9 figure
Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals
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 . 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 .Comment: 4 pages, 6 figure
Topological Effects on the Magnetoconductivity in Topological Insulators
Three-dimensional strong topological insulators (TIs) guarantee the existence
of a 2-D conducting surface state which completely covers the surface of the
TI. The TI surface state necessarily wraps around the TI's top, bottom, and two
sidewalls, and is therefore topologically distinct from ordinary 2-D electron
gases (2DEGs) which are planar. This has several consequences for the
magnetoconductivity , a frequently studied measure of weak
antilocalization which is sensitive to the quantum coherence time
and to temperature. We show that conduction on the TI sidewalls systematically
reduces , multiplying it by a factor which is always less than
one and decreases in thicker samples. In addition, we present both an
analytical formula and numerical results for the tilted-field
magnetoconductivity which has been measured in several experiments. Lastly, we
predict that as the temperature is reduced will enter a wrapped
regime where it is sensitive to diffusion processes which make one or more
circuits around the TI. In this wrapped regime the magnetoconductivity's
dependence on temperature, typically in 2DEGs, disappears. We present
numerical and analytical predictions for the wrapped regime at both small and
large field strengths. The wrapped regime and topological signatures discussed
here should be visible in the same samples and at the same temperatures where
the Altshuler-Aronov-Spivak (AAS) effect has already been observed, when the
measurements are repeated with the magnetic field pointed perpendicularly to
the TI's top face
Disorder-quenched Kondo effect in mesosocopic electronic systems
Nonmagnetic disorder is shown to quench the screening of magnetic moments in
metals, the Kondo effect. The probability that a magnetic moment remains free
down to zero temperature is found to increase with disorder strength.
Experimental consequences for disordered metals are studied. In particular, it
is shown that the presence of magnetic impurities with a small Kondo
temperature enhances the electron's dephasing rate at low temperatures in
comparison to the clean metal case. It is furthermore proven that the width of
the distribution of Kondo temperatures remains finite in the thermodynamic
(infinite volume) limit due to wave function correlations within an energy
interval of order , where is the elastic scattering time. When
time-reversal symmetry is broken either by applying a magnetic field or by
increasing the concentration of magnetic impurities, the distribution of Kondo
temperatures becomes narrower.Comment: 17 pages, 7 figures, new results on Kondo effect in quasi-1D wires
added, 6 Refs. adde
Exploring Level Statistics from Quantum Chaos to Localization with the Autocorrelation Function of Spectral Determinants
The autocorrelation function of spectral determinants (ASD) is used to
characterize the discrete spectrum of a phase coherent quasi- 1- dimensional,
disordered wire as a function of its length L in a finite, weak magnetic field.
An analytical function is obtained depending only on the dimensionless
conductance g= xi/L where xi is the localization length, the scaled frequency
x= omega/Delta, where Delta is the average level spacing of the wire, and the
global symmetry of the system. A metal- insulator crossover is observed,
showing that information on localization is contained in the disorder averaged
ASD.Comment: 4 pages, 3 figure
Localization Length in Anderson Insulator with Kondo Impurities
The localization length, , in a 2--dimensional Anderson insulator
depends on the electron spin scattering rate by magnetic impurities,
. For antiferromagnetic sign of the exchange, %constant, the time
is {\em itself a function of }, due to the Kondo correlations. We
demonstrate that the unitary regime of localization is impossible when the
concentration of magnetic impurities, , is smaller than a critical
value, . For , the dependence of on the
dimensionless conductance, , is {\em reentrant}, crossing over to unitary,
and back to orthogonal behavior upon increasing . Sensitivity of Kondo
correlations to a weak {\em parallel} magnetic field results in a giant
parallel magnetoresistance.Comment: 5 pages, 1 figur
RKKY Interactions in Graphene: Dependence on Disorder and Gate Voltage
We report the dependence of Ruderman-Kittel-Kasuya-Yoshida\,(RKKY)
interaction on nonmagmetic disorder and gate voltage in grapheme. First the
semiclassical method is employed to reserve the expression for RKKY interaction
in clean graphene. Due to the pseudogap at Dirac point, the RKKY coupling in
undoped grapheme is found to be proportional to . Next, we investigate
how the RKKY interaction depends on nonmagnetic disorder strength and gate
voltage by studying numerically the Anderson tight-binding model on a honeycomb
lattice. We observe that the RKKY interaction along the armchair direction is
more robust to nonmagnetic disorder than in other directions. This effect can
be explained semiclassically: The presence of multiple shortest paths between
two lattice sites in the armchair directions is found to be responsible for the
reduceddisorder sensitivity. We also present the distribution of the RKKY
interaction for the zigzag and armchair directions. We identify three different
shapes of the distributions which are repeated periodically along the zigzag
direction, while only one kind, and more narrow distribution, is observed along
the armchair direction. Moreover, we find that the distribution of amplitudes
of the RKKY interaction crosses over from a non-Gaussian shape with very long
tails to a completely log-normal distribution when increasing the nonmagnetic
disorder strength. The width of the log-normal distribution is found to
linearly increase with the strength of disorder, in agreement with analytical
predictions. At finite gate voltage near the Dirac point, Friedel oscillation
appears in addition to the oscillation from the interference between two Dirac
points. This results in a beating pattern. We study how these beating patterns
are effected by the nonmagnetic disorder in doped graphene
- …