63 research outputs found
Quantum Corrections to Thermopower and Conductivity in Graphene
The quantum corrections to the conductivity and the thermopower in monolayer
graphene are studied. We use the recursive Green's function method to calculate
numerically the conductivity and the thermopower of graphene. We then analyze
these weak localization corrections by fitting with the analytical theory as
function of the impurity parameters and the gate potential. As a result of the
quantum corrections to the thermopower, we find large magnetothermopower which
is shown to provide a very sensitive measure of the size and strength of the
impurities. We compare these analytical and numerical results with existing
experimental measurements of magnetoconductance of single layer graphene and
find that the average size and strength of the impurities in these samples can
thereby be determined. We suggest favorable parameter ranges for future
measurements of the magnetothermopower
Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
We investigate the magnetic susceptibility of quantum spin chains
of spins with power-law long-range antiferromagnetic coupling as a
function of their spatial decay exponent and cutoff length . The
calculations are based on the strong disorder renormalization method which is
used to obtain the temperature dependence of and distribution
functions of couplings at each renormalization step. For the case with only
algebraic decay () we find a crossover at
between a phase with a divergent low-temperature susceptibility
for to a phase with a vanishing
for . For finite cutoff lengths
, this crossover occurs at a smaller . Additionally we
study the localization of spin excitations for by evaluating
the distribution function of excitation energies and we find a delocalization
transition that coincides with the opening of the pseudo-gap at
.Comment: 6 pages, 7 figure
RKKY Interaction in Disordered Graphene
We investigate the effects of nonmagnetic disorder on the
Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction in graphene by studying
numerically the Anderson model with on-site and hopping disorder on a honeycomb
lattice at half filling. We evaluate the strength of the interaction as a
function of the distance R between two magnetic ions, as well as their lattice
positions and orientations. In the clean limit, we find that the strength of
the interaction decays as 1/R^3, with its sign and oscillation amplitude
showing strong anisotropy. With increasing on-site disorder, the mean amplitude
decreases exponentially at distances exceeding the elastic mean free path. At
smaller distances, however, the oscillation amplitude increases strongly and
its sign changes on the same sublattice for all directions but the armchair
direction. For random hopping disorder, no sign change is observed. No
significant changes to the geometrical average values of the RKKY interaction
are found at small distances, while exponential suppression is observed at
distances exceeding the localization length.Comment: 4+\epsilon\ pages, 5 figure
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
Universal Distribution of Kondo Temperatures in Dirty Metals
Kondo screening of diluted magnetic impurities in a disordered host is
studied analytically and numerically in one, two and three dimensions. It is
shown that in the T_K \to 0 limit the distribution of Kondo temperatures has a
universal form, P(T_K) \sim T_K^{-\alpha} that holds in the insulating phase
and persists in the metallic phase close to the metal insulator transition.
Moreover, the exponent \alpha depends only on the dimensionality. The most
important consequence of this result is that the T-dependence of thermodynamic
properties is smooth across the metal-insulator transition in three dimensional
systems.Comment: 4 pages, 3 figures; added referenc
Symmetry Dependence of Localization in Quasi- 1- dimensional Disordered Wires
The crossover in energy level statistics of a quasi-1-dimensional disordered
wire as a function of its length L is used, in order to derive its averaged
localization length, without magnetic field, in a magnetic field and for
moderate spin orbit scattering strength. An analytical function of the magnetic
field for the local level spacing is obtained, and found to be in excellent
agreement with the magnetic field dependent activation energy, recently
measured in low-mobility quasi-one-dimensional wires\cite{khavin}. This formula
can be used to extract directly and accurately the localization length from
magnetoresistance experiments. In general, the local level spacing is shown to
be proportional to the excitation gap of a virtual particle, moving on a
compact symmetric space.Comment: 4 pages, 2 Eqs. added, Eperimental Data included in Fig.
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
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