304 research outputs found
Analytic Trajectories for Mobility Edges in the Anderson Model
A basis of Bloch waves, distorted locally by the random potential, is
introduced for electrons in the Anderson model. Matrix elements of the
Hamiltonian between these distorted waves are averages over infinite numbers of
independent site-energies, and so take definite values rather than
distributions of values. The transformed Hamiltonian is ordered, and may be
interpreted as an itinerant electron interacting with a spin on each site. In
this new basis, the distinction between extended and localized states is clear,
and edges of the bands of extended states, the mobility edges, are calculated
as a function of disorder. In two dimensions these edges have been found in
both analytic and numerical applications of tridiagonalization, but they have
not been found in analytic approaches based on perturbation theory, or the
single-parameter scaling hypothesis; nor have they been detected in numerical
approaches based on scaling or critical distributions of level spacing. In both
two and three dimensions the mobility edges in this work are found to separate
with increasing disorder for all disorders, in contrast with the results of
calculation using numerical scaling for three dimensions. The analytic
trajectories are compared with recent results of numerical tridiagonalization
on samples of over 10^9 sites. This representation of the Anderson model as an
ordered interacting system implies that in addition to transitions at mobility
edges, the Anderson model contains weaker transitions characterized by critical
disorders where the band of extended states decouples from individual sites;
and that singularities in the distribution of site energies, rather than its
second moment, determine localization properties of the Anderson model.Comment: 32 pages, 2 figure
An augmented space recursion study of the electronic structure of rough epitaxial overlayers
In this communication we propose the use of the Augmented Space Recursion as
an ideal methodology for the study of electronic and magnetic structures of
rough surfaces, interfaces and overlayers. The method can take into account
roughness, short-ranged clustering effects, surface dilatation and
interdiffusion. We illustrate our method by an application of Fe overlayer on
Ag (100) surface.Comment: 22 pages, Latex, 6 postscript figure
Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions
We propose a new method for the evaluation of the particle density and
kinetic pressure profiles in inhomogeneous one-dimensional systems of
non-interacting fermions, and apply it to harmonically confined systems of up
to N=1000 fermions. The method invokes a Green's function operator in
coordinate space, which is handled by techniques originally developed for the
calculation of the density of single-particle states from Green's functions in
the energy domain. In contrast to the Thomas-Fermi (local density)
approximation, the exact profiles under harmonic confinement show negative
local pressure in the tails and a prominent shell structure which may become
accessible to observation in magnetically trapped gases of fermionic alkali
atoms.Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev. Let
Krylov Subspace Method for Molecular Dynamics Simulation based on Large-Scale Electronic Structure Theory
For large scale electronic structure calculation, the Krylov subspace method
is introduced to calculate the one-body density matrix instead of the
eigenstates of given Hamiltonian. This method provides an efficient way to
extract the essential character of the Hamiltonian within a limited number of
basis set. Its validation is confirmed by the convergence property of the
density matrix within the subspace. The following quantities are calculated;
energy, force, density of states, and energy spectrum. Molecular dynamics
simulation of Si(001) surface reconstruction is examined as an example, and the
results reproduce the mechanism of asymmetric surface dimer.Comment: 7 pages, 3 figures; corrected typos; to be published in Journal of
the Phys. Soc. of Japa
Efficient Recursion Method for Inverting Overlap Matrix
A new O(N) algorithm based on a recursion method, in which the computational
effort is proportional to the number of atoms N, is presented for calculating
the inverse of an overlap matrix which is needed in electronic structure
calculations with the the non-orthogonal localized basis set. This efficient
inverting method can be incorporated in several O(N) methods for
diagonalization of a generalized secular equation. By studying convergence
properties of the 1-norm of an error matrix for diamond and fcc Al, this method
is compared to three other O(N) methods (the divide method, Taylor expansion
method, and Hotelling's method) with regard to computational accuracy and
efficiency within the density functional theory. The test calculations show
that the new method is about one-hundred times faster than the divide method in
computational time to achieve the same convergence for both diamond and fcc Al,
while the Taylor expansion method and Hotelling's method suffer from numerical
instabilities in most cases.Comment: 17 pages and 4 figure
Site dilution of quantum spins in the honeycomb lattice
We discuss the effect of site dilution on both the magnetization and the
density of states of quantum spins in the honeycomb lattice, described by the
antiferromagnetic Heisenberg spin-S model. For this purpose a real-space
Bogoliubov-Valatin transformation is used. In this work we show that for the
S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin
S=1/2, however, the linear spin wave approximation breaks down. In this case,
we have studied the effect of dilution on the staggered magnetization using the
Stochastic Series Expansion Monte Carlo method. Two main results are to be
stressed from the Monte Carlo method: (i) a better value for the staggered
magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the
staggered magnetization of the percolating cluster at the classical percolation
threshold, showing that there is no quantum critical transition driven by
dilution in the Heisenberg model. In the solution of the problem using linear
the spin wave method we pay special attention to the presence of zero energy
modes. Using a combination of linear spin wave analysis and the recursion
method we were able to obtain the thermodynamic limit behavior of the density
of states for both the square and the honeycomb lattices. We have used both the
staggered magnetization and the density of states to analyze neutron scattering
experiments and Neel temperature measurements on quasi-two- -dimensional
honeycomb systems. Our results are in quantitative agreement with experimental
results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.Comment: 21 pages (REVTEX), 16 figure
Microscopic self-consistent theory of Josephson junctions including dynamical electron correlations
We formulate a fully self-consistent, microscopic model to study the
retardation and correlation effects of the barrier within a Josephson junction.
The junction is described by a series of planes, with electronic correlation
included through a local self energy for each plane. We calculate current-phase
relationships for various junctions, which include non-magnetic impurities in
the barrier region, or an interfacial scattering potential. Our results
indicate that the linear response of the supercurrent to phase across the
barrier region is a good, but not exact indicator of the critical current. Our
calculations of the local density of states show the current-carrying Andreev
bound states and their energy evolution with the phase difference across the
junction.
We calculate the figure of merit for a Josephson junction, which is the
product of the critical current, Ic, and the normal state resistance, R(N), for
junctions with different barrier materials. The normal state resistance is
calculated using the Kubo formula, for a system with zero current flow and no
superconducting order. Semiclassical calculations would predict that these two
quantities are determined by the transmission probabilities of electrons in
such a way that the product is constant for a given superconductor at fixed
temperature. Our self-consistent solutions for different types of barrier
indicate that this is not the case. We suggest some forms of barrier which
could increase the Ic.R(N) product, and hence improve the frequency response of
a Josephson device.Comment: 46 pages, 21 figure
Two--magnon scattering and the spin--phonon interaction beyond the adiabatic approximation
We consider a model of Raman scattering for a two--dimensional
Heisenberg Anti-Ferromagnet which includes a {\it dynamical} spin--phonon
interaction. We observe a broadening of the line shape due to increased
coupling with excited high--energy spin states. Our results are close to a
model of random static exchange interactions, first introduced in this context
by Haas {\it et al.} [J. Appl. Phys. {\bf 75}, 6340, (1994)], which, when
extended to large numbers of spins, explains experiments in the parent
insulating compounds of high- superconductors.Comment: 14 pages (revtex format), 8 postscript figure
Double Exchange Model for Magnetic Hexaborides
A microscopic theory for rare-earth ferromagnetic hexaborides, such as
Eu(1-x)Ca(x)B6, is proposed on the basis of the double-exchange Hamiltonian. In
these systems, the reduced carrier concentrations place the Fermi level near
the mobility edge, introduced in the spectral density by the disordered spin
background. We show that the transport properties such as Hall effect,
magnetoresitance, frequency dependent conductivity, and DC resistivity can be
quantitatively described within the model. We also make specific predictions
for the behavior of the Curie temperature, Tc, as a function of the plasma
frequency, omega_p.Comment: 4 pages, 3 figure
X-ray Absorption Near-Edge Structure calculations with pseudopotentials. Application to K-edge in diamond and alpha-quartz
We present a reciprocal-space pseudopotential scheme for calculating X-ray
absorption near-edge structure (XANES) spectra. The scheme incorporates a
recursive method to compute absorption cross section as a continued fraction.
The continued fraction formulation of absorption is advantageous in that it
permits the treatment of core-hole interaction through large supercells
(hundreds of atoms). The method is compared with recently developed
Bethe-Salpeter approach. The method is applied to the carbon K-edge in diamond
and to the silicon and oxygen K-edges in alpha-quartz for which polarized XANES
spectra were measured. Core-hole effects are investigated by varying the size
of the supercell, thus leading to information similar to that obtained from
cluster size analysis usually performed within multiple scattering
calculations.Comment: 11 pages, 4 figure
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