761 research outputs found
Effects of interactions in transport through Aharonov-Bohm-Casher interferometers
We study the conductance through a ring described by the Hubbard model (such
as an array of quantum dots), threaded by a magnetic flux and subject to Rashba
spin-orbit coupling (SOC). We develop a formalism that is able to describe the
interference effects as well as the Kondo effect when the number of electrons
in the ring is odd. In the Kondo regime, the SOC reduces the conductance from
the unitary limit, and in combination with the magnetic flux, the device acts
as a spin polarizer.Comment: 5 pages, 5 figure
Spectral density of an interacting dot coupled indirectly to conducting leads
We study the spectral density of electrons rho in an interacting quantum dot
(QD) with a hybridization lambda to a non-interacting QD, which in turn is
coupled to a non-interacting conduction band. The system corresponds to an
impurity Anderson model in which the conduction band has a Lorentzian density
of states of width Delta2.
We solved the model using perturbation theory in the Coulomb repulsion U
(PTU) up to second order and a slave-boson mean-field approximation (SBMFA).
The PTU works surprisingly well near the exactly solvable limit Delta2 -> 0.
For fixed U and large enough lambda or small enough Delta2, the Kondo peak in
rho(omega) splits into two peaks. This splitting can be understood in terms of
weakly interacting quasiparticles. Before the splitting takes place the
universal properties of the model in the Kondo regime are lost. Using the
SBMFA, simple analytical expressions for the occurrence of split peaks are
obtained. For small or moderate Delta2, the side bands of rho(omega) have the
form of narrow resonances, that were missed in previous studies using the
numerical renormalization group. This technique also has shortcomings for
describing properly the split Kondo peaks. As the temperature is increased, the
intensity of the split Kondo peaks decreases, but it is not completely
suppressed at high temperatures.Comment: 13 pages, 13 figures, accepted in Phys. Rev.
Valence fluctuations in a lattice of magnetic molecules: application to iron(II) phtalocyanine molecules on Au(111)
We study theoretically a square lattice of the organometallic Kondo adsorbate
iron(II) phtalocyanine (FePc) deposited on top of Au(111), motivated by recent
scanning tunneling microscopy experiments. We describe the system by means of
an effective Hubbard-Anderson model, where each molecule has degenerate
effective orbitals with and symmetry, which we solve for
arbitrary occupation and arbitrary on-site repulsion . To that end, we
introduce a generalized slave-boson mean-field approximation (SBMFA) which
correctly describes both the non-interacting limit (NIL) and the
strongly-interacting limit , where our formalism
reproduces the correct value of the Kondo temperature for an isolated FePc
molecule. Our results indicate that while the isolated molecule can be
described by an SU(4) Anderson model in the Kondo regime, the case of the
square lattice corresponds to the intermediate-valence regime, with a total
occupation of nearly 1.65 holes in the FePc molecular orbitals. Our results
have important implications for the physical interpretation of the experiment.Comment: 7 pages, 2 figure
Spectral evolution of the SU(4) Kondo effect from the single impurity to the two-dimensional lattice
We describe the evolution of the SU(4) Kondo effect as the number of magnetic
centers increases from one impurity to the two-dimensional (2D) lattice. We
derive a Hubbard-Anderson model which describes a 2D array of atoms or
molecules with two-fold orbital degeneracy, acting as magnetic impurities and
interacting with a metallic host. We calculate the differential conductance,
observed typically in experiments of scanning tunneling spectroscopy, for
different arrangements of impurities on a metallic surface: a single impurity,
a periodic square lattice, and several sites of a rectangular cluster. Our
results point towards the crucial importance of the orbital degeneracy and
agree well with recent experiments in different systems of iron(II)
phtalocyanine molecules deposited on top of Au(111) [N. Tsukahara et al., Phys.
Rev. Lett. 106, 187201 (2011)], indicating that this would be the first
experimental realization of an artificial 2D SU(4) Kondo-lattice system.Comment: 17 pages, 4 figures. New version contains an Appendix with details of
the derivation of the Hamiltonian Eq.(2), derivation of the slave-boson
mean-field equations, and an estimation of the upper bounds of the RKKY
interactio
Magnetic phases in the one-dimensional Kondo chain on a metallic surface
We study the low-temperature properties of a one-dimensional spin-1/2 chain
of magnetic impurities coupled to a (normal) metal environment by means of
anisotropic Kondo exchange. In the case of easy-plane anisotropy, we obtain the
phase diagram of this system at T=0. We show that the in-plane Kondo coupling
destabilizes the Tomonaga-Luttinger phase of the spin-chain, and leads to two
different phases: i) At strong Kondo coupling, the spins in the chain form
Kondo singlets and become screened by the metallic environment, and ii) At weak
and intermediate Kondo coupling, we find a novel dissipative phase
characterized by diffusive gapless spin excitations. The two phases are
separated by a quantum critical point of the Wilson-Fisher universality class
with dynamical exponent .Comment: 15 pages, 3 figures. New version contains clarifications about the
specific approximations. Accepted for publication in PR
Explicit minimal Scherk saddle towers of arbitrary even genera in
Starting from works by Scherk (1835) and by Enneper-Weierstra\ss \ (1863),
new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see
\cite{Karcher1,Karcher}). In the singly periodic case, Karcher's examples of
positive genera had been unique until Traizet obtained new ones in 1996 (see
\cite{Traizet}). However, Traizet's construction is implicit and excludes {\it
towers}, namely the desingularisation of more than two concurrent planes. Then,
new explicit towers were found only in 2006 by Martin and Ramos Batista (see
\cite{Martin}), all of them with genus one. For genus two, the first such
towers were constructed in 2010 (see \cite{Valerio2}). Back to 2009, implicit
towers of arbitrary genera were found in \cite{HMM}. In our present work we
obtain {\it explicit} minimal Scherk saddle towers, for any given genus ,
Performance analysis of the Least-Squares estimator in Astrometry
We characterize the performance of the widely-used least-squares estimator in
astrometry in terms of a comparison with the Cramer-Rao lower variance bound.
In this inference context the performance of the least-squares estimator does
not offer a closed-form expression, but a new result is presented (Theorem 1)
where both the bias and the mean-square-error of the least-squares estimator
are bounded and approximated analytically, in the latter case in terms of a
nominal value and an interval around it. From the predicted nominal value we
analyze how efficient is the least-squares estimator in comparison with the
minimum variance Cramer-Rao bound. Based on our results, we show that, for the
high signal-to-noise ratio regime, the performance of the least-squares
estimator is significantly poorer than the Cramer-Rao bound, and we
characterize this gap analytically. On the positive side, we show that for the
challenging low signal-to-noise regime (attributed to either a weak
astronomical signal or a noise-dominated condition) the least-squares estimator
is near optimal, as its performance asymptotically approaches the Cramer-Rao
bound. However, we also demonstrate that, in general, there is no unbiased
estimator for the astrometric position that can precisely reach the Cramer-Rao
bound. We validate our theoretical analysis through simulated digital-detector
observations under typical observing conditions. We show that the nominal value
for the mean-square-error of the least-squares estimator (obtained from our
theorem) can be used as a benchmark indicator of the expected statistical
performance of the least-squares method under a wide range of conditions. Our
results are valid for an idealized linear (one-dimensional) array detector
where intra-pixel response changes are neglected, and where flat-fielding is
achieved with very high accuracy.Comment: 35 pages, 8 figures. Accepted for publication by PAS
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