159 research outputs found
Phase diagram of the Mott transition in a two-band Hubbard model in infinite dimensions
The Mott metal-insulator transition in the two-band Hubbard model in infinite
dimensions is studied by using the linearized dynamical mean-field theory
recently developed by Bulla and Potthoff. The phase boundary of the
metal-insulator transition is obtained analytically as a function of the
on-site Coulomb interaction at the -orbital, the charge-transfer energy
between the - and -orbitals and the hopping integrals between ,
and orbitals. The result is in good agreement with the numerical
results obtained from the exact diagonalization method.Comment: 10 pages, 4 figure
Fermi liquids and the Luttinger integral
The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral I L, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of I L with I L = ±π/2, occur in impurity models classified as singular Fermi liquids. Here we show the same values, I L = ±π/2, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological
Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling : Equilibrium properties
We study the low-energy behavior of the vertex function of a single Anderson impurity away from half filling for finite magnetic fields, using the Ward identities with careful consideration of the antisymmetry and analytic properties. The asymptotic form of the vertex function Γ σ σ ′ ; σ ′ σ ( i ω , i ω ′ ; i ω ′ , i ω ) is determined up to terms of linear order with respect to the two frequencies ω and ω ′ , as well as the ω 2 contribution for antiparallel spins σ ′ ≠σ at ω ′ = 0 . From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida [Prog. Theor. Phys. 54, 316 (1975)]. The ω 2 real part of the self-energy Σ σ ( i ω ) is shown to be expressed in terms of the double derivative ∂ 2 Σ σ ( 0 ) / ∂ ε 2 d σ with respect to the impurity energy level ε d σ , and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora (FMvDM) in the Nozières phenomenological Fermi-liquid theory [Phys. Rev. B 95, 165404 (2017)]. We also calculate the T 2 correction of the self-energy and find that the real part can be expressed in terms of the three-body correlation function ∂ χ ↑ ↓ / ∂ ε d , − σ , where χ ↑ ↓ is the static susceptibility between antiparallel spins. We also provide an alternative derivation of the asymptotic form of the vertex function. Specifically, we calculate the skeleton diagrams for the vertex function Γ σ σ ; σ σ ( i ω , 0 ; 0 , i ω ) for parallel spins up to order U 4 in the Coulomb repulsion U . It directly clarifies the fact that the analytic components of order ω vanish as a result of the cancellation of four related Feynman diagrams, which are related to each other through the antisymmetry operation
Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling: Nonequilibrium transport
We extend the microscopic Fermi-liquid theory for the Anderson impurity [Phys. Rev. B 64, 153305 (2001)] to explore nonequilibrium transport at finite magnetic fields. Using the Ward identities in the Keldysh formalism with the analytic and antisymmetric properties of the vertex function, the spin-dependent Fermi-liquid corrections of order T 2 and ( e V ) 2 are determined at low temperatures T and low bias voltages e V . Away from half filling, these corrections can be expressed in terms of the linear and nonlinear static susceptibilities which represent the two-body and three-body fluctuations, respectively. We calculate the nonlinear susceptibilities using the numerical renormalization group, to explore the differential conductance d I / d V through a quantum dot. We find that the two-body fluctuations dominate the corrections in the Kondo regime at zero magnetic field. The contribution of the three-body fluctuations becomes significant far away from half filling, especially in the valence-fluctuation regime and empty-orbital regimes. In finite magnetic fields, the three-body contributions become comparable to the two-body contributions, and play an essential role in the splitting of the zero-bias conductance peak occurring at a magnetic field of the order of the Kondo energy scale. We also apply our microscopic formulation to the magnetoresistance and thermal conductivity of dilute magnetic alloys away from half filling
Nonlinear thermoelectric response of quantum dots: renormalized dual fermions out of equilibrium
The thermoelectric transport properties of nanostructured devices continue to
attract attention from theorists and experimentalist alike as the spatial
confinement allows for a controlled approach to transport properties of
correlated matter. Most of the existing work, however, focuses on
thermoelectric transport in the linear regime despite the fact that the
nonlinear conductance of correlated quantum dots has been studied in some
detail throughout the last decade. Here, we review our recent work on the
effect of particle-hole asymmetry on the nonlinear transport properties in the
vicinity of the strong coupling limit of Kondo-correlated quantum dots and
extend the underlying method, a renormalized superperturbation theory on the
Keldysh contour, to the thermal conductance in the nonlinear regime. We
determine the charge, energy, and heat current through the nanostructure and
study the nonlinear transport coefficients, the entropy production, and the
fate of the Wiedemann-Franz law in the non-thermal steady-state. Our approach
is based on a renormalized perturbation theory in terms of dual fermions around
the particle-hole symmetric strong-coupling limit.Comment: chapter contributed to 'New Materials for Thermoelectric
Applications: Theory and Experiment' Springer Series: NATO Science for Peace
and Security Series - B: Physics and Biophysics, Veljko Zlatic (Editor), Alex
Hewson (Editor). ISBN: 978-9400749863 (2012
Long-range Kondo signature of a single magnetic impurity
The Kondo effect, one of the oldest correlation phenomena known in condensed
matter physics, has regained attention due to scanning tunneling spectroscopy
(STS) experiments performed on single magnetic impurities. Despite the
sub-nanometer resolution capability of local probe techniques one of the
fundamental aspects of Kondo physics, its spatial extension, is still subject
to discussion. Up to now all STS studies on single adsorbed atoms have shown
that observable Kondo features rapidly vanish with increasing distance from the
impurity. Here we report on a hitherto unobserved long range Kondo signature
for single magnetic atoms of Fe and Co buried under a Cu(100) surface. We
present a theoretical interpretation of the measured signatures using a
combined approach of band structure and many-body numerical renormalization
group (NRG) calculations. These are in excellent agreement with the rich
spatially and spectroscopically resolved experimental data.Comment: 7 pages, 3 figures + 8 pages supplementary material; Nature Physics
(Jan 2011 - advanced online publication
Kondo physics in carbon nanotubes
The connection of electrical leads to wire-like molecules is a logical step
in the development of molecular electronics, but also allows studies of
fundamental physics. For example, metallic carbon nanotubes are quantum wires
that have been found to act as one-dimensional quantum dots, Luttinger-liquids,
proximity-induced superconductors and ballistic and diffusive one-dimensional
metals. Here we report that electrically-contacted single-wall nanotubes can
serve as powerful probes of Kondo physics, demonstrating the universality of
the Kondo effect. Arising in the prototypical case from the interaction between
a localized impurity magnetic moment and delocalized electrons in a metallic
host, the Kondo effect has been used to explain enhanced low-temperature
scattering from magnetic impurities in metals, and also occurs in transport
through semiconductor quantum dots. The far higher tunability of dots (in our
case, nanotubes) compared with atomic impurities renders new classes of
Kondo-like effects accessible. Our nanotube devices differ from previous
systems in which Kondo effects have been observed, in that they are
one-dimensional quantum dots with three-dimensional metal (gold) reservoirs.
This allows us to observe Kondo resonances for very large electron number (N)
in the dot, and approaching the unitary limit (where the transmission reaches
its maximum possible value). Moreover, we detect a previously unobserved Kondo
effect, occurring for even values of N in a magnetic field.Comment: 7 pages, pdf onl
A gentle introduction to the functional renormalization group: the Kondo effect in quantum dots
The functional renormalization group provides an efficient description of the
interplay and competition of correlations on different energy scales in
interacting Fermi systems. An exact hierarchy of flow equations yields the
gradual evolution from a microscopic model Hamiltonian to the effective action
as a function of a continuously decreasing energy cutoff. Practical
implementations rely on suitable truncations of the hierarchy, which capture
nonuniversal properties at higher energy scales in addition to the universal
low-energy asymptotics. As a specific example we study transport properties
through a single-level quantum dot coupled to Fermi liquid leads. In
particular, we focus on the temperature T=0 gate voltage dependence of the
linear conductance. A comparison with exact results shows that the functional
renormalization group approach captures the broad resonance plateau as well as
the emergence of the Kondo scale. It can be easily extended to more complex
setups of quantum dots.Comment: contribution to Les Houches proceedings 2006, Springer styl
Nonequilibrium Singlet-Triplet Kondo Effect in Carbon Nanotubes
The Kondo-effect is a many-body phenomenon arising due to conduction
electrons scattering off a localized spin. Coherent spin-flip scattering off
such a quantum impurity correlates the conduction electrons and at low
temperature this leads to a zero-bias conductance anomaly. This has become a
common signature in bias-spectroscopy of single-electron transistors, observed
in GaAs quantum dots as well as in various single-molecule transistors. While
the zero-bias Kondo effect is well established it remains uncertain to what
extent Kondo correlations persist in non-equilibrium situations where inelastic
processes induce decoherence. Here we report on a pronounced conductance peak
observed at finite bias-voltage in a carbon nanotube quantum dot in the spin
singlet ground state. We explain this finite-bias conductance anomaly by a
nonequilibrium Kondo-effect involving excitations into a spin triplet state.
Excellent agreement between calculated and measured nonlinear conductance is
obtained, thus strongly supporting the correlated nature of this nonequilibrium
resonance.Comment: 21 pages, 5 figure
Orbital Kondo effect in carbon nanotubes
Progress in the fabrication of nanometer-scale electronic devices is opening
new opportunities to uncover the deepest aspects of the Kondo effect, one of
the paradigmatic phenomena in the physics of strongly correlated electrons.
Artificial single-impurity Kondo systems have been realized in various
nanostructures, including semiconductor quantum dots, carbon nanotubes and
individual molecules. The Kondo effect is usually regarded as a spin-related
phenomenon, namely the coherent exchange of the spin between a localized state
and a Fermi sea of electrons. In principle, however, the role of the spin could
be replaced by other degrees of freedom, such as an orbital quantum number.
Here we demonstrate that the unique electronic structure of carbon nanotubes
enables the observation of a purely orbital Kondo effect. We use a magnetic
field to tune spin-polarized states into orbital degeneracy and conclude that
the orbital quantum number is conserved during tunneling. When orbital and spin
degeneracies are simultaneously present, we observe a strongly enhanced Kondo
effect, with a multiple splitting of the Kondo resonance at finite field and
predicted to obey a so-called SU(4) symmetry.Comment: 26 pages, including 4+2 figure
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