277 research outputs found
Transport of interacting electrons through a potential barrier: nonperturbative RG approach
We calculate the linear response conductance of electrons in a Luttinger
liquid with arbitrary interaction g_2, and subject to a potential barrier of
arbitrary strength, as a function of temperature. We first map the Hamiltonian
in the basis of scattering states into an effective low energy Hamiltonian in
current algebra form. Analyzing the perturbation theory in the fermionic
representation the diagrams contributing to the renormalization group (RG)
\beta-function are identified. A universal part of the \beta-function is given
by a ladder series and summed to all orders in g_2. First non-universal
corrections beyond the ladder series are discussed. The RG-equation for the
temperature dependent conductance is solved analytically. Our result agrees
with known limiting cases.Comment: 6 pages, 5 figure
Diagrammatic theory of the Anderson impurity model with finite Coulomb interaction
We have developed a self-consistent conserving pseudo particle approximation
for the Anderson impurity model with finite Coulomb interaction, derivable from
a Luttinger Ward functional. It contains an infinite series of skeleton
diagrams built out of fully renormalized Green's functions. The choice of
diagrams is motivated by the Schrieffer Wolff transformation which shows that
singly and doubly occupied states should appear in all bare diagrams
symmetrically. Our numerical results for are in excellent agreement with
the exact values known from the Bethe ansatz solution. The low energy physics
of non-Fermi liquid Anderson impurity systems is correctly described while the
present approximation fails to describe Fermi liquid systems, since some
important coherent spin flip and charge transfer processes are not yet
included. It is believed that CTMA (Conserving T-matrix approximation) diagrams
will recover also Fermi liquid behavior for Anderson models with finite Coulomb
interaction as they do for infinite Coulomb interaction.Comment: 4 pages, 2 figures, presented at the NATO Advanced Research Workshop
on "Size Dependent MAgnetic Scattering", Pecs, Hungary, May 28 - June 1, 200
Interference of quantum critical excitations and soft diffusive modes in a disordered antiferromagnetic metal
We study the temperature-dependent quantum correction to conductivity due to
the interplay of spin density fluctuations and weak disorder for a
two-dimensional metal near an antiferromagnetic (AFM) quantum critical point.
AFM spin density fluctuations carry large momenta around the ordering vector
and, at lowest order of the spin-fermion coupling, only scatter
electrons between "hot spots" of the Fermi surface which are connected by
. Earlier, it was seen that the quantum interference between AFM
spin density fluctuations and soft diffusive modes of the disordered metal is
suppressed, a consequence of the large-momentum scattering. The suppression of
this interference results in a non-singular temperature dependence of the
corresponding interaction correction to conductivity. However, at higher order
of the spin-fermion coupling, electrons on the entire Fermi surface can be
scattered successively by two spin density fluctuations and, in total, suffer a
small momentum transfer. This higher-order process can be described by
composite modes which carry small momenta. We show that the interference
between formally subleading composite modes and diffusive modes generates
singular interaction corrections which ultimately dominate over the
non-singular first-order correction at low temperatures. We derive an effective
low-energy theory from the spin-fermion model which includes the
above-mentioned higher-order process implicitly and show that for weak
spin-fermion coupling the small-momentum transfer is mediated by a composite
propagator. Employing the conventional diagrammatic approach to impurity
scattering, we find the correction for
temperatures above an exponentially small crossover scale.Comment: 13 pages, 7 figures. Published versio
Nonequilibrium Cotunneling through a Three-Level Quantum Dot
We calculate the nonlinear cotunneling conductance through a quantum dot with
3 electrons occupying the three highest lying energy levels. Starting from a
3-orbital Anderson model, we apply a generalized Schrieffer-Wolff
transformation to derive an effective Kondo model for the system. Within this
model we calculate the nonequilibrium occupation numbers and the corresponding
cotunneling current to leading order in the exchange couplings. We identify the
inelastic cotunneling thresholds and their splittings with applied magnetic
field, and make a qualitative comparison to recent experimental data on carbon
nanotube and InAs quantum-wire quantum dots. Further predictions of the model
like cascade resonances and a magnetic-field dependence of the orbital level
splitting are not yet observed but within reach of recent experimental work on
carbon nanotube and InAs nanowire quantum dots.Comment: 12 pages, 13 figure
Elastic properties of graphene flakes: boundary effects and lattice vibrations
We present a calculation of the free energy, the surface free energy and the
elastic constants ("Lam'e parameters" i.e, Poisson ratio, Young's modulus) of
graphene flakes on the level of the density functional theory employing
different standard functionals. We observe that the Lam'e parameters in small
flakes can differ from the bulk values by 30% for hydrogenated zig-zag edges.
The change results from the edge of the flake that compresses the interior.
When including the vibrational zero point motion, we detect a decrease in the
bending rigidity by ~26%. This correction is depending on the flake size, N,
because the vibrational frequencies flow with growing N due to the release of
the edge induced compression. We calculate Grueneisen parameters and find good
agreement with previous authors.Comment: 11 pages, 12 figure
Multiscale quantum criticality: Pomeranchuk instability in isotropic metals
As a paradigmatic example of multi-scale quantum criticality, we consider the
Pomeranchuk instability of an isotropic Fermi liquid in two spatial dimensions,
d=2. The corresponding Ginzburg-Landau theory for the quadrupolar fluctuations
of the Fermi surface consists of two coupled modes, critical at the same point,
and characterized by different dynamical exponents: one being ballistic with
dynamical exponent z=2 and the other one is Landau-damped with z=3, thus giving
rise to multiple dynamical scales. We find that at temperature T=0, the
ballistic mode governs the low-energy structure of the theory as it possesses
the smaller effective dimension d+z. Its self-interaction leads to logarithmic
singularities, which we treat with the help of the renormalization group. At
finite temperature, the coexistence of two different dynamical scales gives
rise to a modified quantum-to-classical crossover. It extends over a
parametrically large regime with intricate interactions of quantum and
classical fluctuations leading to a universal T-dependence of the correlation
length independent of the interaction amplitude. The multiple scales are also
reflected in the phase diagram and in the critical thermodynamics. In
particular, we find that the latter cannot be interpreted in terms of only a
single dynamical exponent: whereas, e.g., the critical specific heat is
determined by the z=3 mode, the critical compressibility is found to be
dominated by the z=2 fluctuations.Comment: 15 pages, 6 figures; (v2) RG implementation with arbitrary dynamical
exponent z, discussion on fixed-points adde
Structure and transport in multi-orbital Kondo systems
We consider Kondo impurity systems with multiple local orbitals, such as rare
earth ions in a metallic host or multi--level quantum dots coupled to metallic
leads. It is shown that the multiplet structure of the local orbitals leads to
multiple Kondo peaks above the Fermi energy , and to ``shadow'' peaks
below . We use a slave boson mean field theory, which recovers the strong
coupling Fermi liquid fixed point, to calculate the Kondo peak positions,
widths, and heights analytically at T=0, and NCA calculations to fit the
temperature dependence of high--resolution photoemission spectra of Ce
compounds. In addition, an approximate conductance quantization for transport
through multi--level quantum dots or single--atom transistors in the Kondo
regime due to a generalized Friedel sum rule is demonstrated.Comment: 4 pages, 3 figures. Invited article, 23rd International Conference on
Low Temperature Physics LT23, Hiroshima, Japan 200
Conductance distribution in disordered quantum wires: Crossover between the metallic and insulating regimes
We calculate the distribution of the conductance P(g) for a
quasi-one-dimensional system in the metal to insulator crossover regime, based
on a recent analytical method valid for all strengths of disorder. We show the
evolution of P(g) as a function of the disorder parameter from a insulator to a
metal. Our results agree with numerical studies reported on this problem, and
with analytical results for the average and variance of g.Comment: 8 pages, 5 figures. Final version (minor changes
Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance
We study long-range correlations of equilibrium current densities in a
two-dimensional mesoscopic system with the time reversal invariance broken by a
random or homogeneous magnetic field. Our result is universal, i.e. it does not
depend on the type (random potential or random magnetic field) or correlation
length of disorder. This contradicts recent sigma-model calculations of
Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well
as for the renormalization of the conductivity. We show explicitly that the new
term in the sigma-model derived by TS&E and claimed to lead to delocalization
does not exist. The error in the derivation of TS&E is traced to an incorrect
ultraviolet regularization procedure violating current conservation and gauge
invariance.Comment: 8 pages, 3 figure
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