V. Meden

Nonequilibrium functional renormalization group for interacting quantum systems

We propose a nonequilibrium version of functional renormalization within the Keldysh formalism by introducing a complex-valued flow parameter in the Fermi or Bose functions of each reservoir. Our cutoff scheme provides a unified approach to equilibrium and nonequilibrium situations. We apply it to nonequilibrium transport through an interacting quantum wire coupled to two reservoirs and show that the nonequilibrium occupation induces new power law exponents for the conductance.

Correlation-induced resonances in transport through coupled quantum dots.

We investigate the effect of local electron correlations on transport through parallel quantum dots. The linear conductance as a function of gate voltage is strongly affected by the interplay of the interaction U and quantum interference. We find a pair of novel correlation-induced resonances separated by an energy scale that depends exponentially on U. The effect is robust against a small detuning of the dot energy levels and occurs for arbitrary generic tunnel couplings. It should be observable in experiments on the basis of presently existing double-dot setups.

Functional renormalization group for nonequilibrium quantum many-body problems

We extend the concept of the functional renormalization for quantum many-body problems to nonequilibrium situations. Using a suitable generating functional based on the Keldysh approach, we derive a system of coupled differential equations for the

Fermion–boson transmutation and comparison of statistical ensembles in one dimension

m

Charge transport through single molecules, quantum dots and quantum wires

-particle vertex functions. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations at finite bias voltage employing two different truncation schemes for the infinite hierarchy of equations arising in the functional renormalization group scheme.

Josephson current through a single Anderson impurity coupled to BCS leads

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low‐energy excitations can be described in terms of bosonic degrees of freedom. This fermion–boson transmutation (FBT) which lies at the heart of the Luttinger liquid concept is presented in a way which does not require a knowledge of quantum field theoretical methods. As the basic facts can already be introduced for noninteracting fermions they are mainly discussed. As an application we use the FBT to present exact results for the low‐temperature thermodynamics and the occupation numbers in the microcanonical and the canonical ensemble. They are compared with the standard grand canonical results.

Tuning the Josephson current in carbon nanotubes with the Kondo effect

We review recent progress in the theoretical description of correlation and quantum fluctuation phenomena in charge transport through single molecules, quantum dots and quantum wires. Various physical phenomena are addressed, relating to cotunneling, pair-tunneling, adiabatic quantum pumping, charge and spin fluctuations, and inhomogeneous Luttinger liquids. We review theoretical many-body methods to treat correlation effects, quantum fluctuations, non-equilibrium physics, and the time evolution into the stationary state of complex nanoelectronic systems.

Functional renormalization group approach to transport through correlated quantum dots

We investigate the Josephson current J through a quantum dot embedded between two superconductors showing a phase difference . The system is modeled as a single Anderson impurity coupled to BCS leads, and the functional and the numerical renormalization group frameworks are employed to treat the local Coulomb interaction U. We reestablish the picture of a quantum phase transition occurring if the ratio between the Kondo temperature TK and the superconducting energy gap or, at appropriate TK /, the phase difference or the impurity energy is varied. We present accurate zero- as well as finite-temperature T data for the current itself, thereby settling a dispute raised about its magnitude. For small to intermediate U and at T = 0 the truncated functional renormalization group is demonstrated to produce reliable results without the need to implement demanding numerics. It thus provides a tool to extract characteristics from experimental currentvoltage measurements.

Improved Transport Equations Including Correlations for Electron–Phonon Systems: Comparison with Exact Solutions in One Dimension

We investigate the Josephson current in a single wall carbon nanotube connected to superconducting electrodes. We focus on the parameter regime in which transport is dominated by Kondo physics. A sizeable supercurrent is observed for odd number of electrons on the nanotube when the Kondo temperature TK is sufficiently large compared to the superconducting gap. On the other hand when, in the center of the Kondo ridge, TK is slightly smaller than the superconducting gap, the supercurrent is found to be extremely sensitive to the gate voltage VBG. Whereas it is largely suppressed at the center of the ridge, it shows a sharp increase at a finite value of VBG. This increase can be attributed to a doublet-singlet transition of the spin state of the nanotube island leading to a phase shift in the current phase relation. This transition is very sensitive to the asymmetry of the contacts and is in good agreement with theoretical predictions.

Nonuniversal spectral properties of the Luttinger model

We investigate the effect of local Coulomb correlations on electronic transport through a variety of coupled quantum dot systems connected to Fermi liquid leads. We use a newly developed functional renormalization group scheme to compute the gate voltage dependence of the linear conductance, the transmission phase, and the dot occupancies. A detailed derivation of the flow equations for the dot level positions, the inter-dot hybridizations, and the effective interaction is presented. For specific setups and parameter sets we compare the results to existing accurate numerical renormalization group data. This shows that our approach covers the essential physics and is quantitatively correct up to fairly large Coulomb interactions while being much faster, very flexible, and simple to implement. We then demonstrate the power of our method to uncover interesting new physics. In several dots coupled in series the combined effect of correlations and asymmetry leads to a vanishing of transmission resonances. In contrast, for a parallel double-dot we find parameter regimes in which the two-particle interaction generates additional resonances.