arXiv subjects

V. Meden

Publications and source records attributed to V. Meden.

At least 55 records · Page 3Linked to original sources

arXiv2010

Charge transport through single molecules, quantum dots, and quantum wires

We review recent progresses in the theoretical description of correlation and quantum fluctuation phenomena in charge transport through single molecules, quantum dots, and quantum wires. A variety of physical phenomena is addressed, relating to co-tunneling, 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, nonequilibrium physics, and the time evolution into the stationary state of complex nanoelectronic systems.

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arXiv2010

Functional renormalization group study of the interacting resonant level model in and out of equilibrium

We investigate equilibrium and steady-state non-equilibrium transport properties of a spinless resonant level locally coupled to two conduction bands of width ~Γvia a Coulomb interaction U and a hybridization t'. In order to study the effects of finite bias voltages beyond linear response, a generalization of the functional renormalization group to Keldysh frequency space is employed. Being mostly unexplored in the context of quantum impurity systems out of equilibrium, we benchmark this method against recently-published time-dependent density matrix renormalization group data. We thoroughly investigate the scaling limit Γ\to\infty characterized by the appearance of power laws. Most importantly, at the particle-hole symmetric point the steady-state current decays like J ~ V^{-α_J} as a function of the bias voltage V>>t', with an exponent α_J(U) that we calculate to leading order in the Coulomb interaction strength. In contrast, we do not observe a pure power-law (but more complex) current-voltage-relation if the energy εof the resonant level is pinned close to either one of the chemical potentials \pm V/2.

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arXiv2009

Renormalization group study of Luttinger liquids with boundaries

We use Wilsons weak coupling ``momentum'' shell renormalization group method to show that two-particle interaction terms commonly neglected in bosonization of one-dimensional correlated electron systems with open boundaries are indeed irrelevant in the renormalization group sense. Our study provides a more solid ground for many investigations of Luttinger liquids with open boundaries.

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arXiv2009

Tuning the Josephson current in carbon nanotubes with the Kondo effect

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 pi 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.

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arXiv2009

Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

We study electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (two-dimensional) leads, thereby bringing theory closer towards systems closer to setups realized in experiments. In particular, we compute the temperature dependence of the linear conductance $G$ of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of overhanging parts of the leads and the wire implies a $G(T)$ which is much more complex than the power-law behavior described so far for end-coupled wires. Depending on the precise setup the wide temperature regime of power-law scaling found in the end-coupled case is broken up in up to five fairly narrow regimes interrupted by extended crossover regions. Our results can be used to optimize the experimental setups designed for a verification of Luttinger liquid power-law scaling.

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arXiv2009

A quantum criticality perspective on the charging of narrow quantum-dot levels

Understanding the charging of exceptionally narrow levels in quantum dots in the presence of interactions remains a challenge within mesoscopic physics. We address this fundamental question in the generic model of a narrow level capacitively coupled to a broad one. Using bosonization we show that for arbitrary capacitive coupling charging can be described by an analogy to the magnetization in the anisotropic Kondo model, featuring a low-energy crossover scale that depends in a power-law fashion on the tunneling amplitude to the level. Explicit analytical expressions for the exponent are derived and confirmed by detailed numerical and functional renormalization-group calculations.

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arXiv2009

Supercurrent and multiple singlet-doublet phase transitions of a quantum dot Josephson junction inside an Aharonov-Bohm ring

We study a quantum dot Josephson junction inside an Aharonov-Bohm environment. The geometry is modeled by an Anderson impurity coupled to two directly-linked BCS leads. We illustrate that the well-established picture of the low-energy physics being governed by an interplay of two distinct (singlet and doublet) phases is still valid for this interferometric setup. The phase boundary depends, however, non-monotonically on the coupling strength between the superconductors, causing the system to exhibit re-entrance behavior and multiple phase transitions. We compute the zero-temperature Josephson current and demonstrate that it can become negative in the singlet phase by virtue of the Coulomb interaction U. As a starting point, the limit of large superconducting energy gaps Δ=\infty is solved analytically. In order to tackle arbitrary Δ<\infty and U>0, we employ a truncated functional renormalization group scheme which was previously demonstrated to give quantitatively reliable results for the quantum dot Josephson problem.

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arXiv2008

Spin-polarized currents through interacting quantum wires with nonmagnetic leads

We study the performance of a quantum wire spin filter that is based on the Rashba spin-orbit interaction in the presence of the electron-electron interaction. The finite length wire is attached to two semi-infinite nonmagnetic leads. Analyzing the spin polarization of the linear conductance at zero temperature, we show that spin-filtering is possible by adequate tuning of the system parameters first considering noninteracting electrons. Next, the functional renormalization group method is used to capture correlation effects induced by the Coulomb interaction. For short wires we show that the energy regime in which spin polarization is found is strongly affected by the Coulomb interaction. For long wires we find the power-law suppression of the total conductance on low energy scales typical for inhomogeneous Luttinger liquids while the degree of spin polarization stays constant.

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arXiv2008

A finite-frequency functional RG approach to the single impurity Anderson model

We use the Matsubara functional renormalization group (FRG) to describe electronic correlations within the single impurity Anderson model. In contrast to standard FRG calculations, we account for the frequency-dependence of the two-particle vertex in order to address finite-energy properties (e.g, spectral functions). By comparing with data obtained from the numerical renormalization group (NRG) framework, the FRG approximation is shown to work well for arbitrary parameters (particularly finite temperatures) provided that the electron-electron interaction U is not too large. We demonstrate that aspects of (large U) Kondo physics which are described well by a simpler frequency-independent truncation scheme are no longer captured by the 'higher-order' frequency-dependent approximation. In contrast, at small to intermediate U the results obtained by the more elaborate scheme agree better with NRG data. We suggest to parametrize the two-particle vertex not by three independent energy variables but by introducing three functions each of a single frequency. This considerably reduces the numerical effort to integrate the FRG flow equations.

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arXiv2008

Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids

We compare two fermionic renormalization group methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger liquids) and local inhomogeneities. The first one is a poor man's method setup to resum ``leading-log'' divergences of the effective transmission at the Fermi momentum. Generically the resulting equations can be solved analytically. The second approach is based on the functional renormalization group method and leads to a set of differential equations which can only for certain setups and in limiting cases be solved analytically, while in general it must be integrated numerically. Both methods are claimed to be applicable for inhomogeneities of arbitrary strength and to capture effects of the two-particle interaction, such as interaction dependent exponents, up to leading order. We critically review this for the simplest case of a single impurity. While on first glance the poor man's approach seems to describe the crossover from the ``perfect'' to the ``open chain fixed point'' we collect evidence that difficulties may arise close to the ``perfect chain fixed point''. Due to a subtle relation between the scaling dimensions of the two fixed points this becomes apparent only in a detailed analysis. In the functional renormalization group method the coupling of the different scattering channels is kept which leads to a better description of the underlying physics.

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arXiv2008

Spin-charge separation in transport through Luttinger liquid rings

We investigate how the different velocities characterizing the low-energy spectral properties and the low-temperature thermodynamics of one-dimensional correlated electron systems (Luttinger liquids) affect the transport properties of ring-like conductors. The Luttinger liquid ring is coupled to two noninteracting leads and pierced by a magnetic flux. We study the flux dependence of the linear conductance. It shows a dip structure which is governed by the interaction dependent velocities. Our work extends an earlier study which was restricted to rather specific choices of the interaction parameters. We show that for generic repulsive two-particle interactions the number of dips can be estimated from the ratio of the charge current velocity and the spin velocity. In addition, we clarify the range of validity of the central approximation underlying the earlier study.

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arXiv2008

Josephson current through a single Anderson impurity coupled to BCS leads

We investigate the Josephson current J(ϕ) through a quantum dot embedded between two superconductors showing a phase difference ϕ. 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 T_K and the superconducting energy gap Δor, at appropriate T_K/Δ, the phase difference ϕor 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 current-voltage measurements.

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arXiv2007

Spin-orbit coupling effects in one-dimensional ballistic quantum wires

We study the spin-dependent electronic transport through a one-dimensional ballistic quantum wire in the presence of Rashba spin-orbit interaction. In particular, we consider the effect of the spin-orbit interaction resulting from the lateral confinement of the two-dimensional electron gas to the one-dimensional wire geometry. We generalize a situation suggested earlier [P. Streda and P. Seba, Phys. Rev. Lett. 90, 256601 (2003)] which allows for spin-polarized electron transport. As a result of the lateral confinement, the spin is rotated out of the plane of the two-dimensional system. We furthermore investigate the spin-dependent transmission and the polarization of an electron current at a potential barrier. Finally, we construct a lattice model which shows similar low-energy physics. In the future, this lattice model will allow us to study how the electron-electron interaction affects the transport properties of the present setup.

cond-mat.mes-hall↗

arXiv2007

Charging of a quantum dot coupled to Luttinger liquid leads

Luttinger liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter K. We suggest a setup to study Luttinger liquid behavior in quantum wires which allows to determine K from two independent measurements: resonant transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two measured values of K for a single probe would provide strong experimental evidence for the Luttinger liquid paradigm.

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arXiv2007

Mesoscopic to universal crossover of transmission phase of multi-level quantum dots

Transmission phase αmeasurements of many-electron quantum dots (small mean level spacing δ) revealed universal phase lapses by πbetween consecutive resonances. In contrast, for dots with only a few electrons (large δ), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multi-level quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of αfor small δfollows from Fano-type antiresonances of the renormalized single-particle levels.

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arXiv2007

Indirect forces between impurities in one-dimensional quantum liquids

We investigate the indirect interaction between two isolated impurities in a Luttinger liquid described by a microscopic lattice model. To treat the electron-electron interaction U the functional renormalization group method is used. For comparison we also study the U=0 case. We find that for a wide range of impurity parameters the impurity interaction V_{12} as a function of their separation r oscillates with decaying amplitude between being attractive and repulsive. For half-filling of the band and in a crossover regime between weak and strong impurities the interaction becomes purely attractive. For U=0 and independent of the impurity strength the amplitude of the interaction energy falls off as 1/r. For U>0 the decay for small separations and weak to intermediate impurities is governed by a U dependent exponent larger than -1, which crosses over to -1 for large r. The crossover scale depends on the impurity strength and U. We present simple pictures which explain our results in the limits of weak and strong impurities. We finally also consider attractive interactions U<0.

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arXiv2006

Phase lapses in transmission through interacting two-level quantum dots

We investigate the appearance of pi lapses in the transmission phase theta of a two-level quantum dot with Coulomb interaction U. Using the numerical and functional renormalization group methods we study the entire parameter space for spin-polarized as well as spin-degenerate dots, modeled by spinless or spinful electrons, respectively. We investigate the effect of finite temperatures T. For small T and sufficiently small single-particle spacings delta of the dot levels we find pi phase lapses between two transmission peaks in an overwhelming part of the parameter space of the level-lead couplings. For large delta the appearance or not of a phase lapse between resonances depends on the relative sign of the level-lead couplings in analogy to the U=0 case. We show that this generic scenario is the same for spin-polarized and spin-degenerate dots. We emphasize that in contrast to dots with more levels, for a two-level dot with small delta and generic dot-lead couplings (that is up to cases with special symmetry) the "universal" phase lapse behavior is already established at U=0. The most important effect of the Coulomb interaction is to increase the separation of the transmission resonances. The relation of the appearance of phase lapses to the inversion of the population of the dot levels is discussed. For the spin-polarized case and low temperatures we compare our results to recent mean-field studies. For small delta correlations are found to strongly alter the mean-field picture.

cond-mat.mes-hall↗

arXiv2006

Functional renormalization group for non-equilibrium quantum many-body problems

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

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