arXiv subjects
Publications and source records attributed to R. Egger.
Nonlinear transport through interacting single-wall nanotubes containing a few impurities is studied theoretically. Extending the Luttinger liquid theory to incorporate trigonal warping and chirality effects, we derive the current contribution $I_e$ {\sl even} in the applied voltage $V$ and {\sl odd} in an orbital magnetic field $B$, which is non-zero only for chiral tubes and in the presence of interactions.
Nonequilibrium electronic transport through a molecular level weakly coupled to a single coherent phonon/vibration mode has been studied for superconducting leads. The Keldysh Green function formalism is used to compute the current for the entire bias voltage range. In the subgap regime, Multiple Andreev Reflection (MAR) processes accompanied by phonon emission cause rich structure near the onset of MAR channels, including an even-odd parity effect that can be interpreted in terms of an inelastic MAR ladder picture. Thereby we establish a connection between the Keldysh formalism and the Landauer scattering approach for inelastic MAR.
We develop path-integral Monte Carlo simulations for a parabolic two-dimensional (2D) quantum dot containing $N$ interacting electrons in the presence of Dresselhaus and/or Rashba spin-orbit couplings. Our method solves in a natural way the spin contamination problem and allows for numerically exact finite-temperature results at weak spin-orbit coupling. For $N<10$ electrons, we present data for the addition energy, the particle density, and the total spin $S$ in the Wigner molecule regime of strong Coulomb interactions. We identify magic numbers at N=3 and N=7 via a peak in the addition energy. These magic numbers differ both from weak-interaction and classical predictions, and are stable with respect to (weak) spin-orbit couplings.
We propose an experimentally viable setup for the realization of one-dimensional ultracold atom gases in a nanoscale magnetic waveguide formed by single doubly-clamped suspended carbon nanotubes. We show that all common decoherence and atom loss mechanisms are small guaranteeing a stable operation of the trap. Since the extremely large current densities in carbon nanotubes are spatially homogeneous, our proposed architecture allows to overcome the problem of fragmentation of the atom cloud. Adding a second nanowire allows to create a double-well potential with a moderate tunneling barrier which is desired for tunneling and interference experiments with the advantage of tunneling distances being in the nanometer regime.
The Rashba spin-orbit coupling in carbon nanotubes and its effect on spin-dependent transport properties are analyzed theoretically. We focus on clean non-interacting nanotubes with tunable number of subbands $N$. The peculiar band structure is shown to allow in principle for Datta-Das oscillatory behavior in the tunneling magnetoresistance as a function of gate voltage, despite the presence of multiple bands. We discuss the conditions for observing Datta-Das oscillations in carbon nanotubes.
The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length $a_{aa}$ displays a confinement-induced resonance. We compute the dimer-dimer scattering length $a_{dd}$, and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.
The problem of resonant tunneling through a quantum dot weakly coupled to spinless Tomonaga-Luttinger liquids has been studied. We compute the linear conductance due to sequential tunneling processes upon employing a master equation approach. Besides the previously used lowest-order golden rule rates describing uncorrelated sequential tunneling (UST) processes, we systematically include higher-order correlated sequential tunneling (CST) diagrams within the standard Weisskopf-Wigner approximation. We provide estimates for the parameter regions where CST effects can be important. Focusing mainly on the temperature dependence of the peak conductance, we discuss the relation of these findings to previous theoretical and experimental results.
We solve the two-particle s-wave scattering problem for ultracold atom gases confined in arbitrary quasi-one-dimensional trapping potentials, allowing for two different atom species. As a consequence, the center-of-mass and relative degrees of freedom do not factorize. We derive bound-state solutions and obtain the general scattering solution, which exhibits several resonances in the 1D scattering length induced by the confinement. We apply our formalism to two experimentally relevant cases: (i) interspecies scattering in a two-species mixture, and (ii) the two-body problem for a single species in a non-parabolic trap.
We study one-dimensional incommensurate bosons with strong repulsive interactions and weak disorder. In analogy to the clean Tonks-Girardeau gas, a Bose-Fermi mapping expresses this problem in terms of disordered free fermions. Thereby many known results apply, in particular for the density-density correlations, the distribution function of the local density of states, and the complete spectral statistics. We also analyze the bosonic momentum distribution, and comment on the experimental observability of these predictions in ultracold atomic gases.
We study the three-body problem for both fermionic and bosonic cold atom gases in a parabolic transverse trap of lengthscale $a_\perp$. For this quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length $a$, and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths, $a_{ad}$ and $b_{ad}$. In the tightly bound `dimer limit', $a_\perp/a\to\infty$, we find $b_{ad}=0$, and $a_{ad}$ is linked to the 3D atom-dimer scattering length. In the weakly bound `BCS limit', $a_\perp/a\to-\infty$, a connection to the Bethe Ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is non-universal: $a_{ad}$ and $b_{ad}$ depend both on $a_\perp/a$ and on a parameter $R^*$ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.
We propose an experimentally viable setup for the realization of one-dimensional ultracold atom gases in a nanoscale magnetic waveguide formed by two doubly-clamped suspended carbon nanotubes. All common decoherence and atom loss mechanisms are shown to be small. We discuss general consequences of a non-parabolic confinement potential, in particular novel two-body shape resonances, which could be observed in this trap.
We solve the three-body problem of an ultracold Fermi gas with parabolic confinement length $a_\perp$ and 3D scattering length $a$. On the two-body level, there is a Feshbach-type resonance at $a_\perp/a\approx 1.46$, and a dimer state for arbitrary $a_\perp/a$. The three-body problem is shown to be universal, an d described by the atom-dimer scattering length $a_{ad}$ and a range parameter $b_{ad}$. In the dimer limit $a_\perp/a\gg 1$, we find a repulsive zero-range atom-dimer interaction. For $a_\perp/a\ll -1$, however, the potential has long range, with $a_{ad}>0$ and $b_{ad}\gg a_{ad}$. There is no trimer state, and despite $a_{ad}=0$ at $a_\perp/a\approx 2.6$, there is no resonance enhancement of the interaction.
We present theoretical results for the equilibrium Josephson current through an Anderson dot tuned into the magnetic regime, using Hirsch-Fye Monte Carlo simulations covering the complete crossover from Kondo-dominated physics to $π$ junction behavior in a numerically exact way. Within the `magnetic' regime, $U/Γ\gg 1$ and $ε_0/Γ\leq 1$, the Josephson current is found to depend only on $Δ/T_K$, where $Δ$ is the BCS gap and $T_K$ the Kondo temperature. The junction behavior can be classified into four different quantum phases. We describe these behaviors, specify the associated three transition points, and identify a local minimum in the critical current of the junction as a function of $Δ/T_K$.
Recent experimental and theoretical results on intrinsic superconductivity in ropes of single-wall carbon nanotubes are reviewed and compared. We find strong experimental evidence for superconductivity when the distance between the normal electrodes is large enough. This indicates the presence of attractive phonon-mediated interactions in carbon nanotubes, which can even overcome the repulsive Coulomb interactions. The effective low-energy theory of rope superconductivity explains the experimental results on the temperature-dependent resistance below the transition temperature in terms of quantum phase slips. Quantitative agreement with only one fit parameter can be obtained. Nanotube ropes thus represent superconductors in an extreme 1D limit never explored before.
We derive and analyze the low-energy theory of superconductivity in carbon nanotube ropes. A rope is modelled as an array of metallic nanotubes, taking into account phonon-mediated as well as Coulomb interactions, and arbitrary Cooper pair hopping amplitudes (Josephson couplings) between different tubes. We use a systematic cumulant expansion to construct the Ginzburg-Landau action including quantum fluctuations. The regime of validity is carefully established, and the effect of phase slips is assessed. Quantum phase slips are shown to cause a depression of the critical temperature $T_c$ below the mean-field value, and a temperature-dependent resistance below $T_c$. We compare our theoretical results to recent experimental data of Kasumov {\sl et al.} [Phys. Rev. B {\bf 68}, 214521 (2003)] for the sub-$T_c$ resistance, and find good agreement with only one free fit parameter. Ropes of nanotubes therefore represent superconductors in the one-dimensional few-channel limit.
We review the theoretical description of spin-orbit scattering and electron spin resonance in carbon nanotubes. Particular emphasis is laid on the effects of electron-electron interactions. The spin-orbit coupling is derived, and the resulting ESR spectrum is analyzed both using the effective low-energy field theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard ladders. For single-wall tubes, the field theoretical description predicts a double peak spectrum linked to the existence of spin-charge separation. The numerical analysis basically confirms this picture, but also predicts additional features in finite-size samples.
A numerically exact dynamical quantum Monte Carlo approach has been developed and applied to transport through a double barrier in a Luttinger liquid with arbitrary transmission. For strong transmission, we find broad Fabry-Perot Coulomb blockade peaks, with a lineshape parametrized by a single parameter, but at sufficiently low temperatures, non-Lorentzian universal lineshapes characteristic of coherent resonant tunneling emerge, even for strong interactions. For weak transmission, our data supports the recently proposed correlated sequential tunneling picture and is consistent with experimental results on intrinsic nanotube dots.
Experimental and theoretical results for transport through crossed metallic single-wall nanotubes are presented. We observe a zero-bias anomaly in one tube which is suppressed by a current flowing through the other nanotube. The phenomenon is shown to be consistent with the picture of strongly correlated electrons within the Luttinger liquid model. The most relevant coupling between the nanotubes is the electrostatic interaction generated via crossing-induced backscattering processes. Explicit solution of a simplified model is able to describe qualitatively the observed experimental data with only one adjustable parameter.