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.Comment: 7 pages, 6 figures, revised versio

Improved transport equations including correlations for electron-phonon systems. Comparison with exact solutions in one dimension

We study transport equations for quantum many-particle systems in terms of correlations by applying the general formalism developed in an earlier paper to exactly soluble electron-phonon models. The one-dimensional models considered are the polaron model with a linear energy dispersion for the electrons and a finite number of electrons and the same model including a Fermi sea (Tomonaga-Luttinger model). The inclusion of two-particle correlations shows a significant and systematic improvement in comparison with the usual non-Markovian equations in Born approximation. For example, the improved equations take into account the renormalization of the propagation by the self-energies to second order in the coupling.Comment: 20 pages, 15 Postscript figures, uses RevTeX, to be published in: Annals of Physics (N.Y.

Luttinger liquid universality in the time evolution after an interaction quench

We provide strong evidence that the relaxation dynamics of one-dimensional, metallic Fermi systems resulting out of an abrupt amplitude change of the two-particle interaction has aspects which are universal in the Luttinger liquid sense: The leading long-time behavior of certain observables is described by universal functions of the equilibrium Luttinger liquid parameter and the renormalized velocity. We analytically derive those functions for the Tomonaga-Luttinger model and verify our hypothesis of universality by considering spinless lattice fermions within the framework of the density matrix renormalization group

RG transport theory for open quantum systems: Charge fluctuations in multilevel quantum dots in and out of equilibrium

We present the real-time renormalization group (RTRG) method as a method to describe the stationary state current through generic multi-level quantum dots with a complex setup in nonequilibrium. The employed approach consists of a very rudiment approximation for the RG equations which neglects all vertex corrections while it provides a means to compute the effective dot Liouvillian self-consistently. Being based on a weak-coupling expansion in the tunneling between dot and reservoirs, the RTRG approach turns out to reliably describe charge fluctuations in and out of equilibrium for arbitrary coupling strength, even at zero temperature. We confirm this in the linear response regime with a benchmark against highly-accurate numerically renormalization group data in the exemplary case of three-level quantum dots. For small to intermediate bias voltages and weak Coulomb interactions, we find an excellent agreement between RTRG and functional renormalization group data, which can be expected to be accurate in this regime. As a consequence, we advertise the presented RTRG approach as an efficient and versatile tool to describe charge fluctuations theoretically in quantum dot systems

Spectral sum rules for the Tomonaga-Luttinger model

In connection with recent publications we discuss spectral sum rules for the Tomonaga-Luttinger model without using the explicit result for the one-electron Green's function. They are usefull in the interpretation of recent high resolution photoemission spectra of quasi-one-dimensional conductors. It is shown that the limit of infinite frequency and band cut\-off do not commute. Our result for arbitrary shape of the interaction potential generalizes an earlier discussion by Suzumura. A general analytical expression for the spectral function for wave vectors far from the Fermi wave vector $k_{F}$ is presented. Numerical spectra are shown to illustrate the sum rules.Comment: 9 pages, REVTEX 3.0, 2 figures added as postscript file

Renormalization group flows in one-dimensional lattice models: impurity scaling, umklapp scattering and the orthogonality catastrophe

We show that to understand the orthogonality catastrophe in the half-filled lattice model of spinless fermions with repulsive nearest neighbor interaction and a local impurity in its Luttinger liquid phase one has to take into account (i) the impurity scaling, (ii) unusual finite size $L$ corrections of the form $\ln(L)/L$, as well as (iii) the renormalization group flow of the umklapp scattering. The latter defines a length scale $L_u$ which becomes exceedingly large the closer the system is to its transition into the charge-density wave phase. Beyond this transition umklapp scattering is relevant in the renormalization group sense. Field theory can only be employed for length scales larger than $L_u$. For small to intermediate two-particle interactions, for which the regime $L > L_u$ can be accessed, and taking into account the finite size corrections resulting from (i) and (ii) we provide strong evidence that the impurity backscattering contribution to the orthogonality exponent is asymptotically given by $1/16$. While further increasing the two-particle interaction leads to a faster renormalization group flow of the impurity towards the cut chain fixed point, the increased bare amplitude of the umklapp scattering renders it virtually impossible to confirm the expected asymptotic value of $1/16$ given the accessible system sizes. We employ the density matrix renormalization group.Comment: 12 pages, 9 figure

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

Understanding the Josephson current through a Kondo-correlated quantum dot

We study the Josephson current 0-$\pi$ transition of a quantum dot tuned to the Kondo regime. The physics can be quantitatively captured by the numerically exact continuous time quantum Monte Carlo method applied to the single-impurity Anderson model with BCS superconducting leads. For a comparison to an experiment the tunnel couplings are determined by fitting the normal-state linear conductance. Excellent agreement for the dependence of the critical Josephson current on the level energy is achieved. For increased tunnel couplings the Kondo scale becomes comparable to the superconducting gap and the regime of the strongest competition between superconductivity and Kondo correlations is reached; we predict the gate voltage dependence of the critical current in this regime.Comment: 5 pages, 3 figure