Conduction of a weakly interacting one-dimensional electron gas through a single barrier

Fluctuation-Induced Quantum Zeno Effect

An isolated quantum gas with a localized loss features a nonmonotonic behavior of the particle loss rate as an incarnation of the quantum Zeno effect, as recently shown in experiments with cold atomic gases. While this effect can be understood in terms of local, microscopic physics, we show that novel many-body effects emerge when nonlinear gapless quantum fluctuations become important. To this end, we investigate the effect of a local dissipative impurity on a one-dimensional gas of interacting fermions. We show that the escape probability for modes close to the Fermi energy vanishes for an arbitrary strength of the dissipation. In addition, transport properties across the impurity are qualitatively modified, similarly to the Kane-Fisher barrier problem. We substantiate these findings using both a microscopic model of spinless fermions and a Luttinger liquid description.

Breaking a one-parameter 'poor man's' scaling approach in the Luttinger liquid

Using a previously derived effective theory we explore the conductance in the Luttinger model with one impurity. A new approach to the renormalization group (RG) analysis of this model is developed. It is based on the original Gell-Mann-Low formulation of RG. We sum up infrared logarithmic contributions to conductance in the leading and a few subsequent approximations. We analyze the validity of the widely used 'poor man's' scaling approach and find that it is applicable only in the leading approximation. Our results for corrections to this approximation are different from results obtained in other papers. This should be expected beforehand, as the Gell-Mann-Low function of the model is not regularization scheme invariant. For this reason the observed quantity (e.g. conductance) can not satisfy the Gell-Mann-Low equation beyond the 'leading-log' approximation as it is supposed in the 'poor man's' approach. We formulate the method to calculate the conductance from the renormalized hamiltonian in post-leading approximations and match our results to the case of weak impurity where the answer is known in any order of electron-electron interaction.

Kondo Impurities Coupled to a Helical Luttinger Liquid: RKKY-Kondo Physics Revisited

We show that the paradigmatic Ruderman-Kittel-Kasuya-Yosida (RKKY) description of two local magnetic moments coupled to propagating electrons breaks down in helical Luttinger liquids when the electron interaction is stronger than some critical value. In this novel regime, the Kondo effect overwhelms the RKKY interaction over all macroscopic interimpurity distances. This phenomenon is a direct consequence of the helicity (realized, for instance, at edges of a time-reversal invariant topological insulator) and does not take place in usual (nonhelical) Luttinger liquids.

Quasiparticles in condensed matter systems

Quasiparticles are a powerful concept of condensed matter quantum theory. In this review, the appearence and the properties of quasiparticles are presented in a unifying perspective. The principles behind the existence of quasiparticle excitations in both quantum disordered and ordered phases of fermionic and bosonic systems are discussed. The lifetime of quasiparticles is considered in particular near a continuous classical or quantum phase transition, when the nature of quasiparticles on both sides of a transition into an ordered state changes. A new concept of critical quasiparticles near a quantum critical point is introduced, and applied to quantum phase transitions in heavy fermion metals. Fractional quasiparticles in systems of restricted dimensionality are reviewed. Dirac quasiparticles emerging in so-called Dirac materials are discussed. The more recent discoveries of topologically protected chiral quasiparticles in topological matter and Majorana quasiparticles in topological superconductors are briefly reviewed.

Finite-temperature fluid-insulator transition of strongly interacting 1D disordered bosons

We consider the many-body localization-delocalization transition for strongly interacting one-dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator-fluid transitions at any finite temperature when varying the interaction strength. At weak interactions, an increase in the interaction strength leads to insulator [Formula: see text] fluid transition, and, for large interactions, there is a reentrance to the insulator regime. It is feasible to experimentally verify these predictions by tuning the interaction strength with the use of Feshbach or confinement-induced resonances, for example, in (7)Li or (39)K.

Optimal persistent currents for interacting bosons on a ring with a gauge field

We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U(1) gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction, and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.

Nonequilibrium transport through a gate-controlled barrier on the quantum spin Hall edge

The quantum spin Hall insulator is characterized by the presence of gapless helical edge states where the spin of the charge carriers is locked to their direction of motion. In order to probe the properties of the edge modes, we propose a design of a tunable quantum impurity realized by a local gate under an external magnetic field. Using the integrability of the impurity model, the conductance is computed for arbitrary interactions, temperatures and voltages, including the effect of Fermi liquid leads. The result can be used to infer the strength of interactions from transport experiments.

Numerical renormalization group at marginal spectral density: application to tunneling in Luttinger liquids

Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a numerical renormalization group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a nonperturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single static defect.

Tunneling into a Luttinger liquid revisited

We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced breakup of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.

Scaling and interaction-assisted transport in graphene with one-dimensional defects

We analyze the scattering from one-dimensional defects in intrinsic graphene. The Coulomb repulsion between electrons is found to be able to induce singularities of such scattering at zero temperature as in one-dimensional conductors. In striking contrast to electrons in one space dimension, however, repulsive interactions here can enhance transport. We present explicit calculations for the scattering from vector potentials that appear when strips of the material are under strain. There the predicted effects are exponentially large for strong scatterers.

Charge transport through single molecules, quantum dots and quantum wires

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.

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 resembling set-ups realized in experiments. In particular, we compute the temperature dependence of the linear conductance G of a system without bulk impurities on the temperature T. 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 set-up the wide temperature regime of power-law scaling found in the end-coupled case is broken up into up to five fairly narrow regimes interrupted by extended crossover regions. Our results can be used to optimize the experimental set-ups designed for a verification of Luttinger liquid power-law scaling.

Magnetoconductance of carbon nanotube p-n junctions

The magnetoconductance of p-n junctions formed in clean single wall carbon nanotubes is studied in the geometry where a magnetic field is along the tube axis. For long junctions the low temperature magnetoconductance is anomalously large; the relative change in the conductance becomes of order unity even when the flux through the tube is much smaller than the flux quantum. The magnetoconductance is negative for metallic tubes. For semiconducting and small gap tubes the magnetoconductance is nonmonotonic: positive at small and negative at large fields. The identified magnetoconductance mechanism is relevant to magnetotransport in undoped metallic and small gap tubes in the presence of a long range disorder potential.

Interaction-induced renormalization of Andreev reflection

We analyze the charge transport between a one-dimensional weakly interacting electron gas and a superconductor within the scaling approach in the basis of scattering states. We derive the renormalization group equations, which fully account for the intrinsic energy dependence due to Andreev reflection. A strong renormalization of the corresponding reflection phase is predicted even for a perfectly transparent metal-superconductor interface. The interaction-induced suppression of the Andreev conductance is shown to be highly sensitive to the normal-state resistance, providing a possible explanation of experiments with carbon-nanotube/superconductor junctions by Morpurgo et al. [Science 286, 263 (1999)].

Junction of three quantum wires: restoring time-reversal symmetry by interaction

We investigate the transport of correlated fermions through a junction of three one-dimensional quantum wires pierced by a magnetic flux. We determine the flow of the conductance as a function of a low-energy cutoff in the entire parameter space. For attractive interactions and generic flux the fixed point with maximal asymmetry of the conductance is the stable one, as conjectured recently. For repulsive interactions and arbitrary flux we find a line of stable fixed points with vanishing conductance as well as stable fixed points with symmetric conductance (4/9)(e(2)/h).

Resonant tunneling of interacting electrons in a one-dimensional wire

We consider the conductance of a one-dimensional wire interrupted by a double-barrier structure allowing for a resonant level. Using the electron-electron interaction strength as a small parameter, we are able to build a nonperturbative analytical theory of the conductance valid in a broad region of temperatures and for a variety of the barrier parameters. We find that the conductance may have a nonmonotonic crossover dependence on temperature, specific for a resonant tunneling in an interacting electron system.

Zeeman splitting of zero-bias anomaly in Luttinger liquids

Tunneling density of states (DOS) in Luttinger liquid has a dip at zero energy, commonly known as the zero-bias anomaly. In the presence of a magnetic field, in addition to the zero-bias anomaly, the DOS develops two peaks separated from the origin by the Zeeman energy. We show that these finite-bias anomalies are characterized by a power-law behavior of the DOS and the differential conductance, and find the corresponding exponents at arbitrary strength of the electron-electron interaction. The developed theory is applicable to various kinds of quantum wires, including carbon nanotubes.

Tunneling spectroscopy of the elementary excitations in a one-dimensional wire

The collective excitation spectrum of interacting electrons in one dimension has been measured by controlling the energy and momentum of electrons tunneling between two closely spaced, parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the resulting conductance. The excitation spectrum deviates from the noninteracting spectrum, attesting to the importance of Coulomb interactions. An observed 30% enhancement of the excitation velocity relative to noninteracting electrons with the same density, a parameter determined experimentally, is consistent with theories on interacting electrons in one dimension. In short wires, 6 and 2 micrometers long, finite size effects, resulting from the breaking of translational invariance, are observed.

Experimental evidence for resonant tunneling in a luttinger liquid

We have measured the low-temperature conductance of a one-dimensional island embedded in a single mode quantum wire. The quantum wire is fabricated using the cleaved edge overgrowth technique and the tunneling is through a single state of the island. Our results show that while the resonance line shape fits the derivative of the Fermi function the intrinsic linewidth decreases in a power law fashion as the temperature is reduced. This behavior agrees quantitatively with Furusaki's model for resonant tunneling in a Luttinger liquid.