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arXiv:0712.0951 · Acta Physica Polonica A

Tunneling of Interacting Fermions in 1D Systems

Andrej Gendiar, Martin Moško, Pavel Vagner, R. Németh

Published Oct 1, 2005• 0 citations
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Abstract

Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study tunneling of the interacting electron gas through a single δ barrier in a finite one-dimensional wire connected to contacts.Our results exhibit features known from correlated many-body models.In particular, the conductance decays with the wire length as ∝ L -2α , where the power α is universal.We also show that a similar result for a wire conductance can be extracted from the persistent current (I) through the δ barrier in a one-dimensional ring, where it is known that I ∝ L -1-α .

DOI
10.12693/aphyspola.108.661

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Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study tunneling of the interacting electron gas through a single δ barrier in a finite one-dimensional wire connected to contacts.Our results exhibit features known from correlated many-body models.In particular, the conductance decays with the wire length as ∝ L -2α , where the power α is universal.We also show that a similar result for a wire conductance can be extracted from the persistent current (I) through the δ barrier in a one-dimensional ring, where it is known that I ∝ L -1-α .
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier.Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction.The persistent current is a sine-like function of magnetic flux.It decays with the ring length (L) faster than L -1 and eventually like L -α-1 , where α > 0 is universal.
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study the persistent current of the interacting electron gas in a one-dimensional continuous ring containing a single δδδ barrier. We calculate the persistent current as a function of the ring circumference, magnetic flux threading the ring, barrier strength, etc. We compare our results with the results of correlated models like the Luttinger liquid model and the Hubbard model solved by means of the renormalization group. A good agreement is found. First, the persistent current decays with the increasing ring circumference (LLL) faster than L−1L^{-1}L−1 and eventually like L−α−1L^{-α-1}L−α−1, where α>0α>0α>0 depends only on the electron-electron interaction. Second, the persistent current is a sine-shaped function of magnetic flux. This sine-like dependence and in particular the universal power law L−α−1L^{-α-1}L−α−1 have sofar been believed to arise only in the correlated many-body models. Observation of these features within the Hartree-Fock model is a surprising result.
We study theoretically transport of a one-dimensional single-channel interacting electron gas through barriers or constrictions. We find that electrons with repulsive interactions, incident upon a single barrier, are completely reflected at zero temperature. At finite temperature (T), the conductance is shown to vanish as a power of T, and at zero temperature, power-law current-voltage characteristics are predicted. For attractive interactions, we predict perfect transmission at zero temperature, with similar power-law corrections. We also study resonant tunneling through a double-barrier structure and related effects associated with the Coulomb blockade. Resonant peaks in the transmission are possible, provided the interactions are not too strongly repulsive. However, in contrast to resonant tunneling in a noninteracting electron gas, we find that in the presence of interactions the width of the resonance vanishes, as a power of temperature, in the zero-temperature limit. Moreover, the resonance line shapes are shown to be described by a universal scaling function, which has power law, but non-Lorentzian tails. For a particular choice of interaction strengths, we present an exact solution of our model, which verifies the scaling assumptions and provides an explicit expression for the scaling function. We also consider the role played by the electron-spin degree of freedom in modifying the trasnsmission through barriers. With spin, there are four possible phases corresponding to perfect transmission or perfect reflection of charge and spin. We present phase diagrams for these different behaviors and analyze the nontrivial transitions between them. At these transitions we find that the conductance or transmission is universal---depending only on the dimensionless conductance of the leads and not on the details of the barriers. In the case of resonant tunneling with spin, we discuss the ``Kondo'' resonance, which occurs when there is a spin degeneracy for electrons between the two barriers. Many of the predictions should be directly testable in gated GaAs wires.
We investigate transport of spinless fermions through a single site dot junction of MMM one-dimensional quantum wires. The semi-infinite wires are described by a tight-binding model. Each wire consists of two parts, the noninteracting leads and a region of finite extent in which the fermions interact via a nearest-neighbor interaction. The functional renormalization group method is used to determine the flow of the linear conductance as a function of a low-energy cutoff for a wide range of parameters. Several fixed points are identified and their stability is analyzed. We determine the scaling exponents governing the low-energy physics close to the fixed points. Some of our results can already be derived using the non-self-consistent Hartree-Fock approximation.
We study transport through a one-dimensional quantum wire of correlated fermions connected to semi-infinite leads. The wire contains either a single impurity or two barriers, the latter allowing for resonant tunneling. In the leads the fermions are assumed to be noninteracting. The wire is described by a microscopic lattice model. Using the functional renormalization group we calculate the linear conductance for wires of mesoscopic length and for all relevant temperature scales. For a single impurity, either strong or weak, we find power-law behavior as a function of temperature. In addition, we can describe the complete crossover from the weak- to the strong-impurity limit. For two barriers, depending on the parameters of the enclosed quantum dot, we find temperature regimes in which the conductance follows power laws with ``universal'' exponents as well as nonuniversal behavior. Our approach leads to a comprehensive picture of resonant tunneling. We compare our results with those of alternative approaches.
We investigate the tunneling current between a one-dimensional (1D) wave guide and a metallic electrode. To be specific, we consider as an electrode a two-dimensional electron gas (2DEG) coupled to the 1D system over a finite length L by a thin tunnel barrier. Treating the 1D electrons within the Luttinger liquid model, we evaluate the tunneling current which flows through the barrier. Tunneling is assumed to be local (rather than being described by a constant matrix element in reciprocal space) and the spatial extent of the contact is taken into account. A characteristic maximum of the current for optimal barrier lengths is found. We calculate the finite-temperature spectral density of the 1D correlated electrons, which is needed to evaluate the current in the peak region.