Coherent transport of charge through a double barrier in a Luttinger liquid

Sassetti, Maura; Napoli, Francesco; Weiß, Ulrich

doi:10.1103/physrevb.52.11213

Cited by 33 publications

(52 citation statements)

References 26 publications

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“…At low temperatures, the thermal electronic energies are smaller than the level separation between the discrete energy states of the island and tunneling occurs via these discrete levels. Resonant tunneling in Luttinger liquids has been investigated theoretically by many authors [8,9,10,11,12]. The onedimensional nature of the correlated electrons is responsible for the differences to the quantum Coulomb blockade theory for conventional, e.g., semiconducting quantum dots [13].…”

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Correlated Tunneling in Intramolecular Carbon Nanotube Quantum Dots

et al. 2002

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We investigate correlated electronic transport in single-walled carbon nanotubes with two intramolecular tunneling barriers. We suggest that below a characteristic temperature the long range nature of the Coulomb interaction becomes crucial to determine the temperature dependence of the maximum Gmax of the conductance peak. Correlated sequential tunneling dominates transport yielding the power-law Gmax ∝ T α end−end −1 , typical for tunneling between the ends of two Luttinger liquids. Our predictions are in agreement with recent measurements.PACS numbers: 71.10. Pm, 71.20.Tx, 72.80.Rj Electronic correlations have been predicted to dominate the characteristic features in single-walled metallic carbon nanotubes (SWNTs) [1,2], which has recently been observed in experiments [3,4,5]. The onedimensional nature of the electronic conduction bands reveals itself in typical Luttinger liquid [6], rather than Fermi liquid behavior. The manipulation of individual nanotubes with an atomic force microscope permits the creation of intra-tube buckles acting as tunneling barriers [5]. Recently, SWNTs with two intramolecular buckles have been reported to behave as room-temperature single-electron transistors [7]. At low temperatures, the thermal electronic energies are smaller than the level separation between the discrete energy states of the island and tunneling occurs via these discrete levels. Resonant tunneling in Luttinger liquids has been investigated theoretically by many authors [8,9,10,11,12]. The onedimensional nature of the correlated electrons is responsible for the differences to the quantum Coulomb blockade theory for conventional, e.g., semiconducting quantum dots [13]. Varying the gate voltage results in a sequence of conductance peaks. In the (uncorrelated) sequential tunneling (UST) approximation the temperature dependence of the maxima of those peaks follows the power-law [11]with α end being the density of states exponent for tunneling into the end of a Luttinger liquid. However, recent experiments [7] suggest a different power-law,with α end−end = 2α end . In this Letter, we propose that a novel tunneling mechanism, correlated sequential tunneling (CST), gives rise to the power law (2). It originates from the finite range nature of the Coulomb interaction in SWNTs and replaces conventional uncorrelated sequential tunneling. It dominates resonant transport at low temperatures and strong interactions. CST leads to a renormalization of the intrinsic linewidth of the resonance, which is reflected in an increase of G max with increasing temperature. In contrast, UST would predict the opposite behavior [14]. A good agreement with the experimental results [7] is found.We describe an individual metallic SWNT with two buckles by the Hamiltonian H = H 0 + H B + H ext . Here, H 0 characterizes the one-dimensional homogeneous wire including the finite-range electronic interaction. Metallic carbon nanotubes possess two gap-less one-dimensional bands [1,2] with Fermi velocity v F ≃ 8 × 10 5 m/s [7], which dominate the ...

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“…3 together with the power law (2). Note that cotunneling events, which should dominate the tails of a conductance peak [9,10,19], are not considered here. The absolute value of G max is fitted by the parameter ∆ L/R (we have chosen ω c = 9∆E σ ).…”

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Correlated Tunneling in Intramolecular Carbon Nanotube Quantum Dots

et al. 2002

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“…This approach has been successfully used to describe inelastic tunneling in different situations in 9,25,26,27,33,34,35 . The analysis which leads to Eq.…”

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confidence: 99%

“…This expression, which can be seen as the exponential of the leading frequency dependent selfenergy correction to the electron propagator, has been extensively used in studies of tunneling in zero dimensional systems (single electron transistors) which show Coulomb blockade 33 , one dimensional conductors 34 , and disordered systems in arbitrary dimensions 35 . The effective interaction can, in turn, be written in terms of the response function as:…”

Section: The Methods Of Calculationmentioning

confidence: 99%

“…The influence of inelastic scattering on electron tunneling has been studied, using equivalent methods, in mesoscopic devices which show Coulomb blockade 33 , Luttinger liquids 25,26,27,34 , and dirty metals 35 . The simplest formulation of the method replaces the excitations of the system (such as electron-hole pairs) by a bath of harmonic oscillators with the same excitation spectrum.…”

Section: The Methods Of Calculationmentioning

confidence: 99%

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Interlayer hopping properties of electrons in layered metals

2003

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A formalism is proposed to study the electron tunneling between extended states, based on the spin-boson Hamiltonian previously used in two-level systems. It is applied to analyze the out-ofplane tunneling in layered metals considering different models. By studying the effects of in-plane interactions on the interlayer tunneling of electrons near the Fermi level, we establish the relation between departure from Fermi liquid behavior driven by electron correlations inside the layer and the out of plane coherence. Response functions, directly comparable with experimental data are obtained.

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Correlated sequential tunneling in Tomonaga–Luttinger liquid quantum dots

Thorwart

Egger

Grifoni

2005

Physica Status Solidi (b)

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We investigate tunneling through a quantum dot formed by two strong impurites in a spinless TomonagaLuttinger liquid. Upon employing a Markovian master equation approach, we compute the linear conductance due to sequential tunneling processes. 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 are shown to dominate over UST. Focusing mainly on the temperature dependence of the conductance maximum, we discuss the relation of our results to previous theoretical and experimental results.

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Coherent transport of charge through a double barrier in a Luttinger liquid

Cited by 33 publications

References 26 publications

Correlated Tunneling in Intramolecular Carbon Nanotube Quantum Dots

Correlated Tunneling in Intramolecular Carbon Nanotube Quantum Dots

Interlayer hopping properties of electrons in layered metals

Correlated sequential tunneling in Tomonaga–Luttinger liquid quantum dots

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