Correlated Tunneling in Intramolecular Carbon Nanotube Quantum Dots

Abstract

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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