Energy gaps of semiconducting nanotubules

Yorikawa, H.; Muramatsu, Shogo

doi:10.1103/physrevb.52.2723

Cited by 64 publications

(40 citation statements)

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“…We have checked that the splitting is not negligible for larger NTs: for example, the (80,0) tube, with a diameter of 62.64Å, roughly the same size of the NT measured in [6], has a top VB normalized splitting of 0.04. An analogous family behavior of zigzag CNTs has been observed in other physical properties, such as the band gaps [19,20,21], and it has been related to the trigonal warping effect. The three families can be understood by resorting to the zone folding approach.…”

mentioning

confidence: 84%

“…Spin-orbit effects are more important for bands with larger curvature-induced rehybridization: therefore, curvature effects are responsible for the observed electron-hole anisotropic SO splitting. The different mixing of π and σ orbitals, due to the curvature of the tubes, was shown to affect the energy gaps of semiconducting nanotubes [19] with a similar family dependence. Here we have shown that it also influences the value of spin-orbit splitting in CNTs.…”

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confidence: 99%

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Curvature-induced anisotropic spin-orbit splitting in carbon nanotubes

2009

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We have theoretically explored the spin-orbit interaction in carbon nanotubes. We show that, besides the dependence on chirality and diameter, the effects of spin-orbit coupling are anisotropic: spin splitting is larger for the higher valence or the lower electron band depending on the specific tube. Different tube behaviors can be grouped in three families, according to the so-called chiral index. Curvature-induced changes in the orbital hybridization have a crucial role, and they are shown to be family-dependent. Our results explain recent experimental results which have evidenced the importance of spin-orbit effects in carbon nanotubes. PACS numbers: 71.20.Tx, 71.70.Ej Improvements in the quality of carbon nanotubes (CNTs) have enabled the fabrication of quantum dots aiming at the realization of spintronics devices [1,2,3,4]. CNTs present a high Fermi velocity and a twofold orbital degeneracy originating from the topology of the honeycomb lattice. The unique fourfold degeneracy of CNTs energy states (spin plus orbital moment) has been observed in CNT quantum dots (QDs) by magnetic field spectroscopy measurements [5] and makes them particularly interesting since, besides the spin degree of freedom, they present the orbital moment to allow for quantum manipulation. In a recent experiment [6], spin-orbit coupling has been directly observed in CNT as a splitting of the fourfold degeneracy of a single-electron energy level in ultra-clean QDs. This important finding seems to be in contradiction with the interpretation of earlier experiments in defect-free CNTs, from which independent spin and orbital symmetries and electron-hole symmetry have been deduced [7]. Besides showing the importance of spin-orbit effects in carbon nanotubes, Kuemmeth et al.[6] point out an unexplained anisotropic splitting of electron and holes in carbon nanotube quantum dots, which deserves further exploration.On theoretical grounds, spin-orbit interaction (SOI) has been investigated on CNTs by deriving an effective mass Hamiltonian including a weak SOI in carbon orbitals to the lowest order in perturbation theory [8]. Band splitting was found considering surface curvature effects [9], as well as in the electron spin resonance spectra of achiral CNTs derived by low-energy theory [10]. In an earlier work, we showed that the inclusion of the full lattice symmetry is essential for deriving spin-orbit (SO) effects in CNTs [11]. Employing an empirical tightbinding model, we demonstrated an intrinsic symmetry dependence of SOI effects. As confirmed by recent experimental results [6], we showed that, in the absence of a magnetic field, CNTs present spin-orbit split bands at the Fermi level. In addition, SOI induces zero-field spin splitting in chiral CNTs, while Kramers theorem on time-reversal symmetry alongside the inversion symmetry preserve the spin-degeneracy in achiral-i.e., (n, n) armchair and (n, 0) zigzag-nanotubes [12]. More recent works [13] have indicated the importance of curvature in the SOI effects investigated with a continuum ...

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confidence: 84%

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confidence: 99%

Curvature-induced anisotropic spin-orbit splitting in carbon nanotubes

2009

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“…44 For the SWNTs discussed in Secs. IV A and IV H, guesses for the chiral indices are given only if the atomic lattice could be sufficiently well resolved to determine .…”

Section: B Sample Preparationmentioning

confidence: 99%

Modifying the electronic structure of semiconducting single-walled carbon nanotubes byAr+ion irradiation

et al. 2009

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Local controllable modification of the electronic structure of carbon nanomaterials is important for the development of carbon-based nanoelectronics. By combining density-functional theory simulations with Arion-irradiation experiments and low-temperature scanning tunneling microscopy and spectroscopy ͑STM/STS͒ characterization of the irradiated samples, we study the changes in the electronic structure of single-walled carbon nanotubes due to the impacts of energetic ions. As nearly all irradiation-induced defects look as nondistinctive hillocklike features in the STM images, we compare the experimentally measured STS spectra to the computed local density of states of the most typical defects with an aim to identify the type of defects and assess their abundance and effects on the local electronic structure. We show that individual irradiationinduced defects can give rise to single and multiple peaks in the band gap of the semiconducting nanotubes and that a similar effect can be achieved when several defects are close to each other. We further study the stability of defects and their evolution during STM measurements. Our results not only shed light on the abundance of the irradiation-induced defects in carbon nanotubes and their signatures in STS spectra but also suggest a way the STM can be used for engineering the local electronic structure of defected carbon nanotubes.

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“…There are many trial reports about chirality control, which indicates that this methodology has succeeded in controlling the chirality distribution to some extent. However, as theoretical studies have predicted, the distortion energy due to the chiral difference is too small to regulate the chirality uniquely [6]. In spite of the difficulty of this situation, recent studies have been reported in which attempts have been made to synthesize SWCNT with control of the chirality.…”

Section: Introductionmentioning

confidence: 99%

“…The equations and the parameter sets for the Brenner potential are given in Eqs. (6)(7)(8)(9)(10)(11)(12) and Table 2, respectively. The parameters for the carbon-carbon interaction have been adopted from the reference.…”

Section:      mentioning

confidence: 99%

Molecular Dynamics Observation of Iron–Carbon precursors of Carbon Nanotube and Development of Iron–Carbon Potential

Nishi¹,

Inoue²,

Matsumura³

2013

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Abstract.We have focused on the growth process of metal and carbon mixed clusters that are precursors for carbon nanotubes. The molecular dynamics method using the Brenner potential was employed for modeling carbon-carbon interactions as well as carbon-iron interactions. As for carbon-iron interactions, the parameters were derived using DFT calculation. The Finnis-Sinclair potential was employed for irons. In order to observe the deposition process of carbon atoms, we adjusted the potential parameters to reproduce the bulk melting points of graphite, iron, and cementite, which was a model material of ironcarbon composite. We observed the initial growth process by preparing iron-carbon mixed clusters (approximately 200 iron atoms and 70 carbon atoms) as precursor clusters. Additional carbon atoms were then gradually supplied to this mixture at 1000 K and 1200 K. Consequently, the graphite structure was formed on the mixture surface, but at some phases, the cap structure was observed at 1200 K.

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Energy gaps of semiconducting nanotubules

Cited by 64 publications

References 12 publications

Curvature-induced anisotropic spin-orbit splitting in carbon nanotubes

Curvature-induced anisotropic spin-orbit splitting in carbon nanotubes

Modifying the electronic structure of semiconducting single-walled carbon nanotubes byAr+ion irradiation

Molecular Dynamics Observation of Iron–Carbon precursors of Carbon Nanotube and Development of Iron–Carbon Potential

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