Spin Splitting Induced by Spin-Orbit Interaction in Chiral Nanotubes

Chico, Leonor; Sancho, M. P. López; Muñoz, M. C.

doi:10.1103/physrevlett.93.176402

Cited by 72 publications

(96 citation statements)

References 26 publications

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“…Only recently was it proven experimentally 9 that in the spectrum of ultraclean CNT's, the effects of this coupling between spin and orbital degrees of freedom are clearly visible. This observation is in agreement with previous theoretical predictions, [10][11][12] which argued that SOI could be significant in CNT's due to their curvature. Understanding the effects of this coupling on the spectrum of CNT's is essential for the successful manipulation of the different degrees of freedom of these systems.…”

Section: Introductionsupporting

confidence: 83%

Signatures of spin-orbit interaction in transport properties of finite carbon nanotubes in a parallel magnetic field

2011

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The transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated. Upon including spin-orbit coupling and curvature effects, two main phenomena are analyzed that crucially depend on the tube's chirality: (i) Finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise conducting states. This phenomenon occurs due to the magnetic-field-dependent open boundary conditions obeyed by the carbon nanotube's wave functions. The transport is fully suppressed above threshold values of the magnetic field, which depend on the nanotube chirality, length, and on the spin-orbit coupling. (ii) Reversible spin-polarized currents can be obtained upon tuning the magnetic field, exploiting the curvature-induced spin-orbit splitting.

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Section: Introductionsupporting

confidence: 83%

Signatures of spin-orbit interaction in transport properties of finite carbon nanotubes in a parallel magnetic field

2011

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“…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.…”

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confidence: 99%

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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“…18 While the curvature-induced SO coupling was envisioned previously for semiconductors, 25,26 for nanotubes it is the dominant mechanism. It was Ando 27 and others 28,29 who developed the first theories of SO coupling in nanotubes. More recent theoretical investigations extended this work by including the and bands in full as well as the curved bonds between neighboring atoms.…”

Section: Introductionmentioning

confidence: 99%

Spin-orbit effects in carbon-nanotube double quantum dots

Weiss¹,

Rashba²,

Kuemmeth³

et al. 2010

Phys. Rev. B

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We study the energy spectrum of symmetric double quantum dots in narrow-gap carbon nanotubes with one and two electrostatically confined electrons in the presence of spin-orbit and Coulomb interactions. Compared to GaAs quantum dots, the spectrum exhibits a much richer structure because of the spin-orbit interaction that couples the electron's isospin to its real spin through two independent coupling constants. In a single dot, both constants combine to split the spectrum into two Kramers doublets while the antisymmetric constant solely controls the difference in the tunneling rates of the Kramers doublets between the dots. For the two-electron regime, the detailed structure of the spin-orbit split energy spectrum is investigated as a function of detuning between the quantum dots in a 22-dimensional Hilbert space within the framework of a single-longitudinalmode model. We find a competing effect of the tunneling and Coulomb interaction. The former favors a left-right symmetric two-particle ground state while in the regime where the Coulomb interaction dominates over tunneling, a left-right antisymmetric ground state is found. As a result, ground states on both sides of the ͑11͒-͑02͒ degeneracy point may possess opposite left-right symmetry, and the electron dynamics when tuning the system from one side of the ͑11͒-͑02͒ degeneracy point to the other is controlled by three selection rules ͑in spin, isospin, and left-right symmetry͒. We discuss implications for the spin-dephasing and Pauli blockade experiments.

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Spin Splitting Induced by Spin-Orbit Interaction in Chiral Nanotubes

Cited by 72 publications

References 26 publications

Signatures of spin-orbit interaction in transport properties of finite carbon nanotubes in a parallel magnetic field

Signatures of spin-orbit interaction in transport properties of finite carbon nanotubes in a parallel magnetic field

Curvature-induced anisotropic spin-orbit splitting in carbon nanotubes

Spin-orbit effects in carbon-nanotube double quantum dots

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