π-band contribution to the optical properties of carbon nanotubes: Effects of chirality

Tasaki, Seiji; Maekawa, Koji; Yamabe, Tokio

doi:10.1103/physrevb.57.9301

Cited by 150 publications

(141 citation statements)

References 48 publications

Supporting

Mentioning

135

Contrasting

Order By: Relevance

“…The novel conserved parities refine the momenta conservation rules. The coincidence of the z-reversal odd and even states with the systematic van Hove singularities proves substantial influence of the parities to the physical processes in nanotubes and related spectra 16,23 . Therefore, these additional rules must not be overlooked in calculations.…”

Section: Discussionmentioning

confidence: 99%

“…To illustrate further the relevance of the derived parity selection rules, let us briefly discuss armchair tubes and the parallel component of the dielectric tensor ǫ ij (k, ω), which is the corner stone in the analysis of various optical properties 16 . The contribution of the direct interband transitions caused by the electric field along the z-axis are to be included in calculations.…”

Section: Discussionmentioning

confidence: 99%

“…Although optical absorption and diffraction are well described within the long-wavelength limit, for the optical activity the terms of ε ij linear in the components of the wave vector k (having different symmetry from the k-independent ones) should be considered. These linear terms define the tensor γ ijk and its symmetric and antisymmetric 16 parts with respect to the last two subscripts:…”

Section: Selection Rulesmentioning

confidence: 99%

See 2 more Smart Citations

Carbon nanotubes band assignation, topology, Bloch states, and selection rules

2002

View full text Add to dashboard Cite

Various properties of the energy band structures (electronic, phonon, etc.), including systematic band degeneracy, sticking and extremes, following from the full line group symmetry of the singlewall carbon nanotubes are established. The complete set of quantum numbers consists of quasi momenta (angular and linear or helical) and parities with respect to the z-reversal symmetries and, for achiral tubes, the vertical plane. The assignation of the electronic bands is performed, and the generalized Bloch symmetry adapted eigen functions are derived. The most important physical tensors are characterized by the same set of quantum numbers. All this enables application of the presented exhaustive selection rules. The results are discussed by some examples, e.g. allowed interband transitions, conductivity, Raman tensor, etc.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Selection Rulesmentioning

confidence: 99%

See 1 more Smart Citation

Carbon nanotubes band assignation, topology, Bloch states, and selection rules

2002

View full text Add to dashboard Cite

show abstract

“…A theoretical framework for discussion of the optical activity [26] and Faraday rotation phenomena [27] in CNTs has been proposed within the tight-binding (TB) formalism. An alternative simplified TB approach was originally proposed by Romanov and Kibis [28] and developed further in [29,30].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear coherent magneto-optical response of a single chiral carbon nanotube

Slavcheva

Roussignol

2010

New J. Phys.

View full text Add to dashboard Cite

View the article online for updates and enhancements. Abstract. We propose a theoretical framework and dynamical model for the description of the natural optical activity and Faraday rotation in an individual chiral single-wall carbon nanotube (CNT) in the highly nonlinear coherent regime. The model is based on a discrete-level representation of the optically active states near the band edge. Chirality is modelled by a system Hamiltonian in a four-level basis corresponding to energy-level configurations, specific for each handedness, that are mirror reflections of each other. The axial magnetic field is introduced through the Aharonov-Bohm and Zeeman energylevel shifts. The time evolution of the quantum system, describing a single nanotube with defined chirality, under an ultrashort polarized pulse excitation is studied using the coupled coherent vector Maxwell-pseudospin equations (Slavcheva 2008 Phys. Rev. B 77 115347). We provide an estimate for the effective dielectric constant and the optical dipole matrix element for transitions excited by circularly polarized light in a single nanotube and calculate the magnitude of the circular dichroism and the specific rotatory power in the absence and in the presence of an axial magnetic field. Giant natural gyrotropy (polarization rotatory power ∼3000 • mm −1 (B = 0 T)), superior to that of the crystal birefringent materials, liquid crystals and comparable or exceeding that of the artificially made helical photonic structures, is numerically demonstrated for the specific case of a (5, 4) nanotube. A quantitative estimate of the coherent nonlinear magneto-chiral optical effect in an axial magnetic field is given 3 Authors to whom any correspondence should be addressed. . The model provides a framework for the investigation of the chirality and magnetic field dependence of the ultrafast nonlinear optical response of a single CNT.

show abstract

“…Each line, i.e each value of j, defines a subband of the nanotube spectrum which corresponds to a definite angular momentum of the electron around the cylinder (see for example Refs. [10,12,13]). …”

Section: Single Particle Picturementioning

confidence: 99%

Manifestations of electron interactions in photogalvanic effect in chiral nanotubes

et al. 2012

View full text Add to dashboard Cite

Carbon nanotubes provide one of the most accessible experimental realizations of one dimensional electron systems. In the experimentally relevant regime of low doping the Luttinger liquid formed by electrons may be approximated by a Wigner crystal. The crystal-like electronic order suggests that nanotubes exhibit effects similar to the Mössbauer effect where the momentum of an emitted photon is absorbed by the whole crystal. We show that the circular photovoltaic effect in chiral nanotubes is of the same nature. We obtain the frequency dependence of the photovoltage and characterize its singularities in a broad frequency range where the electron correlations are essential. Our predictions provide a basis for using the photogalvanic effect as a new experimental probe of electron correlations in nanotubes.

show abstract

π-band contribution to the optical properties of carbon nanotubes: Effects of chirality

Cited by 150 publications

References 48 publications

Carbon nanotubes band assignation, topology, Bloch states, and selection rules

Carbon nanotubes band assignation, topology, Bloch states, and selection rules

Nonlinear coherent magneto-optical response of a single chiral carbon nanotube

Manifestations of electron interactions in photogalvanic effect in chiral nanotubes

Contact Info

Product

Resources

About