Dielectric screening effects on transition energies in aligned carbon nanotubes

Olga A. Dyatlova, Jordi Gomis-Bresco, Ermin Malic, Hagen Telg, Janina Maultzsch, Guofang Zhong, Junfeng Geng, and Ulrike Woggon

Phys. Rev. B 85, 245449 – Published 29 June 2012

Abstract

The optical transition energies $E_{i i}$ of carbon nanotubes (CNTs) strongly depend on the dielectric function $ɛ_{q}$ of the nanotubes and the dielectric background constant $ɛ_{bg}$ of their surroundings. It becomes particularly evident when CNTs in solution and free-standing, vertically aligned CNTs are compared via their optical spectra. Using photoluminescence-excitation spectroscopy, we determine the first two transition energies for these two types of carbon-nanotube samples, i.e., for CNT-solution and CNT-forest samples. We observe considerable energy shifts and explain them by microscopic calculations based on the density-matrix formalism. Combining experiment and theory, we determine the dielectric background constant of the CNT-forest and CNT-solution samples to be $1.3 \pm 0.1$ and $1.8 \pm 0.1$ , respectively.

Received 29 February 2012

DOI:https://doi.org/10.1103/PhysRevB.85.245449

Authors & Affiliations

Olga A. Dyatlova¹, Jordi Gomis-Bresco^1,*, Ermin Malic², Hagen Telg^3,†, Janina Maultzsch³, Guofang Zhong⁴, Junfeng Geng⁵, and Ulrike Woggon¹

¹Institut für Optik und Atomare Physik, Technische Universität Berlin, 10623 Berlin, Germany
²Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
³Institut für Festkörperphysik, Technische Universität Berlin, 10623 Berlin, Germany
⁴Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
⁵Institute for Renewable Energy and Environmental Technologies, University of Bolton, Bolton, BL3 5AB, United Kingdom

^*Current address: “Juan de la Cierva” Fellow, Phononic and Photonic Nanostructures Group (P2N), Catalan Institute of Nanotechnology, Campus de la UAB—Edifici CM3, 08193-Bellaterra (Barcelona), Spain.
^†Current address: Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

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Issue

Vol. 85, Iss. 24 — 15 June 2012

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Images

Figure 1
Cross-sectional SEM image of the $\sim$ 20- $μ$ m-long, vertically aligned carbon nanotubes forming the CNT-forest sample, grown by the MPCVD method (for growth details see the text).Reuse & Permissions
Figure 2
3D contour plots of photoluminescence intensity versus excitation and emission energies for the CNT-forest sample. The eight spots of high emission intensity are assigned to the corresponding $(n, m)$ tube index (black points). (b) In the lower-right corner, the 2D and G Raman modes are seen as straight lines at emission energies approximately 300 meV and 200 meV below the excitation energy, respectively.Reuse & Permissions
Figure 3
3D contour plots of photoluminescence intensity versus excitation and emission energies for the SWCNTs suspended in SDS and deuterium oxide (CNT-solution sample). The 17 spots of high emission intensity are assigned to the corresponding $(n, m)$ tube index (black points). The Raman 2D modes are barely visible; the G mode is out of the range of the measurements.Reuse & Permissions
Figure 4
Absorption spectrum of the exemplary (7,5) carbon nanotube, taking into account different dielectric background constants $ɛ_{bg}$ . The dashed line illustrates the free-particle Van Hove singularity.Reuse & Permissions
Figure 5
Comparison of the PLE-peak positions assigned for nanotubes in CNT-forest (red dots) and CNT-solution (black dots) samples. The numbers indicate $(n, m)$ , the family, and the Kataura branch $(2 n + m)$ of the tubes. The transition energies of CNT-solution samples appear at lower energies with respect to the CNT forest. Additionally, data from the literature are shown detected for air-suspended tubes grown on a quartz substrate (Ref. 19, green square), for “as-grown” tubes synthesized by the DIPS method (Ref. 17, blue triangles), and for tubes suspended on top of a CNT forest (Ref. 18, cyan rhombus).Reuse & Permissions
Figure 6
Dielectric background constants predicted for the CNT-solution and CNT-forest samples (black points and red squares, respectively). The numbers indicate the chiral indices $(n, m)$ . The dashed lines show the calculated dielectric background constant for the CNT-solution (black) and CNT-forest (red) samples. For both samples, averaging is made for bigger diameter and chirality angle tubes (7,5), (7,6), and (8,7). For tubes with smaller chiral angles [(9,4) and (9,5)], the deviation from the averaged $ɛ_{bg}$ is caused by the underestimation of the chirality dependence within the tight-binding approximation.Reuse & Permissions

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