Tunable electronic correlation effects in nanotube-light interactions

Yuhei Miyauchi, Zhengyi Zhang, Mitsuhide Takekoshi, Yuh Tomio, Hidekatsu Suzuura, Vasili Perebeinos, Vikram V. Deshpande, Chenguang Lu, Stéphane Berciaud, Philip Kim, James Hone, and Tony F. Heinz

Phys. Rev. B 92, 205407 – Published 4 November 2015

Abstract

Electronic many-body correlation effects in one-dimensional (1D) systems such as carbon nanotubes have been predicted to strongly modify the nature of photoexcited states. Here we directly probe this effect using broadband elastic light scattering from individual suspended carbon nanotubes under electrostatic gating conditions. We observe significant shifts in optical transition energies, as well as line broadening, as the carrier density is increased. The results demonstrate the role of screening of many-body electronic interactions on the different length scales, a feature inherent to quasi-1D systems. Our findings further demonstrate the possibility of electrical tuning of optical transitions and provide a basis for understanding of various optical phenomena in carbon nanotubes and other quasi-1D systems in the presence of charge carrier doping.

Received 2 September 2013
Revised 16 August 2015

DOI:https://doi.org/10.1103/PhysRevB.92.205407

Authors & Affiliations

Yuhei Miyauchi^1,2,3,*, Zhengyi Zhang^4,5, Mitsuhide Takekoshi⁶, Yuh Tomio⁷, Hidekatsu Suzuura⁷, Vasili Perebeinos^8,9, Vikram V. Deshpande^10,11, Chenguang Lu^12,13, Stéphane Berciaud¹⁴, Philip Kim¹¹, James Hone⁴, and Tony F. Heinz^3,†

¹Institute of Advanced Energy, Kyoto University, Gokasho, Uji 611-0011, Japan
²Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602, Japan
³Departments of Physics and Electrical Engineering, Columbia University, New York, New York 10027, USA
⁴Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA
⁵SanDisk, 951 SanDisk Drive, Milpitas, California 95035, USA
⁶Department of Electrical Engineering, Columbia University, New York, New York 10027, USA
⁷Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
⁸IBM Research Division, T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
⁹Skolkovo Institute of Science and Technology, 3 Nobel Street, Skolkovo 143025, Russian Federation
¹⁰Department of Physics & Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
¹¹Department of Physics, Columbia University, New York, New York 10027, USA
¹²Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
¹³National Center for Nanoscience and Technology, Beijing 100080, China
¹⁴Institut de Physique et Chimie des Matériaux de Strasbourg and NIE, UMR 7504, Université de Strasbourg and CNRS, 23 rue du Loess, Boîte Postale 43, 67034 Strasbourg Cedex 2, France

^*miyauchi@iae.kyoto-u.ac.jp
^†tony.heinz@columbia.edu

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Vol. 92, Iss. 20 — 15 November 2015

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Images

Figure 1
(a) Schematic of our individual nanotube device. The inset shows a microscope image of a substrate with the slit and electrodes used in this study. (b) Schematic diagram of the band structure of a semiconducting nanotube under electrostatic gating conditions (hole doping). (c) Elastic (Rayleigh) and (d) inelastic (Raman) light scattering spectra of a single undoped nanotube. The inset shows the spectrum around the radial breathing mode (RBM). We present all the Rayleigh spectra corrected for the $ω^{3}$ scattering efficiency factor to reflect directly the optical susceptibility.
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Figure 2
Rayleigh scattering spectra for the observed semiconducting nanotube for gating voltages from $V_{G} = 0 to - 25 V$ . Similar spectral changes were observed for positive gating voltages (Supplemental Material [65]). The inset shows Rayleigh scattering spectra of the semiconducting nanotube at $V_{G} = 0 V$ (black solid circles) and $V_{G} = - 25 V$ (red solid circles). The solid green curves are fits based on an excitonic model of the optical susceptibility described in the text.
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Figure 3
(a) Dependence of the exciton resonance energy shifts of the semiconducting nanotube on the carrier (hole) density. The dotted curve indicates a power-law function. (b) Calculated $S_{33}$ and $S_{44}$ shifts of the exciton transition energies $Δ E_{33}$ and $Δ E_{44}$ (red dot-dashed and dotted curves) and their average (red solid curve) for a (26, 0) nanotube as a function of carrier density ρ. The calculated changes in $E_{b}$ and $Σ (Δ E_{b} and Δ Σ)$ ) (blue and green curves, averaged for $S_{33}$ and $S_{44}$ excitons), and the experimental data $Δ E_{av}$ shown in (a) (blue circles) are plotted together for comparison. (c) Schematic diagram of the physical mechanisms for the redshift in the transition energy with doping.
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Figure 4
(a) Dependence of the $S_{33}$ and $S_{44}$ exciton resonance linewidths of the semiconducting nanotube on carrier density. The dotted lines are fits of the function $Γ_{i i} (ρ) = Γ_{i i 0} + β_{i i} ρ$ to the linewidths for the $S_{i i}$ exciton. The right axis indicates the dephasing time of excitons corresponding to the linewidth. (b) Calculated decay rates (red and green solid lines for $S_{33}$ and $S_{44}$ , respectively) of a photoexcited electron-hole pair in a (26, 0) nanotube due to the free-carrier doping. The calculated data are plotted together with the experimental data (opaque symbols) shown in (a) with 65-meV offset between the left (for calculated results) and right (for experimental data) vertical axes to account for decay channels of the undoped nanotube.
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Figure 5
Raman $G$ -mode spectra for gate voltages of $V_{G} = 0$ (black curve) and −25 V (red curve) taken from an individual chiral metallic nanotube suspended over the same slit where the near-zigzag semiconducting nanotube employed in the measurements described in the main text was located. The inset displays the measured width of this mode (red circles) as a function of the gate voltage $V_{G}$ . The green curve is a fit to Eq. (A1)) for the variation with charge density.
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Figure 6
Schematic representation of the electronic band structure of a nanotube near the $K$ and $K$ ′ valleys and possible electron (hole) scattering pathways (pairs of arrows with the same colors) contributing to the observed increase in linewidth. Only the case for an electron-doped nanotube is shown. For $S_{33} (S_{44})$ , only the pathways where a photoexcited electron and a hole in $K$ ( $K$ ′) valley are involved are shown.
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