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Terahertz spectroscopy of individual carbon nanotube quantum dots Takuma Tsurugaya, Kenji Yoshida, Fumiaki Yajima, Maki Shimizu, Yoshikazu Homma, and Kazuhiko Hirakawa Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03801 • Publication Date (Web): 12 Dec 2018 Downloaded from http://pubs.acs.org on December 12, 2018

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Terahertz spectroscopy of individual carbon nanotube quantum dots Takuma Tsurugaya,1,

‡

Kenji Yoshida,1,*, ‡ Fumiaki Yajima,2 Maki Shimizu,2 Yoshikazu

Homma,2 and Kazuhiko Hirakawa1,3　

1Institute

of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo

153-8505, Japan 2Department

of Physics and Research Institute for Science & Technology, Tokyo

University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan 3Institute

for Nano Quantum Information Electronics, University of Tokyo, 4-6-1 Komaba,

Meguro-ku, Tokyo 153-8505, Japan

Keywords: Carbon nanotubes, Terahertz spectroscopy, Quantum dots, Single-electron transistors, Intersublevel transition

ABSTRACT. We have investigated the electronic structures of metallic carbon nanotube quantum dots (CNT QDs) by terahertz-induced photocurrent spectroscopy. Sharp peaks

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due to intersublevel transitions in the CNT QDs are observed at the sublevel energy spacings expected from the linear band dispersion. The linewidth of the photocurrent peak is as narrow as 0.3 meV and is governed by the tunnel coupling with the electrodes, indicating that the scattering time of electrons in the present CNTs is comparable to or longer than 10 ps. The observation of a sharp absorption peak at the bare quantization energy was not consistent with the Tomonaga-Luttinger liquid theory.


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Carbon nanotubes (CNTs) are unique electronic materials of one-dimensional character and have been extensively studied as promising materials for optoelectronic devices.

Characteristic energy scales in CNTs, such as plasmon energies1,

curvature-induced bandgaps,3 lie in the terahertz (THz) frequency range.

2

and THz

spectroscopy is, therefore, an ideal tool for investigating electronic structures and carrier dynamics in CNTs and many studies on THz properties of CNTs have so far been done in various systems.4-10 To investigate THz dynamical properties intrinsic to CNTs, THz measurements at single nanotube level are particularly important to avoid severe inhomogeneous broadening of THz spectrum, which originates from the following three reasons; first, as-grown CNTs are a mixture of diverse types of CNTs (different chirality, conduction types, etc). Second, electronic properties of CNTs are altered by tube-tube interactions. Third, the dielectric properties of CNTs have a strong polarization anisotropy because of their shape anisotropy.11

From these reasons, THz spectroscopy on

individual CNTs is very crucial. In addition, CNTs are known to be a platform of studies on quantum physics. When a zero-dimensional quantum dot (QD) is formed in a CNT,


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other energy scales related with the orbital quantization,13-17 vibrational excitations,18-20 electron-electron interactions,14 and spin correlation21 also fall into the THz range.

To perform THz spectroscopy on single CNT-QDs, however, we need to go beyond the diffraction limit and focus THz electromagnetic wave onto a nm-scale single CNT QD. Furthermore, since the THz absorption by electrons in an individual CNT QD is extremely weak, the conventional transmission/absorption measurements do not work. Experimental works on THz-response of CNT-QDs have been limited to the observation of the photon-assisted tunneling effect under the illumination of a strong, monochromatic THz light source22, 23 and only a few THz spectroscopic studies on CNT-QDs have so far been attempted.

In this work, we have investigated dynamical properties of CNT QDs by utilizing the single electron transistor (SET) geometry with nanogap metal electrodes and


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measuring THz-induced photocurrents in the CNT SETs.24 By using this method, we have successfully detected THz spectral signals from individual CNTs. We have found that sharp resonant peaks appear in the THz spectra and their energies are quantitatively in agreement with the sublevel energy spacing expected from the linear band dispersion in metallic CNTs, which indicates that the observed peaks originate from the intersublevel transitions between two neighboring quantized orbitals in the CNT-QDs. The linewidth of the photocurrent peaks is as narrow as 0.3 meV, which is consistent with the tunnel escape time from the CNT-QDs to the electrodes. The linewidth of the photocurrent peaks is governed by the tunnel coupling with the electrodes, suggesting that electrons in the CNT QD have a scattering time comparable to or longer than 10 ps.

The

observation of a sharp absorption peak at the bare quantization energy was not consistent with the Tomonaga-Luttinger liquid theory.

Figure 1(a) shows a schematic illustration of our CNT SET samples used in this study. A semi-transparent metal gate layer was deposited on a resistive Si substrate by


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electron beam (EB) evaporation and a 150-nm-thick SiO2 layer was then sputtered. CNTs were grown from Co nanoparticles on the substrate by the chemical vapor deposition (CVD) using ethanol as the carbon feedstock.25 Finally, we deposited Ti/Au layers for the source and drain electrodes on the CNTs, which were first mapped out with an atomic force microscope (AFM).

To achieve a good coupling efficiency between the THz

radiation and the CNT QDs, we employed a bowtie-antenna shape for the source and drain electrodes,26 as shown in Fig. 1(b). The bowtie-antenna used in this work had a broad resonance around 2 THz (Fig. 1(c)). AFM images of the samples studied in this work are shown in Figs. 1(d) and 1(e), together with a designed pattern of the nanogap electrodes. The gap length for sample A (Fig. 1(d)) and sample B (Fig. 1(e)) were 150 nm and 250 nm, respectively. The diameter of the CNTs was determined to be less than 1 nm by AFM measurements, indicating that they were single-walled CNTs. The currentvoltage (I-V) characteristics of the fabricated CNT transistors at 300 K showed very weak dependence on the gate voltage ranging from -5 V to 5 V, indicating that the CNTs were metallic.

Figure 1(f) illustrates our measurement setup for the THz photocurrent

spectroscopy.

We used a Fourier transform infrared spectrometer for spectral


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measurements.27 A weak, broadband THz radiation from a globar was guided into a Michelson interferometer and focused on a sample mounted on a hyper-hemispherical Si lens. The THz-induced photocurrent was measured with a lock-in amplifier referenced to an optical chopper.

Figure 2(a) plots a differential conductance map, dI/dV, of sample A (L = 150 nm) measured at 4.7 K as a function of the gate voltage VG and the source-drain voltage VSD. Observation of clear Coulomb diamonds indicates that the CNT contacted by the nanogap electrodes serves as a Coulomb island. From the Coulomb stability diagram, the charging energies of this sample were determined to be ~23 meV, which is reasonable for CNTQDs with 150-nm-length.15 Furthermore, as seen in the figure, excited states at 10±1 meV can be observed.


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Figure 2(b) shows a color-coded map of the photocurrent excited by a broadband THz radiation from a blackbody light source when the position of the movable mirror was fixed. We found that there flows a photocurrent of the order of a few nA inside the Coulomb blockaded regions. This behavior can be well explained by the photoexcitation of confined electrons24 in the CNT QD. When an electron on the ground state resonantly absorbs a photon and makes a transition to an excited state, it subsequently tunnels out to the source or drain electrode, which results in a photocurrent generation.

As seen in

Fig. 2(c), it is found that there flows a finite photocurrent even at zero bias voltage. This means that this sample exhibits a photovoltaic effect. As discussed in Ref. 24, the photovoltaic effect originates from the asymmetry in the four tunneling rates: G, G,  S D E, and E. Superscripts G and E denote the ground and excited states, respectively. S S Subscripts S and D denote the source and drain electrodes, respectively. Assuming that a two-level system is tunnel-coupled with the electrodes, as illustrated in Fig. 3, the photocurrent generated by the photovoltaic effect is described as below (see Supplementary Information for details):


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det

(

)

ΓES ΓED ΓGS ΓGD

det

(

)

ΓES ΓED ΓgS ΓgD

𝐼𝑝ℎ = |𝑒|(ΓG + ΓG)(ΓE + ΓE + Γ ) + (ΓG + ΓG + ΓE + ΓE )Γ ΓE ~ |𝑒|(ΓG + ΓG)(ΓE + ΓE + Γ )ΓE . S D S D S D S D E S D S D R R

(1)

Here, e is the elementary charge, R the electron relaxation rate from the excited state to the ground state, and E the photo-excitation rate. When ΓE is much smaller than the tunneling rates and the relaxation rate, the second term of the denominator can be neglected and the photocurrent, Iph, becomes proportional to E. The determinant of the matrix expressed by the four tunneling rates in the numerator indicates that an asymmetry in the tunneling rates generates finite a photocurrent.

Next, we investigated photocurrent spectra by performing Fourier analysis on the photocurrent generated by illuminating the samples with THz waves with a variable time delay . We used the photocurrent signals around VSD = 0 for obtaining THz spectra to minimize the shot noise. Figure 4(a) shows an example of an interferogram of the THz-


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induced photocurrent, Iph(), measured at VG = -2370 mV for sample A.

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We then

performed Fourier analysis on the interferograms taken at various gate voltages to obtain the photocurrent spectra Iph(). Figure 4(b) shows Iph()’s measured for sample A (L = 150 nm) at three different gate voltages (VG = -2590 mV, -2370 mV, -2080 mV), which correspond to different charge states. As seen in the figure, sharp resonant peaks are clearly observed at 11.8 meV, 10.4 meV, and 9.5 meV for point a (VG = -2590 mV), b (VG = -2370 mV), and c (VG = -2080 mV), respectively. Figure 4(c) shows Iph() measured at

VG = 4400 mV for sample B (L = 250 nm) and a peak is observed at 7.8 meV, which suggests that the THz peak position depends on the CNT length.

For the case of metallic CNT-QDs, if the confinement potential can be regarded as a box-like one, the energy spacing between two adjacent electron sublevels, E, is given by

E 

hv F 2L ,

(2)


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being independent of the quantum numbers. Here, h is the Planck constant, vF the Fermi velocity (~8.1×105 m/s), and L the confinement length. Assuming that L is equal to the gap length between the source and drain electrodes, we can estimate E = 11.2 meV and 6.7 meV for L = 150 nm and 250 nm, respectively, which quantitatively agree with the experimental results. Since the THz electric field applied to the CNT-QDs is linearly polarized along the axis of the CNTs, only transitions between the electronic states with the same spin states in the same valleys are allowed due to the selection rule. Therefore, we can conclude that the sharp THz peaks originate from the intersublevel transitions between the two adjacent electron sublevels. As shown in Fig. 4(d), the peaks of the obtained spectra are well fitted by a single Lorentzian curve, which suggests that the linewidth (full width at half maximum FWHM) of the obtained spectra, E, is mainly determined by the dephasing time, T2, of the electrons photoexcited to the upper quantized sublevel. The relationship between E and

T2 can be expressed as E/2h = 1/T2. Since the CNT-QDs are tunnel-coupled to the source and drain electrodes in this system, T2 is determined not only by scattering28 but also by tunneling, Ttunnel. By substituting the observed E’s of the THz photocurrent peaks


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for sample A (FWHM ~ 0.3 meV) and sample B (FWHM ~ 1.7 meV) to the relationship, we obtain T2 ~ 28 ps for sample A and ~ 4.8 ps for sample B, respectively. According to the single-electron tunneling theory,29 the current amplitude at a charge degeneracy point

IPeak is given by eGG/(G+G) and the tunneling time Ttunnel is expressed as (G +  S D

S

D

S

G)-1. If we assume symmetrical tunneling rates for the source and drain electrodes, we D have G = G = 2IPeak/e. Since IPeak was a few nA for sample A and 12 nA for sample B, S D respectively (see Fig. S3 in Supplementary Information), Ttunnel is roughly estimated to be 16 ps for sample A and 3.3 ps for sample B, which explains well the linewidth difference between the two samples. Therefore, we can say that T2 in the present samples is governed by Ttunnel and the scattering time is on the order of 10 ps or more.

Finally, we make a comment on how the one-dimensionality of the electron system in the CNTs affects the intersublevel transition. It is widely known that electrons in the CNTs behave as a Tomonaga-Luttinger liquid (TLL), reflecting strong electron-electron interaction due to their one-dimensionality.5, 6, 30-33 One of the most striking features is


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the correction in the plasmon group velocity vpl = vF/g.30

g (0 < g < 1) is the Luttinger

parameter that expresses the strength of electron-electron interaction and is expressed as the ratio between the charging energy EC and the sublevel spacing E:34

 2 EC  g  1   E  

0.5

(3)

Theory predicts that g is nearly 0.28 for metallic carbon nanotubes. Therefore, the intersublevel transition energy is expected to have an upshift due to a manybody plasmon effect and is given as follows:

E pl 

1 hv F g 2L

(4)

Let us consier the case of sample A for example. Substituting the observed EC (~23 meV) and the ∆E calculated from the electron dispersion (~11 meV) into Eqs. (3) and (4), we obtain g ~ 0.44 and ∆Epl ~ 25 meV. However, from the THz spectrum, E was found to be 11.2 meV and was almost equal to hvF/2L for L =150 nm, which indicates that the effective g for sample A was almost equal to 1 and the manybody plasmonic


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correction was not observed, as is the case in Ref. 8. One of the possible reasons for the absence of the manybody plasmonic effect is electron screening by the backgate electrodes placed just under the CNTs,5,

6

which may reduce the effective Coulomb

interaction of the electrons in the CNTs. To comprehensively understand this issue, we need further systematic experiments using different geometries of gate electrodes, such as the side-gates and top-gates, which provide different electromagnetic environments to the CNTs.

In summary, we have investigated the electronic structures in individual metallic carbon nanotube quantum dots by terahertz photocurrent spectroscopy. We observed sharp peaks due to intersublevel transitions in the CNT QDs, whose energy positions are in agreement with the sublevel energy spacing expected from the linear band dispersion and the correction by the manybody plasmonic effect was not clearly observed. The linewidth of the photocurrent peak was as narrow as 0.3 meV and governed by the tunnel escape time of electrons from the CNT QDs to the electrodes, suggesting that the


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scattering time of electrons in the present CNTs is comparable to or longer than 10 ps. The result demonstrated here is the first step toward THz-spectroscopic studies of other kinds of CNTs such as multi-walled CNTs and CNT-peapods at the individual level.


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FIGURES.

Figure 1. (a) Schematic illustration of the sample structure.

(b) Scanning electron

microscopy (SEM) image of the fabricated CNT-SET sample with a bowtie antenna structure. S and D denote the source and drain electrodes. (c) The resonance spectrum of the bowtie-antenna calculated by using the finite element method. (d, e) Atomic force microscopy (AFM) images of the nanojunction region: (d) sample A (L = 150 nm) and (e) sample B (L = 250 nm). The CNTs measured in this work are indicated by black arrows.


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The areas shaded in yellow correspond to the nanogap electrodes.

(f) Schematic

illustration of the measurement system of the THz-induced photocurrent spectroscopy.


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Figure 2. (a) Coulomb stability diagram measured at 4.7K in the dark condition. Black dashed lines are eyeguides for the boundaries of the Coulomb diamonds. Excited state lines at approximately 10 meV are indicated by white dotted lines. (b) A mapping of the THz-induced photocurrent measured at 4.7 K for the same bias region as that of (a). Black dashed and green dotted lines are eyeguides for the boundaries of the Coulomb diamonds and the excited state lines, respectively. (c) THz-induced photocurrent as a function of the gate voltage at VSD = 0mV.

Figure 3. Schematic for the electron transitions in a single-electron transistor under THz radiation. G denotes the tunnel rates between the ground state and the source S ACS Paragon Plus Environment

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electrode. G, E, and E have similar meanings. E is the excitation rate from the D S D ground state to the excited state by THz radiation. R is the relaxation rate from the excited state to the ground state.

Figure 4. (a) Interferogram of the THz induced photocurrent measured at VSD = 0mV and at VG = -2370 mV for sample A.

(b) Fourier spectra of the interferograms (i.e.,


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photocurrent spectra) measured at point a (VG = -2590 mV), point b (VG = -2370 mV), and point c (VG = -2080 mV) (indicated in Fig. 2(a)) for sample A. (c) Photocurrent spectrum measured at VG = 4400 mV for sample B. (d) An enlarged view of the Fourier spectrum measured at point b (VG = -2370 mV) for sample A. Dots are measured data points. The red curve is a fitting curve with a Lorentzian function.

ASSOCIATED CONTENT

Supporting Information.

The derivation of equation (1) in the main text and Coulomb

oscillation peaks of the CNT devices without THz irradiation for sample A and B.

AUTHOR INFORMATION Corresponding Author * To whom correspondence should be addressed. E-mail: [email protected]

Author Contributions ‡These authors contributed equally to this work.

ACKNOWLEDGMENT


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We thank Y. Arakawa for his continuous encouragement. We also thank T. Ando, T. Nakanishi, M. Eto, R. Okuyama, W. Izumida, Y. Kawano, S. Q. Du, and Y. Zhang for fruitful discussion. This work is supported by MEXT KAKENHI on Innovative Areas “Science of hybrid quantum systems” (15H05868, 15H058691), KAKENHI from JSPS (17H01038, 18K14077), Project for Developing Innovation Systems of MEXT, Ozawa and Yoshikawa Memorial Electronics Research Foundation, Kondo Foundation, and Iketani Foundation.

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(27) For example, Griffiths, P. R.; De Haseth, J. A., Fourier transform infrared spectrometry; Wiley: New York, 1986. (28) Since the electron-phonon scattering time is long at low temperatures, it is likely that the main scatterers in the CNTs are localized lattice defects, electrostatic potential fluctuations induced from the substrates [Biercuk, M.; Ilani, S.; Marcus, C.; McEuen, P., Electrical Transport in Single-Wall Carbon Nanotubes. In Carbon Nanotubes; Springer: Berlin, 2008; Vol. 111, pp 455– 493.]. (29) Datta, S. Quantum Transport: Atom to Transistor; Cambridge University Press: Cambridge, 2005. (30) Kane, C.; Balents, L.; Fisher, M. P. A. Phys. Rev. Lett. 1997, 79, 5086. (31) Ishii, H.; Kataura, H.; Shiozawa, H.; Yoshioka, H.; Otsubo, H.; Takayama, Y.; Miyahara, T.; Suzuki, S.; Achiba, Y.; Nakatake, M.; Narimura, T.; Higashiguchi, M.; Shimada, K.; Namatame, H.; Taniguchi, M. Nature 2003, 426, 540. (32) Shi, Z. W.; Hong, X. P.; Bechtel, H. A.; Zeng, B.; Martin, M. C.; Watanabe, K.; Taniguchi, T.; Shen, Y. R.; Wang, F. Nat. Photon. 2015, 9, 515. (33) Tans, S. J.; Devoret, M. H.; Dai, H. J.; Thess, A.; Smalley, R. E.; Geerligs, L. J.; Dekker, C. Nature 1997, 386, 474. (34) Bockrath, M.; Cobden, D. H.; Lu, J.; Rinzler, A. G.; Smalley, R. E.; Balents, L.; McEuen, P. L. Nature 1999, 397, 598.


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Terahertz Spectroscopy of Individual Carbon ... - ACS Publications

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