Generating and detecting radiation in the technologically relevant range of the so-called terahertz gap (0.1–10 THz) is challenging because of a lack of efficient sources and detectors. Quantum dots in carbon nanotubes have shown great potential to build sensitive terahertz detectors, usually based on photon-assisted tunneling. A recently reported mechanism combining resonant quantum dot transitions and tunneling barrier asymmetries results in a narrow linewidth photocurrent response with a large signal-to-noise ratio under weak THz radiation. That device was sensitive to one frequency, corresponding to transitions between equidistant quantized states. In this work we show, using numerical simulations together with scanning tunneling spectroscopy studies of a defect-induced metallic zigzag single-walled carbon nanotube quantum dot, that breaking simultaneously various symmetries in metallic nanotube quantum dots of arbitrary chirality strongly relaxes the selection rules in the electric dipole approximation and removes energy degeneracies. This leads to a richer set of allowed optical transitions spanning frequencies from 1 THz to several tens of THz, for a ∼10 nm quantum dot. Based on these findings, we propose a terahertz detector device based on a metallic single-walled carbon nanotube quantum dot defined by artificial defects. Depending on its length and contacts transparency, the operating regimes range from a high-resolution gate-tunable terahertz sensor to a broadband terahertz detector. Our calculations indicate that the device is largely unaffected by temperatures up to 100 K, making carbon nanotube quantum dots with broken symmetries a promising platform to design tunable terahertz detectors that could operate at liquid nitrogen temperatures.

1.
S. S.
Dhillon
 et al., “
The 2017 terahertz science and technology roadmap
,”
J. Phys. D: Appl. Phys.
50
,
043001
(
2017
).
2.
M.
Tonouchi
, “
Cutting-edge terahertz technology
,”
Nat. Photonics
1
,
97
105
(
2007
).
3.
B.
Ferguson
and
X.-C.
Zhang
, “
Materials for terahertz science and technology
,”
Nat. Mater.
1
,
26
33
(
2002
).
4.
M.
Lee
and
M. C.
Wanke
, “
Applied Physics: Searching for a solid-state terahertz technology
,”
Science
316
,
64
65
(
2007
).
5.
D.
Mittleman
, ed.,
Sensing with Terahertz Radiation
(
Springer
,
Berlin Heidelberg
,
2003
).
6.
R.
Appleby
and
H. B.
Wallace
, “
Standoff detection of weapons and contraband in the 100 GHz to 1 THz region
,”
IEEE Trans. Antennas Propag.
55
,
2944
2956
(
2007
).
7.
J. F.
Federici
,
B.
Schulkin
,
F.
Huang
,
D.
Gary
,
R.
Barat
,
F.
Oliveira
, and
D.
Zimdars
, “
THz imaging and sensing for security applications—explosives, weapons and drugs
,”
Semicond. Sci. Technol.
20
,
S266
S280
(
2005
).
8.
P.
Siegel
, “
Terahertz technology in biology and medicine
,”
IEEE Trans. Microwave Theory Tech.
52
,
2438
2447
(
2004
).
9.
D.
Saeedkia
,
Handbook of Terahertz Technology for Imaging, Sensing and Communications
(
WP Woodhead Publishing
,
Oxford, UK
,
2013
).
10.
R. A.
Lewis
, “
A review of terahertz detectors
,”
J. Phys. D: Appl. Phys.
52
,
433001
(
2019
).
11.
M. H.
Alsharif
,
A. H.
Kelechi
,
M. A.
Albreem
,
S. A.
Chaudhry
,
M. S.
Zia
, and
S.
Kim
, “
Sixth generation (6G) wireless networks: Vision, research activities, challenges and potential solutions
,”
Symmetry
12
,
676
(
2020
).
12.
L.
Vicarelli
,
M. S.
Vitiello
,
D.
Coquillat
,
A.
Lombardo
,
A. C.
Ferrari
,
W.
Knap
,
M.
Polini
,
V.
Pellegrini
, and
A.
Tredicucci
, “
Graphene field-effect transistors as room-temperature terahertz detectors
,”
Nat. Mater.
11
,
865
871
(
2012
).
13.
A.
Tomadin
,
A.
Tredicucci
,
V.
Pellegrini
,
M. S.
Vitiello
, and
M.
Polini
, “
Photocurrent-based detection of terahertz radiation in graphene
,”
Appl. Phys. Lett.
103
,
211120
(
2013
).
14.
S.
Castilla
,
B.
Terrés
,
M.
Autore
,
L.
Viti
,
J.
Li
,
A. Y.
Nikitin
,
I.
Vangelidis
,
K.
Watanabe
,
T.
Taniguchi
,
E.
Lidorikis
,
M. S.
Vitiello
,
R.
Hillenbrand
,
K.-J.
Tielrooij
, and
F. H.
Koppens
, “
Fast and sensitive terahertz detection using an antenna-integrated graphene pn junction
,”
Nano Lett.
19
,
2765
2773
(
2019
).
15.
E.
Riccardi
,
S.
Massabeau
,
F.
Valmorra
,
S.
Messelot
,
M.
Rosticher
,
J.
Tignon
,
K.
Watanabe
,
T.
Taniguchi
,
M.
Delbecq
,
S.
Dhillon
,
R.
Ferreira
,
S.
Balibar
,
T.
Kontos
, and
J.
Mangeney
, “
Ultrasensitive photoresponse of graphene quantum dots in the Coulomb blockade regime to THz radiation
,”
Nano Lett.
20
,
5408
(
2020
).
16.
R.
Wang
,
L.
Xie
,
S.
Hameed
, and
Y.
Ying
, “
Mechanisms and applications of carbon nanotubes in terahertz devices: A review
,”
Carbon
132
,
42
58
(
2018
).
17.
J.-C.
Charlier
,
X.
Blase
, and
S.
Roche
, “
Electronic and transport properties of nanotubes
,”
Rev. Mod. Phys.
79
,
677
(
2007
).
18.
E. A.
Laird
,
F.
Kuemmeth
,
G. A.
Steele
,
K.
Grove-Rasmussen
,
J.
Nygård
,
K.
Flensberg
, and
L. P.
Kouwenhoven
, “
Quantum transport in carbon nanotubes
,”
Rev. Mod. Phys.
87
,
703
764
(
2015
).
19.
R. R.
Hartmann
,
A.
Saroka
, and
M. E.
Portnoi
, “
Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons
,”
J. Appl. Phys.
125
,
151607
(
2019
).
20.
G.
Buchs
,
D.
Bercioux
,
P.
Ruffieux
,
P.
Gröning
,
H.
Grabert
, and
O.
Gröning
, “
Electron scattering in intrananotube quantum dots
,”
Phys. Rev. Lett
102
,
245505
(
2009
).
21.
D.
Bercioux
,
G.
Buchs
,
H.
Grabert
, and
O.
Gröning
, “
Defect-induced multicomponent electron scattering in single-walled carbon nanotubes
,”
Phys. Rev. B
83
,
165439
(
2011
).
22.
G.
Buchs
,
D.
Bercioux
,
L.
Mayrhofer
, and
O.
Gröning
, “
Confined electron and hole states in semiconducting carbon nanotube sub-10 nm artificial quantum dots
,”
Carbon
132
,
304
311
(
2018
).
23.
H. W. C.
Postma
,
T.
Teepen
,
Z.
Yao
,
M.
Grifoni
, and
C.
Dekker
, “
Carbon nanotube single-electron transistors at room temperature
,”
Science
293
,
76
(
2001
).
24.
T.
Fuse
,
Y.
Kawano
,
T.
Yamaguchi
,
Y.
Aoyagi
, and
K.
Ishibashi
, “
Quantum response of carbon nanotube quantum dots to terahertz wave irradiation
,”
Nanotechnology
18
,
044001
(
2006
).
25.
Y.
Kawano
,
T.
Fuse
,
S.
Toyokawa
,
T.
Uchida
, and
K.
Ishibashi
, “
Terahertz photon-assisted tunneling in carbon nanotube quantum dots
,”
J. Appl. Phys.
103
,
034307
(
2008
).
26.
M.
Rinzan
,
G.
Jenkins
,
H. D.
Drew
,
S.
Shafranjuk
, and
P.
Barbara
, “
Carbon nanotube quantum dots as highly sensitive terahertz-cooled spectrometers
,”
Nano Lett.
12
,
3097
3100
(
2012
).
27.
T.
Tsurugaya
,
K.
Yoshida
,
F.
Yajima
,
M.
Shimizu
,
Y.
Homma
, and
K.
Hirakawa
, “
Terahertz spectroscopy of individual carbon nanotube quantum dots
,”
Nano Lett.
19
,
242
246
(
2019
).
28.
Y.
Zhang
,
K.
Shibata
,
N.
Nagai
,
C.
Ndebeka-Bandou
,
G.
Bastard
, and
K.
Hirakawa
, “
Terahertz intersublevel transitions in single self-assembled InAs quantum dots with variable electron numbers
,”
Nano Lett.
15
,
1166
1170
(
2015
).
29.
A.
Ayuela
,
W.
Jaskólski
,
M.
Pelc
,
H.
Santos
, and
L.
Chico
, “
Friedel-like oscillations in carbon nanotube quantum dots
,”
Appl. Phys. Lett.
93
,
133106
(
2008
).
30.
A.
Ayuela
,
L.
Chico
, and
W.
Jaskólski
, “
Electronic band structure of carbon nanotube superlattices from first-principles calculations
,”
Phys. Rev. B
77
,
085435
(
2008
).
31.
In reality, the energy dispersion of a metallic SWNT marginally departs from linear,20 leading to a slightly broadened set of energy transitions.
32.
R.
Saito
,
G.
Dresselhaus
, and, and
M. S.
Dresselhaus
,
Physical Properties of Carbon Nanotubes
(
Imperial College Press
,
London, UK
,
2003
).
33.
A. M.
Lunde
,
K.
Flensberg
, and
A.-P.
Jauho
, “
Intershell resistance in multiwall carbon nanotubes: A Coulomb drag study
,”
Phys. Rev. B
71
,
125408
(
2005
).
34.
M.
Marganska
,
P.
Chudzinski
, and
M.
Grifoni
, “
The two classes of low-energy spectra in finite carbon nanotubes
,”
Phys. Rev. B
92
,
075433
(
2015
).
35.
W.
Izumida
,
R.
Okuyama
, and
R.
Saito
, “
Valley coupling in finite-length metallic single-wall carbon nanotubes
,”
Phys. Rev. B
91
,
235442
(
2015
).
36.
The spin-orbit coupling in nanotubes results in energy splitting of 1 meV; thus, it can be neglected at the energy scales discussed here.
37.
The eigenstates of a finite CNT must be standing waves only in the direction parallel to the axis. They may remain traveling waves in the transverse direction. In zigzag class CNTs, they are formed by the left- and right-moving states from the same valley.
38.
C. T.
White
,
D. H.
Robertson
, and
J. W.
Mintmire
, “
Helical and rotational symmetries of nanoscale graphitic tubules
,”
Phys. Rev. B
47
,
5485
5488
(
1993
).
39.
M.
Damnjanović
,
I.
Milošević
,
T.
Vuković
, and
R.
Sredanović
, “
Full symmetry, optical activity, and potentials of single-wall and multiwall nanotubes
,”
Phys. Rev. B
60
,
2728
2739
(
1999
).
40.
E. B.
Barros
,
A.
Jorio
,
G. G.
Samsonidze
,
R. B.
Capaz
,
A. G. S.
Filho
,
J. M.
Filho
,
G.
Dresselhaus
, and
M. S.
Dresselhaus
, “
Review on the symmetry-related properties of carbon nanotubes
,”
Phys. Rep.
431
,
261
(
2006
).
41.
S.
Reich
,
C.
Thomsen
, and
J.
Maultzsch
,
Carbon Nanotubes
(
Wiley-VCH Verlag
,
Weinheim, Germany
,
2004
).
42.
The photons with polarization transverse to the SWNT axis can induce only intersubband transitions, occurring at much higher energies.
43.
T.
Ando
, “
Spin-orbit interaction in carbon nanotubes
,”
J. Phys. Soc. Jpn.
69
,
1757
1763
(
2000
).
44.
S.
Ryu
and
Y.
Hatsugai
, “
Correlation effects of carbon nanotubes at boundaries: Spin polarization induced by zero-energy boundary states
,”
Phys. Rev. B
67
,
165410
(
2003
).
45.
K.
Sasaki
,
K.
Sato
,
R.
Saito
,
J.
Jiang
,
S.
Onari
, and
Y.
Tanaka
, “
Local density of states at zigzag edges of carbon nanotubes and graphene
,”
Phys. Rev. B
75
,
235430
(
2007
).
46.
A.
Mañanes
,
F.
Duque
,
A.
Ayuela
,
M. J.
López
, and
J. A.
Alonso
, “
Half-metallic finite zigzag single-walled carbon nanotubes from first principles
,”
Phys. Rev. B
78
,
035432
(
2008
).
47.
W.
Izumida
,
R.
Okuyama
,
A.
Yamakage
, and
R.
Saito
, “
Angular momentum and topology in semiconducting single-wall carbon nanotubes
,”
Phys. Rev. B
93
,
195442
(
2016
).
48.
G.
Buchs
, “
Local modification and characterization of the electronic structure of carbon nanotubes
,” Ph.D. thesis (
University of Basel
,
2008
).
49.
A.
Tolvanen
,
G.
Buchs
,
P.
Ruffieux
,
P.
Gröning
,
O.
Gröning
, and
A. V.
Krasheninnikov
, “
Modifying the electronic structure of semiconducting single-walled carbon nanotubes by Ar+ ion irradiation
,”
Phys. Rev. B
79
,
125430
(
2009
).
50.
J.
Tersoff
and
D. R.
Hamann
, “
Theory of the scanning tunneling microscope
,”
Phys. Rev. B
31
,
805
813
(
1985
).
51.
Technical: For a better contrast of the patterns at low frequencies, the 0-frequency component (DC) is suppressed for all bias voltages. This is obtained by subtracting the average value of each d I / d V ( x , V j ) line, for V j = [ 0.5 , 0.6 ] V.
52.
S.
Clair
,
Y.
Kim
, and
M.
Kawai
, “
Energy level alignment of single-wall carbon nanotubes on metal surfaces
,”
Phys. Rev. B
83
,
245422
(
2011
).
53.
S.
Datta
,
Electronic Transport in Mesoscopic Systems
(
Cambridge University Press
,
Cambridge, UK
,
1997
).
54.
S.
Datta
,
Quantum Transport: Atom to Transistor
(
Cambridge University Press
,
Cambridge, UK
,
2005
).
55.
S.
Reich
,
J.
Maultzsch
,
C.
Thomsen
, and
P.
Ordejón
, “
Tight-binding description of graphene
,”
Phys. Rev. B
66
,
035412
(
2002
).
56.
M.
del Valle
,
M.
Margańska
, and
M.
Grifoni
, “
Signatures of spin-orbit interaction in transport properties of finite carbon nanotubes in a parallel magnetic field
,”
Phys. Rev. B
84
,
165427
(
2011
).
57.
P. O.
Lehtinen
,
A. S.
Foster
,
A.
Ayuela
,
T. T.
Vehviläinen
, and
R. M.
Nieminen
, “
Structure and magnetic properties of adatoms on carbon nanotubes
,”
Phys. Rev. B
69
,
155422
(
2004
).
58.
A.
Krasheninnikov
,
K.
Nordlund
,
P.
Lehtinen
,
A.
Foster
,
A.
Ayuela
, and
R.
Nieminen
, “
Adsorption and migration of carbon adatoms on zigzag carbon nanotubes
,”
Carbon
42
,
1021
1025
(
2004
).
59.
J. W.
González
,
L.
Rosales
,
M.
Pacheco
, and
A.
Ayuela
, “
Electron confinement induced by diluted hydrogen-like ad-atoms in graphene ribbons
,”
Phys. Chem. Chem. Phys.
17
,
24707
24715
(
2015
).
60.
V. M.
Pereira
,
F.
Guinea
,
J. M. B. L.
dos Santos
,
N. M. R.
Peres
, and
A. H. C.
Neto
, “
Disorder induced localized states in graphene
,”
Phys. Rev. Lett.
96
,
036801
(
2006
).
61.
T. O.
Wehling
,
S.
Yuan
,
A. I.
Lichtenstein
,
A. K.
Geim
, and
M. I.
Katsnelson
, “
Resonant scattering by realistic impurities in graphene
,”
Phys. Rev. Lett.
105
,
056802
(
2010
).
62.
C.
Sanderson
and
R.
Curtin
, “
Armadillo: A template-based C + + library for linear algebra
,”
J. Open Source Software
1
,
26
(
2016
).
63.
T.
Zhou
,
J.
Wu
,
W.
Duan
, and
B.-L.
Gu
, “
Physical mechanism of transport blocking in metallic zigzag carbon nanotubes
,”
Phys. Rev. B
75
,
205410
(
2007
).
64.
In the GF method, in order to get a smooth LDOS on the surface of the carbon nanotube and account for the finite size of the STM tip, we have performed a convolution of the LDOS with a function of the form exp ( λ r ), where r is the distance of a fictitious tip of a STM from the carbon atom at x, and λ is an opportune constant.120
65.
S.
Sapmaz
,
P.
Jarillo-Herrero
,
J.
Kong
,
C.
Dekker
,
L. P.
Kouwenhoven
, and
H. S. J.
van der Zant
, “
Electronic excitation spectrum of metallic carbon nanotubes
,”
Phys. Rev. B
71
,
153402
(
2005
).
66.
A.
Grüneis
,
R.
Saito
,
G. G.
Samsonidze
,
T.
Kimura
,
M. A.
Pimenta
,
A.
Jorio
,
A. G. S.
Filho
,
G.
Dresselhaus
, and
M. S.
Dresselhaus
, “
Inhomogeneous optical absorption around the K point in graphite and carbon nanotubes
,”
Phys. Rev. B
67
,
165402
(
2003
).
67.
E.
Malić
,
M.
Hirtschulz
,
F.
Milde
,
A.
Knorr
, and
S.
Reich
, “
Analytical approach to optical absorption in carbon nanotubes
,”
Phys. Rev. B
74
,
195431
(
2006
).
68.
D. R.
Schmid
,
S.
Smirnov
,
M.
Margańska
,
A.
Dirnaichner
,
P. L.
Stiller
,
M.
Grifoni
,
A. K.
Hüttel
, and
C.
Strunk
, “
Broken SU(4) symmetry in a Kondo-correlated carbon nanotube
,”
Phys. Rev. B
91
,
155435
(
2015
).
69.
A.
Dirnaichner
,
M.
del Valle
,
K. J. G.
Götz
,
F. J.
Schupp
,
N.
Paradiso
,
M.
Grifoni
,
C.
Strunk
, and
A. K.
Hüttel
, “
Secondary electron interference from trigonal warping in clean carbon nanotubes
,”
Phys. Rev. Lett.
117
,
166804
(
2016
).
70.
G.
Grosso
and
G.
Parravicini
,
Solid State Physics
(
Academic Press
,
Cambridge, MA
,
2000
).
71.
S. K. H.
Haug
,
Quantum Theory of the Optical and Electronic Properties of Semiconductors
(
World Scientific
,
Singapore
,
2004
).
72.
G.
Hills
,
C.
Lau
,
A.
Wright
,
S.
Fuller
,
M. D.
Bishop
,
T.
Srimani
,
P.
Kanhaiya
,
R.
Ho
,
A.
Amer
,
Y.
Stein
,
D.
Murphy
,
Arvind
,
A.
Chandrakasan
, and
M. M.
Shulaker
, “
Modern microprocessor built from complementary carbon nanotube transistors
,”
Nature
572
,
595
602
(
2019
).
73.
J. R.
Sanchez-Valencia
,
T.
Dienel
,
O.
Gröning
,
I.
Shorubalko
,
A.
Mueller
,
M.
Jansen
,
K.
Amsharov
,
P.
Ruffieux
, and
R.
Fasel
, “
Controlled synthesis of single-chirality carbon nanotubes
,”
Nature
512
,
61
64
(
2014
).
74.
F.
Yang
,
X.
Wang
,
D.
Zhang
,
K.
Qi
,
J.
Yang
,
Z.
Xu
,
M.
Li
,
X.
Zhao
,
X.
Bai
, and
Y.
Li
, “
Growing zigzag (16,0) carbon nanotubes with structure-defined catalysts
,”
J. Am. Chem. Soc.
137
,
8688
8691
(
2015
).
75.
Y.
Segawa
,
A.
Yagi
,
K.
Matsui
, and
K.
Itami
, “
Design and synthesis of carbon nanotube segments
,”
Angew. Chem. Int. Ed.
55
,
5136
5158
(
2016
).
76.
B.
Liu
,
F.
Wu
,
H.
Gui
,
M.
Zheng
, and
C.
Zhou
, “
Chirality-controlled synthesis and applications of single-wall carbon nanotubes
,”
ACS Nano
11
,
31
53
(
2017
).
77.
S.
Zhang
,
L.
Kang
,
X.
Wang
,
L.
Tong
,
L.
Yang
,
Z.
Wang
,
K.
Qi
,
S.
Deng
,
Q.
Li
,
X.
Bai
,
F.
Ding
, and
J.
Zhang
, “
Arrays of horizontal carbon nanotubes of controlled chirality grown using designed catalysts
,”
Nature
543
,
234
238
(
2017
).
78.
D.
Janas
, “
Towards monochiral carbon nanotubes: A review of progress in the sorting of single-walled carbon nanotubes
,”
Mater. Chem. Front.
2
,
36
63
(
2018
).
79.
Q.
Gao
,
J.
Chen
,
B.
Lyu
,
A.
Deng
,
L.
Wang
,
T.
Wu
,
K.
Watanabe
,
T.
Taniguchi
, and
Z.
Shi
, “
Detection of chirality of single-walled carbon nanotubes on hexagonal boron nitride
,”
Appl. Phys. Lett.
117
,
023101
(
2020
).
80.
Certificate of Analysis. MilliporeSigma, Merck's Group (
2015
).
81.
Technical Data Sheet. NanoIntegris Technologies, Inc. (
2021
).
82.
K.
Yoshida
,
K.
Shibata
, and
K.
Hirakawa
, “
Terahertz field enhancement and photon-assisted tunneling in single-molecule transistors
,”
Phys. Rev. Lett.
115
,
138302
(
2015
).
83.
N.
Nemec
,
D.
Tománek
, and
G.
Cuniberti
, “
Contact dependence of carrier injection in carbon nanotubes: An ab initio study
,”
Phys. Rev. Lett.
96
,
076802
(
2006
).
84.
Q.
Cao
,
S.-J.
Han
,
J.
Tersoff
,
A. D.
Franklin
,
Y.
Zhu
,
Z.
Zhang
,
G. S.
Tulevski
,
J.
Tang
, and
W.
Haensch
, “
End-bonded contacts for carbon nanotube transistors with low, size-independent resistance
,”
Science
350
,
68
72
(
2015
).
85.
Q.
Cao
,
J.
Tersoff
,
D. B.
Farmer
,
Y.
Zhu
, and
S.-J.
Han
, “
Carbon nanotube transistors scaled to a 40-nanometer footprint
,”
Science
356
,
1369
1372
(
2017
).
86.
4GHz Ultra-Low Bias Current FET Input Op Amp, Linear Technology (
2015
).
87.
500MHz Ultra-Low Bias Current FET Input Op Amp, Linear Technology (
2015
).
88.
C.
Krause
,
D.
Drung
, and
H.
Scherer
, “
Measurement of sub-picoampere direct currents with uncertainties below ten attoamperes
,”
Rev. Sci. Instrum.
88
,
024711
(
2017
).
89.
Ultra-Low-Noise Current Amplifier, FEMTO (
2019
).
90.
R. R.
Clappier
and
R. J.
Kline-Schoder
, “
Precision temperature control of stirling-cycle cryocoolers
,” in
Advances in Cryogenic Engineering
, edited by
P.
Kittel
(
Springer US
,
Boston, MA
,
1994
) pp.
1177
1184
.
91.
Miniature Stirling Cryo-coolers. Air Liquide S.A. (
2021
), https://advancedtech.airliquide.com/miniature-stirling-cryo-coolers.
92.
A.
Tolvanen
,
J.
Kotakoski
,
A. V.
Krasheninnikov
, and
K.
Nordlund
, “
Relative abundance of single and double vacancies in irradiated single-walled carbon nanotubes
,”
Appl. Phys. Lett.
91
,
173109
(
2007
).
93.
A. W.
Robertson
,
C. S.
Allen
,
Y. A.
Wu
,
K.
He
,
J.
Olivier
,
J.
Neethling
,
A. I.
Kirkland
, and
J. H.
Warner
, “
Spatial control of defect creation in graphene at the nanoscale
,”
Nat. Commun.
3
,
1144
(
2012
).
94.
We note in passing that the defect types and their positions on the lattice could be determined from the absorption spectrum in combination with first-principle simulations,49 especially for the case of achiral metallic SWNTs (zigzag and/or armchair) with computationally tractable small unit cells.
95.
A. V.
Krasheninnikov
,
P. O.
Lehtinen
,
A. S.
Foster
, and
R. M.
Nieminen
, “
Bending the rules: Contrasting vacancy energetics and migration in graphite and carbon nanotubes
,”
Chem. Phys. Lett.
418
,
132
136
(
2006
).
96.
L.
Mayrhofer
, private communication.
97.
G.
Gómez-Navarro
,
P. J.
De Pablo
,
J.
Gómez-Herrero
,
B.
Biel
,
F. J.
Garcia-Vidal
,
A.
Rubio
, and
F.
Flores
, “
Tuning the conductance of single-walled carbon nanotubes by ion irradiation in the Anderson localization regime
,”
Nat. Mater.
4
,
534
(
2005
).
98.
M.
Bockrath
,
W.
Liang
,
D.
Bozovic
,
J. H.
Hafner
,
C. M.
Lieber
,
M.
Tinkham
, and
H.
Park
, “
Resonant electron scattering by defects in single-walled carbon nanotubes
,”
Science
291
,
283
285
(
2001
).
99.
S.
He
,
R.
Tian
,
W.
Wu
,
W.-D.
Li
, and
D.
Wang
, “
Helium-ion-beam nanofabrication: Extreme processes and applications
,”
Int. J. Extreme Manuf.
3
,
012001
(
2021
).
100.
J.
Buchheim
,
R. M.
Wyss
,
I.
Shorubalko
, and
H. G.
Park
, “
Understanding the interaction between energetic ions and freestanding graphene towards practical 2D perforation
,”
Nanoscale
8
,
8345
8354
(
2016
).
101.
E.
Mitterreiter
,
B.
Schuler
,
K. A.
Cochrane
,
U.
Wurstbauer
,
A.
Weber-Bargioni
,
C.
Kastl
, and
A. W.
Holleitner
, “
Atomistic positioning of defects in helium ion treated single-layer MoS2
,”
Nano Lett.
20
,
4437
4444
(
2020
).
102.
N.
Fang
,
K.
Otsuka
,
A.
Ishii
,
T.
Taniguchi
,
K.
Watanabe
,
K.
Nagashio
, and
Y. K.
Kato
, “
Hexagonal boron nitride as an ideal substrate for carbon nanotube photonics
,”
ACS Photonics
7
,
1773
1779
(
2020
).
103.
J. C.
Noé
,
M.
Nutz
,
J.
Reschauer
,
N.
Morell
,
I.
Tsioutsios
,
A.
Reserbat-Plantey
,
K.
Watanabe
,
T.
Taniguchi
,
A.
Bachtold
, and
A.
Högele
, “
Environmental electrometry with luminescent carbon nanotubes
,”
Nano Lett.
18
,
4136
4140
(
2018
).
104.
D.
Unuchek
,
A.
Ciarrocchi
,
A.
Avsar
,
K.
Watanabe
,
T.
Taniguchi
, and
A.
Kis
, “
Room-temperature electrical control of exciton flux in a van der Waals heterostructure
,”
Nature
560
,
340
344
(
2018
).
105.
G.
Buchs
,
M.
Barkelid
,
S.
Bagiante
,
G. A.
Steele
, and
V.
Zwiller
, “
Imaging the formation of a p-n junction in a suspended carbon nanotube with scanning photocurrent microscopy
,”
J. Appl. Phys.
110
,
074308
(
2011
).
106.
G.
Buchs
,
S.
Bagiante
, and
G. A.
Steele
, “
Identifying signatures of photothermal current in a double-gated semiconducting nanotube
,”
Nat. Commun.
5
,
4987
(
2014
).
107.
M. C.
Schaafsma
,
H.
Starmans
,
A.
Berrier
, and
J. G.
Rivas
, “
Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides
,”
New J. Phys.
15
,
015006
(
2013
).
108.
Z.
Shi
,
X.
Hong
,
H. A.
Bechtel
,
B.
Zeng
,
M. C.
Martin
,
K.
Watanabe
,
T.
Taniguchi
,
Y.-R.
Shen
, and
F.
Wang
, “
Observation of a Luttinger-liquid plasmon in metallic single-walled carbon nanotubes
,”
Nat. Photonics
9
,
515
519
(
2015
).
109.
T.
Morimoto
,
S.-K.
Joung
,
T.
Saito
,
D. N.
Futaba
,
K.
Hata
, and
T.
Okazaki
, “
Length-dependent plasmon resonance in single-walled carbon nanotubes
,”
ACS Nano
8
,
9897
9904
(
2014
).
110.
I. W.
Chiang
,
B. E.
Brinson
,
A. Y.
Huang
,
P. A.
Willis
,
M. J.
Bronikowski
,
J. L.
Margrave
,
R. E.
Smalley
, and
R. H.
Hauge
, “
Purification and characterization of single-wall carbon nanotubes (SWNTs) obtained from the gas-phase decomposition of CO (HiPco process
),”
J. Phys. Chem. B
105
,
8297
8301
(
2001
).
111.
G.
Buchs
,
P.
Ruffieux
,
P.
Gröning
, and
O.
Gröning
, “
Scanning tunneling microscopy investigations of hydrogen plasma induced electron scattering centers on single-walled carbon nanotubes
,”
Appl. Phys. Lett.
90
,
013104
(
2007
).
112.
This is proportional, in first approximation, to the local density of states (LDOS), cf. Ref. 50.
113.
I.
Horcas
,
R.
Fernández
,
J. M.
Gómez-Rodríguez
,
J.
Colchero
,
J.
Gómez-Herrero
, and
A. M.
Baro
, “
WSXM: A software for scanning probe microscopy and a tool for nanotechnology
,”
Rev. Sci. Instrum.
78
,
013705
(
2007
).
114.
J. W.
Janssen
,
S. G.
Lemay
,
L. P.
Kouwenhoven
, and
C.
Dekker
, “
Scanning tunneling spectroscopy on crossed carbon nanotubes
,”
Phys. Rev. B
65
,
115423
(
2002
).
115.
H. W. C.
Postma
,
A.
Sellmeijer
, and
C.
Dekker
, “
Manipulation and imaging of individual single-walled carbon nanotubes with an atomic force microscope
,”
Adv. Mat.
12
,
1299
1302
(
2000
).
116.
L. C.
Venema
,
V.
Meunier
,
P.
Lambin
, and
C.
Dekker
, “
Atomic structure of carbon nanotubes from scanning tunneling microscopy
,”
Phys. Rev. B
61
,
2991
2996
(
2000
).
117.
H.
Yorikawa
and
S.
Muramatsu
, “
Energy gaps of semiconducting nanotubules
,”
Phys. Rev. B
52
,
2723
2727
(
1995
).
118.
H.
Lin
,
J.
Lagoute
,
V.
Repain
,
C.
Chacon
,
Y.
Girard
,
J.-S.
Lauret
,
F.
Ducastelle
,
A.
Loiseau
, and
S.
Rousset
, “
Many-body effects in electronic bandgaps of carbon nanotubes measured by scanning tunnelling spectroscopy
,”
Nat. Mater.
9
,
235
(
2010
).
119.
L.
Tapasztó
,
G. I.
Márk
,
A. A.
Koós
,
P.
Lambin
, and
L. P.
Biró
, “
Apparent diameter of carbon nanotubes in scanning tunnelling microscopy measurements
,”
J. Phys.: Condens. Matter
18
,
5793
(
2006
).
120.
L.
Mayrhofer
and
D.
Bercioux
, “
Pseudo-spin-dependent scattering in carbon nanotubes
,”
Phys. Rev. B
84
,
115126
(
2011
).
121.
J.
Hutter
,
M.
Iannuzzi
,
F.
Schiffmann
, and
J.
VandeVondele
, “
cp2k: Atomistic simulations of condensed matter systems
,”
Wiley Interdisciplinary Rev.: Comput. Mol. Sci.
4
,
15
25
(
2014
).
122.
J.
VandeVondele
and
J.
Hutter
, “
Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases
,”
J. Chem. Phys.
127
,
114105
(
2007
).
123.
S.
Goedecker
,
M.
Teter
, and
J.
Hutter
, “
Separable dual-space gaussian pseudopotentials
,”
Phys. Rev. B
54
,
1703
1710
(
1996
).
124.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
, “
Generalized gradient approximation made simple
,”
Phys. Rev. Lett.
77
,
3865
3868
(
1996
).
125.
R.
Gaspari
,
S.
Blankenburg
,
C. A.
Pignedoli
,
P.
Ruffieux
,
M.
Treier
,
R.
Fasel
, and
D.
Passerone
, “
S-orbital continuum model accounting for the tip shape in simulated scanning tunneling microscope images
,”
Phys. Rev. B
84
,
125417
(
2011
).
126.
E. N.
Economou
,
Green's Functions in Quantum Physics
(
Springer
,
Berlin/Heidelberg, Germany
,
1984
).
127.
D.
Tománek
and
S. G.
Louie
, “
First-principles calculation of highly asymmetric structure in scanning-tunneling-microscopy images of graphite
,”
Phys. Rev. B
37
,
8327
8336
(
1988
).
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