---
_id: '40523'
abstract:
- lang: eng
text: AbstractTailored nanoscale quantum light
sources, matching the specific needs of use cases, are crucial building blocks
for photonic quantum technologies. Several different approaches to realize solid-state
quantum emitters with high performance have been pursued and different concepts
for energy tuning have been established. However, the properties of the emitted
photons are always defined by the individual quantum emitter and can therefore
not be controlled with full flexibility. Here we introduce an all-optical nonlinear
method to tailor and control the single photon emission. We demonstrate a laser-controlled
down-conversion process from an excited state of a semiconductor quantum three-level
system. Based on this concept, we realize energy tuning and polarization control
of the single photon emission with a control-laser field. Our results mark an
important step towards tailored single photon emission from a photonic quantum
system based on quantum optical principles.
article_number: '1387'
author:
- first_name: B.
full_name: Jonas, B.
last_name: Jonas
- first_name: Dirk Florian
full_name: Heinze, Dirk Florian
id: '10904'
last_name: Heinze
- first_name: E.
full_name: Schöll, E.
last_name: Schöll
- first_name: P.
full_name: Kallert, P.
last_name: Kallert
- first_name: T.
full_name: Langer, T.
last_name: Langer
- first_name: S.
full_name: Krehs, S.
last_name: Krehs
- first_name: A.
full_name: Widhalm, A.
last_name: Widhalm
- first_name: Klaus
full_name: Jöns, Klaus
id: '85353'
last_name: Jöns
- first_name: Dirk
full_name: Reuter, Dirk
id: '37763'
last_name: Reuter
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
- first_name: Artur
full_name: Zrenner, Artur
id: '606'
last_name: Zrenner
orcid: 0000-0002-5190-0944
citation:
ama: Jonas B, Heinze DF, Schöll E, et al. Nonlinear down-conversion in a single
quantum dot. Nature Communications. 2022;13(1). doi:10.1038/s41467-022-28993-3
apa: Jonas, B., Heinze, D. F., Schöll, E., Kallert, P., Langer, T., Krehs, S., Widhalm,
A., Jöns, K., Reuter, D., Schumacher, S., & Zrenner, A. (2022). Nonlinear
down-conversion in a single quantum dot. Nature Communications, 13(1),
Article 1387. https://doi.org/10.1038/s41467-022-28993-3
bibtex: '@article{Jonas_Heinze_Schöll_Kallert_Langer_Krehs_Widhalm_Jöns_Reuter_Schumacher_et
al._2022, title={Nonlinear down-conversion in a single quantum dot}, volume={13},
DOI={10.1038/s41467-022-28993-3},
number={11387}, journal={Nature Communications}, publisher={Springer Science and
Business Media LLC}, author={Jonas, B. and Heinze, Dirk Florian and Schöll, E.
and Kallert, P. and Langer, T. and Krehs, S. and Widhalm, A. and Jöns, Klaus and
Reuter, Dirk and Schumacher, Stefan and et al.}, year={2022} }'
chicago: Jonas, B., Dirk Florian Heinze, E. Schöll, P. Kallert, T. Langer, S. Krehs,
A. Widhalm, et al. “Nonlinear Down-Conversion in a Single Quantum Dot.” Nature
Communications 13, no. 1 (2022). https://doi.org/10.1038/s41467-022-28993-3.
ieee: 'B. Jonas et al., “Nonlinear down-conversion in a single quantum dot,”
Nature Communications, vol. 13, no. 1, Art. no. 1387, 2022, doi: 10.1038/s41467-022-28993-3.'
mla: Jonas, B., et al. “Nonlinear Down-Conversion in a Single Quantum Dot.” Nature
Communications, vol. 13, no. 1, 1387, Springer Science and Business Media
LLC, 2022, doi:10.1038/s41467-022-28993-3.
short: B. Jonas, D.F. Heinze, E. Schöll, P. Kallert, T. Langer, S. Krehs, A. Widhalm,
K. Jöns, D. Reuter, S. Schumacher, A. Zrenner, Nature Communications 13 (2022).
date_created: 2023-01-27T13:41:42Z
date_updated: 2023-04-20T15:18:31Z
department:
- _id: '15'
- _id: '297'
- _id: '230'
- _id: '429'
- _id: '27'
- _id: '623'
- _id: '170'
- _id: '35'
doi: 10.1038/s41467-022-28993-3
intvolume: ' 13'
issue: '1'
keyword:
- General Physics and Astronomy
- General Biochemistry
- Genetics and Molecular Biology
- General Chemistry
- Multidisciplinary
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: TRR 142'
- _id: '54'
name: 'TRR 142 - A: TRR 142 - Project Area A'
- _id: '60'
name: 'TRR 142 - A03: TRR 142 - Subproject A03'
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Nature Communications
publication_identifier:
issn:
- 2041-1723
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Nonlinear down-conversion in a single quantum dot
type: journal_article
user_id: '16199'
volume: 13
year: '2022'
...
---
_id: '40428'
author:
- first_name: Björn
full_name: Jonas, Björn
last_name: Jonas
- first_name: Dirk Florian
full_name: Heinze, Dirk Florian
id: '10904'
last_name: Heinze
- first_name: Eva
full_name: Schöll, Eva
last_name: Schöll
- first_name: Patricia
full_name: Kallert, Patricia
last_name: Kallert
- first_name: Timo
full_name: Langer, Timo
last_name: Langer
- first_name: Sebastian
full_name: Krehs, Sebastian
last_name: Krehs
- first_name: Alex
full_name: Widhalm, Alex
last_name: Widhalm
- first_name: Klaus
full_name: Jöns, Klaus
id: '85353'
last_name: Jöns
- first_name: Dirk
full_name: Reuter, Dirk
id: '37763'
last_name: Reuter
- first_name: Artur
full_name: Zrenner, Artur
id: '606'
last_name: Zrenner
orcid: 0000-0002-5190-0944
citation:
ama: Jonas B, Heinze DF, Schöll E, et al. Nonlinear Down-Conversion in a Single
Quantum Dot. LibreCat University; 2022. doi:10.5281/ZENODO.6024228
apa: Jonas, B., Heinze, D. F., Schöll, E., Kallert, P., Langer, T., Krehs, S., Widhalm,
A., Jöns, K., Reuter, D., & Zrenner, A. (2022). Nonlinear down-conversion
in a single quantum dot. LibreCat University. https://doi.org/10.5281/ZENODO.6024228
bibtex: '@book{Jonas_Heinze_Schöll_Kallert_Langer_Krehs_Widhalm_Jöns_Reuter_Zrenner_2022,
title={Nonlinear down-conversion in a single quantum dot}, DOI={10.5281/ZENODO.6024228},
publisher={LibreCat University}, author={Jonas, Björn and Heinze, Dirk Florian
and Schöll, Eva and Kallert, Patricia and Langer, Timo and Krehs, Sebastian and
Widhalm, Alex and Jöns, Klaus and Reuter, Dirk and Zrenner, Artur}, year={2022}
}'
chicago: Jonas, Björn, Dirk Florian Heinze, Eva Schöll, Patricia Kallert, Timo Langer,
Sebastian Krehs, Alex Widhalm, Klaus Jöns, Dirk Reuter, and Artur Zrenner. Nonlinear
Down-Conversion in a Single Quantum Dot. LibreCat University, 2022. https://doi.org/10.5281/ZENODO.6024228.
ieee: B. Jonas et al., Nonlinear down-conversion in a single quantum dot.
LibreCat University, 2022.
mla: Jonas, Björn, et al. Nonlinear Down-Conversion in a Single Quantum Dot.
LibreCat University, 2022, doi:10.5281/ZENODO.6024228.
short: B. Jonas, D.F. Heinze, E. Schöll, P. Kallert, T. Langer, S. Krehs, A. Widhalm,
K. Jöns, D. Reuter, A. Zrenner, Nonlinear Down-Conversion in a Single Quantum
Dot, LibreCat University, 2022.
date_created: 2023-01-26T15:38:28Z
date_updated: 2023-04-20T15:18:48Z
department:
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '290'
- _id: '292'
- _id: '642'
- _id: '230'
- _id: '429'
- _id: '35'
doi: 10.5281/ZENODO.6024228
project:
- _id: '53'
name: 'TRR 142: TRR 142'
- _id: '54'
name: 'TRR 142 - A: TRR 142 - Project Area A'
- _id: '60'
name: 'TRR 142 - A3: TRR 142 - Subproject A3'
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publisher: LibreCat University
status: public
title: Nonlinear down-conversion in a single quantum dot
type: research_data
user_id: '16199'
year: '2022'
...
---
_id: '23816'
abstract:
- lang: eng
text: Employing the ultrafast control of electronic states of a semiconductor quantum
dot in a cavity, we introduce an approach to achieve on-demand emission of single
photons with almost perfect indistinguishability and photon pairs with near ideal
entanglement. Our scheme is based on optical excitation off resonant to a cavity
mode followed by ultrafast control of the electronic states using the time-dependent
quantum-confined Stark effect, which then allows for cavity-resonant emission.
Our theoretical analysis considers cavity-loss mechanisms, the Stark effect, and
phonon-induced dephasing, allowing realistic predictions for finite temperatures.
author:
- first_name: David
full_name: Bauch, David
last_name: Bauch
- first_name: Dirk Florian
full_name: Heinze, Dirk Florian
id: '10904'
last_name: Heinze
- first_name: Jens
full_name: Förstner, Jens
id: '158'
last_name: Förstner
orcid: 0000-0001-7059-9862
- first_name: Klaus
full_name: Jöns, Klaus
id: '85353'
last_name: Jöns
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
citation:
ama: Bauch D, Heinze DF, Förstner J, Jöns K, Schumacher S. Ultrafast electric control
of cavity mediated single-photon and photon-pair generation with semiconductor
quantum dots. Physical Review B. 2021;104:085308. doi:10.1103/physrevb.104.085308
apa: Bauch, D., Heinze, D. F., Förstner, J., Jöns, K., & Schumacher, S. (2021).
Ultrafast electric control of cavity mediated single-photon and photon-pair generation
with semiconductor quantum dots. Physical Review B, 104, 085308.
https://doi.org/10.1103/physrevb.104.085308
bibtex: '@article{Bauch_Heinze_Förstner_Jöns_Schumacher_2021, title={Ultrafast electric
control of cavity mediated single-photon and photon-pair generation with semiconductor
quantum dots}, volume={104}, DOI={10.1103/physrevb.104.085308},
journal={Physical Review B}, author={Bauch, David and Heinze, Dirk Florian and
Förstner, Jens and Jöns, Klaus and Schumacher, Stefan}, year={2021}, pages={085308}
}'
chicago: 'Bauch, David, Dirk Florian Heinze, Jens Förstner, Klaus Jöns, and Stefan
Schumacher. “Ultrafast Electric Control of Cavity Mediated Single-Photon and Photon-Pair
Generation with Semiconductor Quantum Dots.” Physical Review B 104 (2021):
085308. https://doi.org/10.1103/physrevb.104.085308.'
ieee: 'D. Bauch, D. F. Heinze, J. Förstner, K. Jöns, and S. Schumacher, “Ultrafast
electric control of cavity mediated single-photon and photon-pair generation with
semiconductor quantum dots,” Physical Review B, vol. 104, p. 085308, 2021,
doi: 10.1103/physrevb.104.085308.'
mla: Bauch, David, et al. “Ultrafast Electric Control of Cavity Mediated Single-Photon
and Photon-Pair Generation with Semiconductor Quantum Dots.” Physical Review
B, vol. 104, 2021, p. 085308, doi:10.1103/physrevb.104.085308.
short: D. Bauch, D.F. Heinze, J. Förstner, K. Jöns, S. Schumacher, Physical Review
B 104 (2021) 085308.
date_created: 2021-09-06T18:02:44Z
date_updated: 2023-04-20T15:33:52Z
ddc:
- '530'
department:
- _id: '61'
- _id: '230'
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '429'
- _id: '623'
- _id: '35'
doi: 10.1103/physrevb.104.085308
file:
- access_level: open_access
content_type: application/pdf
creator: fossie
date_created: 2021-09-07T06:32:25Z
date_updated: 2021-09-07T07:43:47Z
file_id: '23818'
file_name: 2021-08 Bauch PhysRevB.104.085308.pdf
file_size: 887439
relation: main_file
file_date_updated: 2021-09-07T07:43:47Z
has_accepted_license: '1'
intvolume: ' 104'
keyword:
- tet_topic_qd
language:
- iso: eng
oa: '1'
page: '085308'
project:
- _id: '53'
name: TRR 142
- _id: '54'
name: TRR 142 - Project Area A
- _id: '60'
name: TRR 142 - Subproject A3
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Physical Review B
publication_identifier:
issn:
- 2469-9950
- 2469-9969
publication_status: published
status: public
title: Ultrafast electric control of cavity mediated single-photon and photon-pair
generation with semiconductor quantum dots
type: journal_article
user_id: '16199'
volume: 104
year: '2021'
...
---
_id: '13351'
author:
- first_name: Dominik
full_name: Breddermann, Dominik
last_name: Breddermann
- first_name: Tom
full_name: Praschan, Tom
last_name: Praschan
- first_name: Dirk Florian
full_name: Heinze, Dirk Florian
id: '10904'
last_name: Heinze
- first_name: Rolf
full_name: Binder, Rolf
last_name: Binder
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
citation:
ama: Breddermann D, Praschan T, Heinze DF, Binder R, Schumacher S. Microscopic theory
of cavity-enhanced single-photon emission from optical two-photon Raman processes.
Physical Review B. 2018;97(12). doi:10.1103/physrevb.97.125303
apa: Breddermann, D., Praschan, T., Heinze, D. F., Binder, R., & Schumacher,
S. (2018). Microscopic theory of cavity-enhanced single-photon emission from optical
two-photon Raman processes. Physical Review B, 97(12). https://doi.org/10.1103/physrevb.97.125303
bibtex: '@article{Breddermann_Praschan_Heinze_Binder_Schumacher_2018, title={Microscopic
theory of cavity-enhanced single-photon emission from optical two-photon Raman
processes}, volume={97}, DOI={10.1103/physrevb.97.125303},
number={12}, journal={Physical Review B}, author={Breddermann, Dominik and Praschan,
Tom and Heinze, Dirk Florian and Binder, Rolf and Schumacher, Stefan}, year={2018}
}'
chicago: Breddermann, Dominik, Tom Praschan, Dirk Florian Heinze, Rolf Binder, and
Stefan Schumacher. “Microscopic Theory of Cavity-Enhanced Single-Photon Emission
from Optical Two-Photon Raman Processes.” Physical Review B 97, no. 12
(2018). https://doi.org/10.1103/physrevb.97.125303.
ieee: 'D. Breddermann, T. Praschan, D. F. Heinze, R. Binder, and S. Schumacher,
“Microscopic theory of cavity-enhanced single-photon emission from optical two-photon
Raman processes,” Physical Review B, vol. 97, no. 12, 2018, doi: 10.1103/physrevb.97.125303.'
mla: Breddermann, Dominik, et al. “Microscopic Theory of Cavity-Enhanced Single-Photon
Emission from Optical Two-Photon Raman Processes.” Physical Review B, vol.
97, no. 12, 2018, doi:10.1103/physrevb.97.125303.
short: D. Breddermann, T. Praschan, D.F. Heinze, R. Binder, S. Schumacher, Physical
Review B 97 (2018).
date_created: 2019-09-19T13:57:23Z
date_updated: 2025-12-05T14:34:12Z
department:
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '230'
- _id: '429'
- _id: '35'
- _id: '27'
doi: 10.1103/physrevb.97.125303
funded_apc: '1'
intvolume: ' 97'
issue: '12'
language:
- iso: eng
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '53'
name: 'TRR 142: TRR 142'
- _id: '54'
name: 'TRR 142 - A: TRR 142 - Project Area A'
- _id: '60'
name: 'TRR 142 - A03: TRR 142 - Subproject A03'
publication: Physical Review B
publication_identifier:
issn:
- 2469-9950
- 2469-9969
publication_status: published
status: public
title: Microscopic theory of cavity-enhanced single-photon emission from optical two-photon
Raman processes
type: journal_article
user_id: '16199'
volume: 97
year: '2018'
...
---
_id: '19210'
author:
- first_name: D.
full_name: Breddermann, D.
last_name: Breddermann
- first_name: Dirk Florian
full_name: Heinze, Dirk Florian
id: '10904'
last_name: Heinze
- first_name: R.
full_name: Binder, R.
last_name: Binder
- first_name: Artur
full_name: Zrenner, Artur
id: '606'
last_name: Zrenner
orcid: 0000-0002-5190-0944
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
citation:
ama: Breddermann D, Heinze DF, Binder R, Zrenner A, Schumacher S. All-optical tailoring
of single-photon spectra in a quantum-dot microcavity system. Physical Review
B. 2016. doi:10.1103/physrevb.94.165310
apa: Breddermann, D., Heinze, D. F., Binder, R., Zrenner, A., & Schumacher,
S. (2016). All-optical tailoring of single-photon spectra in a quantum-dot microcavity
system. Physical Review B. https://doi.org/10.1103/physrevb.94.165310
bibtex: '@article{Breddermann_Heinze_Binder_Zrenner_Schumacher_2016, title={All-optical
tailoring of single-photon spectra in a quantum-dot microcavity system}, DOI={10.1103/physrevb.94.165310},
journal={Physical Review B}, author={Breddermann, D. and Heinze, Dirk Florian
and Binder, R. and Zrenner, Artur and Schumacher, Stefan}, year={2016} }'
chicago: Breddermann, D., Dirk Florian Heinze, R. Binder, Artur Zrenner, and Stefan
Schumacher. “All-Optical Tailoring of Single-Photon Spectra in a Quantum-Dot Microcavity
System.” Physical Review B, 2016. https://doi.org/10.1103/physrevb.94.165310.
ieee: D. Breddermann, D. F. Heinze, R. Binder, A. Zrenner, and S. Schumacher, “All-optical
tailoring of single-photon spectra in a quantum-dot microcavity system,” Physical
Review B, 2016.
mla: Breddermann, D., et al. “All-Optical Tailoring of Single-Photon Spectra in
a Quantum-Dot Microcavity System.” Physical Review B, 2016, doi:10.1103/physrevb.94.165310.
short: D. Breddermann, D.F. Heinze, R. Binder, A. Zrenner, S. Schumacher, Physical
Review B (2016).
date_created: 2020-09-09T13:56:53Z
date_updated: 2022-01-06T06:54:00Z
doi: 10.1103/physrevb.94.165310
language:
- iso: eng
publication: Physical Review B
publication_identifier:
issn:
- 2469-9950
- 2469-9969
publication_status: published
status: public
title: All-optical tailoring of single-photon spectra in a quantum-dot microcavity
system
type: journal_article
user_id: '10904'
year: '2016'
...
---
_id: '19209'
author:
- first_name: Dirk Florian
full_name: Heinze, Dirk Florian
id: '10904'
last_name: Heinze
- first_name: Dominik
full_name: Breddermann, Dominik
last_name: Breddermann
- first_name: Artur
full_name: Zrenner, Artur
id: '606'
last_name: Zrenner
orcid: 0000-0002-5190-0944
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
citation:
ama: Heinze DF, Breddermann D, Zrenner A, Schumacher S. A quantum dot single-photon
source with on-the-fly all-optical polarization control and timed emission. Nature
Communications. 2015. doi:10.1038/ncomms9473
apa: Heinze, D. F., Breddermann, D., Zrenner, A., & Schumacher, S. (2015). A
quantum dot single-photon source with on-the-fly all-optical polarization control
and timed emission. Nature Communications. https://doi.org/10.1038/ncomms9473
bibtex: '@article{Heinze_Breddermann_Zrenner_Schumacher_2015, title={A quantum dot
single-photon source with on-the-fly all-optical polarization control and timed
emission}, DOI={10.1038/ncomms9473},
journal={Nature Communications}, author={Heinze, Dirk Florian and Breddermann,
Dominik and Zrenner, Artur and Schumacher, Stefan}, year={2015} }'
chicago: Heinze, Dirk Florian, Dominik Breddermann, Artur Zrenner, and Stefan Schumacher.
“A Quantum Dot Single-Photon Source with on-the-Fly All-Optical Polarization Control
and Timed Emission.” Nature Communications, 2015. https://doi.org/10.1038/ncomms9473.
ieee: D. F. Heinze, D. Breddermann, A. Zrenner, and S. Schumacher, “A quantum dot
single-photon source with on-the-fly all-optical polarization control and timed
emission,” Nature Communications, 2015.
mla: Heinze, Dirk Florian, et al. “A Quantum Dot Single-Photon Source with on-the-Fly
All-Optical Polarization Control and Timed Emission.” Nature Communications,
2015, doi:10.1038/ncomms9473.
short: D.F. Heinze, D. Breddermann, A. Zrenner, S. Schumacher, Nature Communications
(2015).
date_created: 2020-09-09T13:52:30Z
date_updated: 2022-01-06T06:54:00Z
doi: 10.1038/ncomms9473
language:
- iso: eng
publication: Nature Communications
publication_identifier:
issn:
- 2041-1723
publication_status: published
status: public
title: A quantum dot single-photon source with on-the-fly all-optical polarization
control and timed emission
type: journal_article
user_id: '10904'
year: '2015'
...
---
_id: '22946'
abstract:
- lang: eng
text: The Kane–Mele model was previously used to describe effective spin–orbit couplings
(SOCs) in graphene. Here we extend this model and also incorporate curvature effects
to analyze the combined influence of SOC and curvature on the band structure of
carbon nanotubes (CNTs). The extended model then reproduces the chirality-dependent
asymmetric electron-hole splitting for semiconducting CNTs and in the band structure
for metallic CNTs shows an opening of the band gap and a change of the Fermi wave
vector with spin. For chiral semiconducting CNTs with large chiral angle we show
that the spin-splitting configuration of bands near the Fermi energy depends on
the value of $\text{mod}(2n+m,3)$ .
article_number: '445501'
author:
- first_name: Hong
full_name: Liu, Hong
last_name: Liu
- first_name: Dirk Florian
full_name: Heinze, Dirk Florian
id: '10904'
last_name: Heinze
- first_name: Huynh
full_name: Thanh Duc, Huynh
last_name: Thanh Duc
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
citation:
ama: 'Liu H, Heinze DF, Thanh Duc H, Schumacher S, Meier T. Curvature effects in
the band structure of carbon nanotubes including spin–orbit coupling. Journal
of Physics: Condensed Matter. 2015;27(44). doi:10.1088/0953-8984/27/44/445501'
apa: 'Liu, H., Heinze, D. F., Thanh Duc, H., Schumacher, S., & Meier, T. (2015).
Curvature effects in the band structure of carbon nanotubes including spin–orbit
coupling. Journal of Physics: Condensed Matter, 27(44), Article
445501. https://doi.org/10.1088/0953-8984/27/44/445501'
bibtex: '@article{Liu_Heinze_Thanh Duc_Schumacher_Meier_2015, title={Curvature effects
in the band structure of carbon nanotubes including spin–orbit coupling}, volume={27},
DOI={10.1088/0953-8984/27/44/445501},
number={44445501}, journal={Journal of Physics: Condensed Matter}, author={Liu,
Hong and Heinze, Dirk Florian and Thanh Duc, Huynh and Schumacher, Stefan and
Meier, Torsten}, year={2015} }'
chicago: 'Liu, Hong, Dirk Florian Heinze, Huynh Thanh Duc, Stefan Schumacher, and
Torsten Meier. “Curvature Effects in the Band Structure of Carbon Nanotubes Including
Spin–Orbit Coupling.” Journal of Physics: Condensed Matter 27, no. 44 (2015).
https://doi.org/10.1088/0953-8984/27/44/445501.'
ieee: 'H. Liu, D. F. Heinze, H. Thanh Duc, S. Schumacher, and T. Meier, “Curvature
effects in the band structure of carbon nanotubes including spin–orbit coupling,”
Journal of Physics: Condensed Matter, vol. 27, no. 44, Art. no. 445501,
2015, doi: 10.1088/0953-8984/27/44/445501.'
mla: 'Liu, Hong, et al. “Curvature Effects in the Band Structure of Carbon Nanotubes
Including Spin–Orbit Coupling.” Journal of Physics: Condensed Matter, vol.
27, no. 44, 445501, 2015, doi:10.1088/0953-8984/27/44/445501.'
short: 'H. Liu, D.F. Heinze, H. Thanh Duc, S. Schumacher, T. Meier, Journal of Physics:
Condensed Matter 27 (2015).'
date_created: 2021-08-06T08:49:10Z
date_updated: 2025-12-05T14:48:46Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '297'
- _id: '230'
- _id: '35'
- _id: '27'
doi: 10.1088/0953-8984/27/44/445501
intvolume: ' 27'
issue: '44'
language:
- iso: eng
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: 'Journal of Physics: Condensed Matter'
publication_identifier:
issn:
- 0953-8984
- 1361-648X
publication_status: published
status: public
title: Curvature effects in the band structure of carbon nanotubes including spin–orbit
coupling
type: journal_article
user_id: '16199'
volume: 27
year: '2015'
...
---
_id: '13922'
article_number: '445501'
author:
- first_name: Hong
full_name: Liu, Hong
last_name: Liu
- first_name: Dirk Florian
full_name: Heinze, Dirk Florian
id: '10904'
last_name: Heinze
- first_name: Huynh
full_name: Thanh Duc, Huynh
last_name: Thanh Duc
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
citation:
ama: 'Liu H, Heinze DF, Thanh Duc H, Schumacher S, Meier T. Curvature effects in
the band structure of carbon nanotubes including spin–orbit coupling. Journal
of Physics: Condensed Matter. 2015;27(44). doi:10.1088/0953-8984/27/44/445501'
apa: 'Liu, H., Heinze, D. F., Thanh Duc, H., Schumacher, S., & Meier, T. (2015).
Curvature effects in the band structure of carbon nanotubes including spin–orbit
coupling. Journal of Physics: Condensed Matter, 27(44), Article
445501. https://doi.org/10.1088/0953-8984/27/44/445501'
bibtex: '@article{Liu_Heinze_Thanh Duc_Schumacher_Meier_2015, title={Curvature effects
in the band structure of carbon nanotubes including spin–orbit coupling}, volume={27},
DOI={10.1088/0953-8984/27/44/445501},
number={44445501}, journal={Journal of Physics: Condensed Matter}, author={Liu,
Hong and Heinze, Dirk Florian and Thanh Duc, Huynh and Schumacher, Stefan and
Meier, Torsten}, year={2015} }'
chicago: 'Liu, Hong, Dirk Florian Heinze, Huynh Thanh Duc, Stefan Schumacher, and
Torsten Meier. “Curvature Effects in the Band Structure of Carbon Nanotubes Including
Spin–Orbit Coupling.” Journal of Physics: Condensed Matter 27, no. 44 (2015).
https://doi.org/10.1088/0953-8984/27/44/445501.'
ieee: 'H. Liu, D. F. Heinze, H. Thanh Duc, S. Schumacher, and T. Meier, “Curvature
effects in the band structure of carbon nanotubes including spin–orbit coupling,”
Journal of Physics: Condensed Matter, vol. 27, no. 44, Art. no. 445501,
2015, doi: 10.1088/0953-8984/27/44/445501.'
mla: 'Liu, Hong, et al. “Curvature Effects in the Band Structure of Carbon Nanotubes
Including Spin–Orbit Coupling.” Journal of Physics: Condensed Matter, vol.
27, no. 44, 445501, 2015, doi:10.1088/0953-8984/27/44/445501.'
short: 'H. Liu, D.F. Heinze, H. Thanh Duc, S. Schumacher, T. Meier, Journal of Physics:
Condensed Matter 27 (2015).'
date_created: 2019-10-18T08:55:01Z
date_updated: 2025-12-05T14:48:14Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '297'
- _id: '230'
- _id: '35'
- _id: '27'
doi: 10.1088/0953-8984/27/44/445501
funded_apc: '1'
intvolume: ' 27'
issue: '44'
language:
- iso: eng
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: 'Journal of Physics: Condensed Matter'
publication_identifier:
issn:
- 0953-8984
- 1361-648X
publication_status: published
status: public
title: Curvature effects in the band structure of carbon nanotubes including spin–orbit
coupling
type: journal_article
user_id: '16199'
volume: 27
year: '2015'
...