Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields

Goryca, Mateusz Marek; Li, Jing; Stier, Andreas V.; Taniguchi, Takashi; Watanabe, K.; Courtade, Emmanuel; Shree, S.; Robert, Cedric; Urbaszek, B.; Marie, X.; Crooker, Scott A.

doi:10.1038/s41467-019-12180-y

Title: Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields

Journal Article · Fri Sep 13 00:00:00 EDT 2019 · Nature Communications

DOI:https://doi.org/10.1038/s41467-019-12180-y· OSTI ID:1565907

^[1];

^[1]; Taniguchi, Takashi ^[2];

^[2]; Courtade, Emmanuel ^[3]; Shree, S. ^[3]; Robert, Cedric ^[3];

^[3]; Marie, X. ^[3];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
National Institute for Materials Science, Ibaraki (Japan)
Univ. de Toulouse, Toulouse (France)

In semiconductor physics, many essential optoelectronic material parameters can be experimentally revealed via optical spectroscopy in sufficiently large magnetic fields. For monolayer transition-metal dichalcogenide semiconductors, this field scale is substantial—tens of teslas or more—due to heavy carrier masses and huge exciton binding energies. Here we report absorption spectroscopy of monolayer MoS₂, MoSe₂, MoTe₂, and WS₂ in very high magnetic fields to 91 T. We follow the diamagnetic shifts and valley Zeeman splittings of not only the exciton’s 1s ground state but also its excited 2s,3s,…,ns Rydberg states. This provides a direct experimental measure of the effective (reduced) exciton masses and dielectric properties. Exciton binding energies, exciton radii, and free-particle bandgaps are also determined. The measured exciton masses are heavier than theoretically predicted, especially for Mo-based monolayers. These results provide essential and quantitative parameters for the rational design of opto-electronic van der Waals heterostructures incorporating 2D semiconductors.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1565907

Report Number(s):: LA-UR-19-23579

Journal Information:: Nature Communications, Vol. 10, Issue 1; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 127 works

Citation information provided by
Web of Science

References (106)

Exciton spectra in thin crystals: the diamagnetic effect Evans, B. L.; Young, P. A. Proceedings of the Physical Society, Vol. 91, Issue 2 https://doi.org/10.1088/0370-1328/91/2/327	journal	June 1967
Environmentally sensitive theory of electronic and optical transitions in atomically thin semiconductors Cho, Yeongsu; Berkelbach, Timothy C. Physical Review B, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevB.97.041409	journal	January 2018
Excitonic Valley Effects in Monolayer WS ₂ under High Magnetic Fields Plechinger, Gerd; Nagler, Philipp; Arora, Ashish Nano Letters, Vol. 16, Issue 12 https://doi.org/10.1021/acs.nanolett.6b04171	journal	November 2016
Breaking of Valley Degeneracy by Magnetic Field in Monolayer ${MoSe}_{2}$ MacNeill, David; Heikes, Colin; Mak, Kin Fai Physical Review Letters, Vol. 114, Issue 3 https://doi.org/10.1103/physrevlett.114.037401	journal	January 2015
Magnetic brightening and control of dark excitons in monolayer WSe2 Zhang, Xiao-Xiao; Cao, Ting; Lu, Zhengguang Nature Nanotechnology, Vol. 12, Issue 9 https://doi.org/10.1038/nnano.2017.105	journal	June 2017
Large effective mass and interaction-enhanced Zeeman splitting of $K$ -valley electrons in ${MoSe}_{2}$ Larentis, Stefano; Movva, Hema C. P.; Fallahazad, Babak Physical Review B, Vol. 97, Issue 20 https://doi.org/10.1103/PhysRevB.97.201407	journal	May 2018
Hydrogenic energy levels in two dimensions at arbitrary magnetic fields MacDonald, A. H.; Ritchie, D. S. Physical Review B, Vol. 33, Issue 12 https://doi.org/10.1103/PhysRevB.33.8336	journal	June 1986
Magneto-polarons in monolayer transition-metal dichalcogenides Chen, Qiao; Wang, Weiyang; Peeters, F. M. Journal of Applied Physics, Vol. 123, Issue 21 https://doi.org/10.1063/1.5025907	journal	June 2018
Orbital, spin and valley contributions to Zeeman splitting of excitonic resonances in MoSe$_2$, WSe$_2$ and WS$_2$ monolayers Koperski, M.; Molas, M. R.; Arora, A. arXiv https://doi.org/10.48550/arxiv.1803.00376	preprint	January 2018
Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla Stier, Andreas V.; McCreary, Kathleen M.; Jonker, Berend T. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10643	journal	February 2016
Spin and pseudospins in layered transition metal dichalcogenides Xu, Xiaodong; Yao, Wang; Xiao, Di Nature Physics, Vol. 10, Issue 5 https://doi.org/10.1038/nphys2942	journal	April 2014
Magnetostriction and magnetic texture to 100.75 Tesla in frustrated SrCu2(BO3)2 Jaime, M.; Daou, R.; Crooker, S. A. Proceedings of the National Academy of Sciences, Vol. 109, Issue 31 https://doi.org/10.1073/pnas.1200743109	journal	July 2012
Brightening of dark excitons in monolayers of semiconducting transition metal dichalcogenides Molas, M. R.; Faugeras, C.; Slobodeniuk, A. O. 2D Materials, Vol. 4, Issue 2 https://doi.org/10.1088/2053-1583/aa5521	journal	January 2017
Substrate interactions with suspended and supported monolayer $Mo S_{2}$ : Angle-resolved photoemission spectroscopy Jin, Wencan; Yeh, Po-Chun; Zaki, Nader Physical Review B, Vol. 91, Issue 12 https://doi.org/10.1103/PhysRevB.91.121409	journal	March 2015
Valley- and spin-polarized Landau levels in monolayer WSe2 Wang, Zefang; Shan, Jie; Mak, Kin Fai Nature Nanotechnology, Vol. 12, Issue 2 https://doi.org/10.1038/nnano.2016.213	journal	October 2016
Single-layer MoS2 Joensen, Per; Frindt, R. F.; Morrison, S. Roy Materials Research Bulletin, Vol. 21, Issue 4 https://doi.org/10.1016/0025-5408(86)90011-5	journal	April 1986
Magneto-optics in transition metal diselenide monolayers Wang, G.; Bouet, L.; Glazov, M. M. arXiv https://doi.org/10.48550/arxiv.1503.04105	text	January 2015
Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides Liu, Gui-Bin; Shan, Wen-Yu; Yao, Yugui Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevB.88.085433	journal	August 2013
XX. Properties of slow electrons in polar materials Fröhlich, H.; Pelzer, H.; Zienau, S. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 41, Issue 314 https://doi.org/10.1080/14786445008521794	journal	March 1950
Luminescent emission of excited Rydberg excitons from monolayer WSe2 Chen, Shao-Yu; Lu, Zhengguang; Goldstein, Thomas arXiv https://doi.org/10.48550/arxiv.1903.07073	text	January 2019
Atomically Thin ${MoS}_{2}$ A New Direct-Gap Semiconductor Mak, Kin Fai; Lee, Changgu; Hone, James Physical Review Letters, Vol. 105, Issue 13, Article No.136805 https://doi.org/10.1103/PhysRevLett.105.136805	journal	September 2010
Brightening of dark excitons in monolayers of semiconducting transition metal dichalcogenides Molas, M. R.; Faugeras, C.; Slobodeniuk, A. O. arXiv https://doi.org/10.48550/arxiv.1612.02867	text	January 2016
Magneto-Optics of Exciton Rydberg States in a Monolayer Semiconductor Stier, Andreas V.; Wilson, Nathan P.; Velizhanin, Kirill A. arXiv https://doi.org/10.48550/arxiv.1709.00123	text	January 2017
High-quality, large-area MoSe ₂ and MoSe ₂ /Bi ₂ Se ₃ heterostructures on AlN(0001)/Si(111) substrates by molecular beam epitaxy Xenogiannopoulou, E.; Tsipas, P.; Aretouli, K. E. Nanoscale, Vol. 7, Issue 17 https://doi.org/10.1039/c4nr06874b	journal	January 2015
Electronics and optoelectronics of two-dimensional transition metal dichalcogenides Wang, Qing Hua; Kalantar-Zadeh, Kourosh; Kis, Andras Nature Nanotechnology, Vol. 7, Issue 11, p. 699-712 https://doi.org/10.1038/nnano.2012.193	journal	November 2012
Spin-resolved photoemission study of epitaxially grown MoSe ₂ and WSe ₂ thin films Mo, Sung-Kwan; Hwang, Choongyu; Zhang, Yi Journal of Physics: Condensed Matter, Vol. 28, Issue 45 https://doi.org/10.1088/0953-8984/28/45/454001	journal	September 2016
Spin- and valley-dependent magneto-optical properties of MoS $_{2}$ Rose, Félix; Goerbig, M. O.; Piéchon, Frédéric Physical Review B, Vol. 88, Issue 12 https://doi.org/10.1103/physrevb.88.125438	journal	September 2013
Interactions and Magnetotransport through Spin-Valley Coupled Landau Levels in Monolayer Pisoni, Riccardo; Kormányos, Andor; Brooks, Matthew ETH Zurich https://doi.org/10.3929/ethz-b-000311260	text	January 2018
Observation of interlayer excitons in ${MoSe}_{2}$ single crystals Horng, Jason; Stroucken, Tineke; Zhang, Long Physical Review B, Vol. 97, Issue 24 https://doi.org/10.1103/PhysRevB.97.241404	journal	June 2018
Direct exciton emission from atomically thin transition metal dichalcogenide heterostructures near the lifetime limit Wierzbowski, Jakob; Klein, Julian; Sigger, Florian Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-09739-4	journal	September 2017
Approaching the intrinsic photoluminescence linewidth in transition metal dichalcogenide monolayers Ajayi, Obafunso A.; Ardelean, Jenny V.; Shepard, Gabriella D. 2D Materials, Vol. 4, Issue 3 https://doi.org/10.1088/2053-1583/aa6aa1	journal	July 2017
Probing the Influence of Dielectric Environment on Excitons in Monolayer WSe ₂ : Insight from High Magnetic Fields Stier, Andreas V.; Wilson, Nathan P.; Clark, Genevieve Nano Letters, Vol. 16, Issue 11 https://doi.org/10.1021/acs.nanolett.6b03276	journal	October 2016
Electronic structure of a single MoS2 monolayer Kadantsev, Eugene S.; Hawrylak, Pawel Solid State Communications, Vol. 152, Issue 10 https://doi.org/10.1016/j.ssc.2012.02.005	journal	May 2012
Band Structures of Transition-Metal-Dichalcogenide Layer Compounds Mattheiss, L. F. Physical Review B, Vol. 8, Issue 8 https://doi.org/10.1103/physrevb.8.3719	journal	October 1973
Robust optical emission polarization in MoS $_{2}$ monolayers through selective valley excitation Sallen, G.; Bouet, L.; Marie, X. Physical Review B, Vol. 86, Issue 8 https://doi.org/10.1103/PhysRevB.86.081301	journal	August 2012
The dielectric impact of layer distances on exciton and trion binding energies in van der Waals heterostructures Florian, M.; Hartmann, M.; Steinhoff, A. arXiv https://doi.org/10.48550/arxiv.1712.05607	text	January 2017
Coulomb engineering of the bandgap and excitons in two-dimensional materials Raja, Archana; Chaves, Andrey; Yu, Jaeeun Universität Regensburg https://doi.org/10.5283/epub.40514	text	January 2017
Valley Zeeman Splitting and Valley Polarization of Neutral and Charged Excitons in Monolayer MoTe ₂ at High Magnetic Fields Arora, Ashish; Schmidt, Robert; Schneider, Robert Nano Letters, Vol. 16, Issue 6 https://doi.org/10.1021/acs.nanolett.6b00748	journal	May 2016
Valley-selective circular dichroism of monolayer molybdenum disulphide Cao, Ting; Wang, Gang; Han, Wenpeng Nature Communications, Vol. 3, Issue 1 https://doi.org/10.1038/ncomms1882	journal	January 2012
Interactions and magnetotransport through spin-valley coupled Landau levels in monolayer MoS$_{2}$ Pisoni, Riccardo; Kormányos, Andor; Brooks, Matthew arXiv https://doi.org/10.48550/arxiv.1806.06402	text	January 2018
Intervalley polaron in atomically thin transition metal dichalcogenides Glazov, M. M.; Semina, M. A.; Robert, C. Physical Review B, Vol. 100, Issue 4 https://doi.org/10.1103/PhysRevB.100.041301	journal	July 2019
Emergence of Interfacial Polarons from Electron–Phonon Coupling in Graphene/h-BN van der Waals Heterostructures Chen, Chaoyu; Avila, José; Wang, Shuopei Nano Letters, Vol. 18, Issue 2 https://doi.org/10.1021/acs.nanolett.7b04604	journal	January 2018
Colloquium : Excitons in atomically thin transition metal dichalcogenides Wang, Gang; Chernikov, Alexey; Glazov, Mikhail M. Universität Regensburg https://doi.org/10.5283/epub.40518	text	January 2018
Interactions and Magnetotransport through Spin-Valley Coupled Landau Levels in Monolayer ${MoS}_{2}$ Pisoni, Riccardo; Kormányos, Andor; Brooks, Matthew Physical Review Letters, Vol. 121, Issue 24 https://doi.org/10.1103/PhysRevLett.121.247701	journal	December 2018
Spatial extent of the excited exciton states in ${WS}_{2}$ monolayers from diamagnetic shifts Zipfel, Jonas; Holler, Johannes; Mitioglu, Anatolie A. Physical Review B, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevB.98.075438	journal	August 2018
Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2 Zhang, Yi; Chang, Tay-Rong; Zhou, Bo arXiv https://doi.org/10.48550/arxiv.1401.3386	text	January 2014
Binding energies of exciton complexes in transition metal dichalcogenide monolayers and effect of dielectric environment Kylänpää, Ilkka; Komsa, Hannu-Pekka Physical Review B, Vol. 92, Issue 20 https://doi.org/10.1103/PhysRevB.92.205418	journal	November 2015
Magneto-optics in GaAs- ${Ga}_{1 - x}$ ${Al}_{x}$ As quantum wells Rogers, D. C.; Singleton, J.; Nicholas, R. J. Physical Review B, Vol. 34, Issue 6 https://doi.org/10.1103/PhysRevB.34.4002	journal	September 1986
Orbital, spin and valley contributions to Zeeman splitting of excitonic resonances in MoSe ₂ , WSe ₂ and WS ₂ Monolayers Koperski, Maciej; Molas, Maciej R.; Arora, Ashish 2D Materials, Vol. 6, Issue 1 https://doi.org/10.1088/2053-1583/aae14b	journal	October 2018
Spatial extent of the excited exciton states in WS2 monolayers from diamagnetic shifts Zipfel, Jonas; Holler, Johannes; Mitioglu, Anatolie A. Universität Regensburg https://doi.org/10.5283/epub.40520	text	January 2018
Corrigendum: k.p theory for two-dimensional transition metal dichalcogenide semiconductors (2015 2D Mater. 2 022001) Kormányos, Andor; Burkard, Guido; Gmitra, Martin 2D Materials, Vol. 2, Issue 4 https://doi.org/10.1088/2053-1583/2/4/049501	journal	November 2015
Valley-splitting and valley-dependent inter-Landau-level optical transitions in monolayer ${MoS}_{2}$ quantum Hall systems Chu, Rui-Lin; Li, Xiao; Wu, Sanfeng Physical Review B, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevB.90.045427	journal	July 2014
In-plane Propagation of Light in Transition Metal Dichalcogenide Monolayers: Optical Selection Rules Wang, G.; Robert, C.; Glazov, M. M. arXiv https://doi.org/10.48550/arxiv.1704.05341	text	January 2017
Interband Optical Transitions in Extremely Anisotropic Semiconductors. II. Coexistence of Exciton and the Landau Levels Akimoto, Okikazu; Hasegawa, Hiroshi Journal of the Physical Society of Japan, Vol. 22, Issue 1 https://doi.org/10.1143/jpsj.22.181	journal	January 1967
Binding energies of exciton complexes in transition metal dichalcogenides and effect of dielectric environment Kylänpää, Ilkka; Komsa, Hannu-Pekka arXiv https://doi.org/10.48550/arxiv.1508.06737	text	January 2015
Magneto-optics in transition metal diselenide monolayers Wang, G.; Bouet, L.; Glazov, M. M. 2D Materials, Vol. 2, Issue 3 https://doi.org/10.1088/2053-1583/2/3/034002	journal	June 2015
Coulomb engineering of the bandgap and excitons in two-dimensional materials Chernikov, Alexey; Raja, Archana; Chaves, Andrey Universität Regensburg https://doi.org/10.5283/epub.35591	text	January 2017
The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties Wilson, J. A.; Yoffe, A. D. Advances in Physics, Vol. 18, Issue 73 https://doi.org/10.1080/00018736900101307	journal	May 1969
Excitons in van der Waals heterostructures: The important role of dielectric screening Latini, S.; Olsen, T.; Thygesen, K. S. Physical Review B, Vol. 92, Issue 24 https://doi.org/10.1103/PhysRevB.92.245123	journal	December 2015
Mirrors made of a single atomic layer Mak, Kin Fai; Shan, Jie Nature, Vol. 556, Issue 7700 https://doi.org/10.1038/d41586-018-04089-1	journal	April 2018
Magnetic brightening and control of dark excitons in monolayer WSe2 Zhang, Xiao-Xiao; Cao, Ting; Lu, Zhengguang arXiv https://doi.org/10.48550/arxiv.1612.03558	text	January 2016
Theory of neutral and charged excitons in monolayer transition metal dichalcogenides Berkelbach, Timothy C.; Hybertsen, Mark S.; Reichman, David R. Physical Review B, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevB.88.045318	journal	July 2013
Quasiparticle band structures and optical properties of strained monolayer MoS $_{2}$ and WS $_{2}$ Shi, Hongliang; Pan, Hui; Zhang, Yong-Wei Physical Review B, Vol. 87, Issue 15 https://doi.org/10.1103/PhysRevB.87.155304	journal	April 2013
Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS $_{2}$ Cheiwchanchamnangij, Tawinan; Lambrecht, Walter R. L. Physical Review B, Vol. 85, Issue 20 https://doi.org/10.1103/PhysRevB.85.205302	journal	May 2012
Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides Mak, Kin Fai; Shan, Jie Nature Photonics, Vol. 10, Issue 4 https://doi.org/10.1038/nphoton.2015.282	journal	March 2016
Exciton diamagnetic shift in semiconductor nanostructures Walck, S. N.; Reinecke, T. L. Physical Review B, Vol. 57, Issue 15 https://doi.org/10.1103/physrevb.57.9088	journal	April 1998
Coupled Spin and Valley Physics in Monolayers of ${MoS}_{2}$ and Other Group-VI Dichalcogenides Xiao, Di; Liu, Gui-Bin; Feng, Wanxiang Physical Review Letters, Vol. 108, Issue 19 https://doi.org/10.1103/PhysRevLett.108.196802	journal	May 2012
Exciton-phonon interactions in nanocavity-integrated monolayer transition metal dichalcogenides Rosser, David; Fryett, Taylor; Ryou, Albert arXiv https://doi.org/10.48550/arxiv.2003.02710	preprint	January 2020
Normal Modes in Hexagonal Boron Nitride Geick, R.; Perry, C. H.; Rupprecht, G. Physical Review, Vol. 146, Issue 2 https://doi.org/10.1103/PhysRev.146.543	journal	June 1966
Emerging Photoluminescence in Monolayer MoS₂ Splendiani, Andrea; Sun, Liang; Zhang, Yuanbo Nano Letters, Vol. 10, Issue 4, p. 1271-1275 https://doi.org/10.1021/nl903868w	journal	April 2010
Polaronic correction to the exciton effective mass Iadonisi, G.; Bassani, F. Il Nuovo Cimento D, Vol. 9, Issue 6 https://doi.org/10.1007/bf02457030	journal	June 1987
In-Plane Propagation of Light in Transition Metal Dichalcogenide Monolayers: Optical Selection Rules Wang, G.; Robert, C.; Glazov, M. M. Physical Review Letters, Vol. 119, Issue 4 https://doi.org/10.1103/PhysRevLett.119.047401	journal	July 2017
Control of valley polarization in monolayer MoS2 by optical helicity Mak, Kin Fai; He, Keliang; Shan, Jie Nature Nanotechnology, Vol. 7, Issue 8 https://doi.org/10.1038/nnano.2012.96	journal	June 2012
Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane Cudazzo, Pierluigi; Tokatly, Ilya V.; Rubio, Angel Physical Review B, Vol. 84, Issue 8 https://doi.org/10.1103/PhysRevB.84.085406	journal	August 2011
Two-Dimensional Heterojunctions from Nonlocal Manipulations of the Interactions Rösner, M.; Steinke, C.; Lorke, M. Nano Letters, Vol. 16, Issue 4 https://doi.org/10.1021/acs.nanolett.5b05009	journal	March 2016
Diamagnetic shift in ${In}_{x}$ ${Ga}_{1 - x}$ As/GaAs strained quantum wells Hou, H. Q.; Staguhn, W.; Takeyama, S. Physical Review B, Vol. 43, Issue 5 https://doi.org/10.1103/PhysRevB.43.4152	journal	February 1991
Theory of Neutral and Charged Excitons in Monolayer Transition Metal Dichalcogenides Berkelbach, Timothy C.; Hybertsen, Mark S.; Reichman, David R. arXiv https://doi.org/10.48550/arxiv.1305.4972	text	January 2013
Optical Spectrum of ${MoS}_{2}$ : Many-Body Effects and Diversity of Exciton States Qiu, Diana Y.; da Jornada, Felipe H.; Louie, Steven G. Physical Review Letters, Vol. 111, Issue 21 https://doi.org/10.1103/PhysRevLett.111.216805	journal	November 2013
Splitting between bright and dark excitons in transition metal dichalcogenide monolayers Echeverry, J. P.; Urbaszek, B.; Amand, T. Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/physrevb.93.121107	journal	March 2016
Magnetoexcitons in large area CVD-grown monolayer ${MoS}_{2}$ and ${MoSe}_{2}$ on sapphire Mitioglu, A. A.; Galkowski, K.; Surrente, A. Physical Review B, Vol. 93, Issue 16 https://doi.org/10.1103/PhysRevB.93.165412	journal	April 2016
Magnetostriction and magnetic texture to 97.4 Tesla in frustrated SrCu2(BO3)2 Jaime, Marcelo; Daou, Ramzy; Crooker, Scott A. arXiv https://doi.org/10.48550/arxiv.1202.0812	text	January 2012
Coulomb engineering of the bandgap and excitons in two-dimensional materials Raja, Archana; Chaves, Andrey; Yu, Jaeeun Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15251	journal	May 2017
Effects of confinement and environment on the electronic structure and exciton binding energy of MoS $_{2}$ from first principles Komsa, Hannu-Pekka; Krasheninnikov, Arkady V. Physical Review B, Vol. 86, Issue 24 https://doi.org/10.1103/PhysRevB.86.241201	journal	December 2012
Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides Ramasubramaniam, Ashwin Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115409	journal	September 2012
Direct exciton emission from atomically thin transition metal dichalcogenide heterostructures near the lifetime limit Wierzbowski, Jakob; Klein, Julian; Sigger, Florian arXiv https://doi.org/10.48550/arxiv.1705.00348	text	January 2017
Exciton Diamagnetic Shifts and Valley Zeeman Effects in Monolayer WS$_2$ and MoS$_2$ to 65 Tesla Stier, Andreas V.; McCreary, Kathleen M.; Jonker, Berend T. arXiv https://doi.org/10.48550/arxiv.1510.07022	text	January 2015
Monolayer MoS2 Bandgap Modulation by Dielectric Environments and Tunable Bandgap Transistors Ryou, Junga; Kim, Yong-Sung; Kc, Santosh Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep29184	journal	July 2016
Magnetooptics of Exciton Rydberg States in a Monolayer Semiconductor Stier, A. V.; Wilson, N. P.; Velizhanin, K. A. Physical Review Letters, Vol. 120, Issue 5 https://doi.org/10.1103/PhysRevLett.120.057405	journal	February 2018
Excitons, trions, and biexcitons in transition-metal dichalcogenides: Magnetic-field dependence Van der Donck, M.; Zarenia, M.; Peeters, F. M. Physical Review B, Vol. 97, Issue 19 https://doi.org/10.1103/PhysRevB.97.195408	journal	May 2018
Colloquium : Excitons in atomically thin transition metal dichalcogenides Wang, Gang; Chernikov, Alexey; Glazov, Mikhail M. Reviews of Modern Physics, Vol. 90, Issue 2 https://doi.org/10.1103/RevModPhys.90.021001	journal	April 2018
Luminescent Emission of Excited Rydberg Excitons from Monolayer WSe ₂ Chen, Shao-Yu; Lu, Zhengguang; Goldstein, Thomas Nano Letters, Vol. 19, Issue 4 https://doi.org/10.1021/acs.nanolett.9b00029	journal	March 2019
Coulomb interaction in monolayer transition-metal dichalcogenides Van Tuan, Dinh; Yang, Min; Dery, Hanan Physical Review B, Vol. 98, Issue 12 https://doi.org/10.1103/PhysRevB.98.125308	journal	September 2018
Environmentally-Sensitive Theory of Electronic and Optical Transitions in Atomically-Thin Semiconductors Cho, Yeongsu; Berkelbach, Timothy C. arXiv https://doi.org/10.48550/arxiv.1709.01094	text	January 2017
Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2 Zhang, Yi; Chang, Tay-Rong; Zhou, Bo Nature Nanotechnology, Vol. 9, Issue 2 https://doi.org/10.1038/nnano.2013.277	journal	December 2013
Van der Waals heterostructures Geim, A. K.; Grigorieva, I. V. Nature, Vol. 499, Issue 7459, p. 419-425 https://doi.org/10.1038/nature12385	journal	July 2013
Probing the influence of dielectric environment on excitons in monolayer WSe2: Insight from high magnetic fields Stier, Andreas V.; Wilson, Nathan P.; Clark, Genevieve arXiv https://doi.org/10.48550/arxiv.1608.05093	text	January 2016
Excitonic valley effects in monolayer WS$_2$ under high magnetic fields Plechinger, Gerd; Nagler, Philipp; Arora, Ashish arXiv https://doi.org/10.48550/arxiv.1612.03004	text	January 2016
Large Excitonic Reflectivity of Monolayer ${MoSe}_{2}$ Encapsulated in Hexagonal Boron Nitride Scuri, Giovanni; Zhou, You; High, Alexander A. Physical Review Letters, Vol. 120, Issue 3 https://doi.org/10.1103/PhysRevLett.120.037402	journal	January 2018
Realization of an Electrically Tunable Narrow-Bandwidth Atomically Thin Mirror Using Monolayer ${MoSe}_{2}$ Back, Patrick; Zeytinoglu, Sina; Ijaz, Aroosa Physical Review Letters, Vol. 120, Issue 3 https://doi.org/10.1103/PhysRevLett.120.037401	journal	January 2018
Optical spectroscopy of excited exciton states in ${MoS}_{2}$ monolayers in van der Waals heterostructures Robert, C.; Semina, M. A.; Cadiz, F. Physical Review Materials, Vol. 2, Issue 1 https://doi.org/10.1103/PhysRevMaterials.2.011001	journal	January 2018
Valley Splitting and Polarization by the Zeeman Effect in Monolayer ${MoSe}_{2}$ Li, Yilei; Ludwig, Jonathan; Low, Tony Physical Review Letters, Vol. 113, Issue 26 https://doi.org/10.1103/PhysRevLett.113.266804	journal	December 2014
The Dielectric Impact of Layer Distances on Exciton and Trion Binding Energies in van der Waals Heterostructures Florian, Matthias; Hartmann, Malte; Steinhoff, Alexander Nano Letters, Vol. 18, Issue 4 https://doi.org/10.1021/acs.nanolett.8b00840	journal	March 2018
Realization of an Electrically Tunable Narrow-Bandwidth Atomically Thin Mirror Using Monolayer MoSe2 Back, Patrick; Zeytinoglu, Sina; Ijaz, Aroosa ETH Zurich https://doi.org/10.3929/ethz-b-000231337	text	January 2018
Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer ${WS}_{2}$ Chernikov, Alexey; Berkelbach, Timothy C.; Hill, Heather M. Physical Review Letters, Vol. 113, Issue 7 https://doi.org/10.1103/PhysRevLett.113.076802	journal	August 2014
Electronic and thermoelectric properties of few-layer transition metal dichalcogenides Wickramaratne, Darshana; Zahid, Ferdows; Lake, Roger K. The Journal of Chemical Physics, Vol. 140, Issue 12 https://doi.org/10.1063/1.4869142	journal	March 2014
Valley polarization in MoS2 monolayers by optical pumping Zeng, Hualing; Dai, Junfeng; Yao, Wang Nature Nanotechnology, Vol. 7, Issue 8 https://doi.org/10.1038/nnano.2012.95	journal	June 2012

Cited By (9)

Rydberg series of dark excitons and the conduction band spin-orbit splitting in monolayer WSe2 Kapuściński, Piotr; Delhomme, Alex; Vaclavkova, Diana Communications Physics, Vol. 4, Issue 1 https://doi.org/10.1038/s42005-021-00692-3	journal	August 2021
Energy Spectrum of Two-Dimensional Excitons in a Nonuniform Dielectric Medium Molas, M. R.; Slobodeniuk, A. O.; Nogajewski, K. Physical Review Letters, Vol. 123, Issue 13 https://doi.org/10.1103/physrevlett.123.136801	journal	September 2019
Excitons in monolayer semiconductors in complex environments and under external fields Zipfel, Jonas Universität Regensburg https://doi.org/10.5283/epub.43395	text	January 2020
Coherent dynamics and mapping of excitons in single-layer MoSe$_2$ and WSe$_2$ at the homogeneous limit Boule, Caroline; Vaclavkova, Diana; Bartos, Miroslav arXiv https://doi.org/10.48550/arxiv.2002.01436	text	January 2020
Spontaneous Valley Polarization of Interacting Carriers in a Monolayer Semiconductor Li, J.; Goryca, M.; Wilson, N. P. Physical Review Letters, Vol. 125, Issue 14 https://doi.org/10.1103/physrevlett.125.147602	journal	October 2020
High optical quality of MoS ₂ monolayers grown by chemical vapor deposition Shree, Shivangi; George, Antony; Lehnert, Tibor 2D Materials, Vol. 7, Issue 1 https://doi.org/10.1088/2053-1583/ab4f1f	journal	November 2019
Tunable quantum confinement of neutral excitons using electric fields and exciton-charge interactions Thureja, Deepankur; Imamoglu, Atac; Smolenski, Tomasz arXiv https://doi.org/10.48550/arxiv.2102.08989	preprint	January 2021
Magnetoexcitons in transition-metal dichalcogenides monolayers, bilayers, and van der Waals heterostructures Kezerashvili, Roman Ya.; Spiridonova, Anastasia arXiv https://doi.org/10.48550/arxiv.2012.07125	text	January 2020
Controlling exciton many-body states by the electric-field effect in monolayer MoS$_2$ Klein, Julian; Hötger, Alexander; Florian, Matthias arXiv https://doi.org/10.48550/arxiv.2007.14441	text	January 2020