Valley-dependent exciton fine structure and Autler–Townes doublets from Berry phases in monolayer MoSe2

Yong, Chaw-Keong; Utama, M. Iqbal Bakti; Ong, Chin Shen; Cao, Ting; Regan, Emma C.; Horng, Jason; Shen, Yuxia; Cai, Hui; Watanabe, Kenji; Taniguchi, Takashi; Tongay, Sefaattin; Deng, Hui; Zettl, Alex; Louie, Steven G.; Wang, Feng

doi:10.1038/s41563-019-0447-8

Valley-dependent exciton fine structure and Autler–Townes doublets from Berry phases in monolayer MoSe₂

Journal Article · Mon Aug 05 00:00:00 EDT 2019 · Nature Materials

DOI:https://doi.org/10.1038/s41563-019-0447-8· OSTI ID:1605255

^[1]; ^[2]; ^[2]; ^[2]; Regan, Emma C. ^[2]; Horng, Jason ^[3]; Shen, Yuxia ^[4]; Cai, Hui ^[5]; ^[6]; Taniguchi, Takashi ^[6]; Tongay, Sefaattin ^[4]; ^[3]; ^[7]; ^[2]; ^[7]

Univ. of California, Berkeley, CA (United States)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Univ. of Michigan, Ann Arbor, MI (United States)
Arizona State Univ., Tempe, AZ (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Science (CNMS)
National Inst. for Materials Science, Tsukuba (Japan)
Univ. of California, Berkeley, CA (United States). Kavli Energy NanoScience Inst.; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

The Berry phase of Bloch states can have profound effects on electron dynamics and lead to novel transport phenomena, such as the anomalous Hall effect and the valley Hall effect. Recently, it was predicted that the Berry phase effect can also modify the exciton states in transition metal dichalcogenide monolayers, and lift the energy degeneracy of exciton states with opposite angular momentum through an effective valley-orbital coupling. Here, we report the observation and control of the Berry phase-induced splitting of the 2p exciton states in monolayer molybdenum diselenide (MoSe₂) using the intraexciton optical Stark spectroscopy. We observe the time-reversal-symmetric analogue of the orbital Zeeman effect resulting from the valley-dependent Berry phase, which leads to energy difference of +14 (-14) meV between the 2p+ and 2p- exciton states in the K (K') valley, consistent with the ordering from our ab initio GW-Bethe–Salpeter equation results. In addition, we show that the light–matter coupling between intraexciton states is remarkably strong, leading to a prominent valley-dependent Autler–Townes doublet under resonant driving. Finally, our study opens up pathways to coherently manipulate the quantum states and excitonic excitation with infrared radiation in two-dimensional semiconductors.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); US Army Research Office (ARO); USDOD; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1605255

Journal Information:: Nature Materials, Journal Name: Nature Materials Journal Issue: 10 Vol. 18; ISSN 1476-1122

Publisher:: Springer Nature - Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (46)

AC stark effect and multiphoton processes in atoms Bakos, J. S. Physics Reports, Vol. 31, Issue 3 https://doi.org/10.1016/0370-1573(77)90016-3	journal	July 1977
BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures Deslippe, Jack; Samsonidze, Georgy; Strubbe, David A. Computer Physics Communications, Vol. 183, Issue 6 https://doi.org/10.1016/j.cpc.2011.12.006	journal	June 2012
Experimental observation of the quantum Hall effect and Berry's phase in graphene Zhang, Yuanbo; Tan, Yan-Wen; Stormer, Horst L. Nature, Vol. 438, Issue 7065, p. 201-204 https://doi.org/10.1038/nature04235	journal	November 2005
Probing excitonic dark states in single-layer tungsten disulphide Ye, Ziliang; Cao, Ting; O’Brien, Kevin Nature, Vol. 513, Issue 7517 https://doi.org/10.1038/nature13734	journal	August 2014
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
Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor Ugeda, Miguel M.; Bradley, Aaron J.; Shi, Su-Fei Nature Materials, Vol. 13, Issue 12 https://doi.org/10.1038/nmat4061	journal	August 2014
Valley-selective optical Stark effect in monolayer WS2 Sie, Edbert J.; McIver, James W.; Lee, Yi-Hsien Nature Materials, Vol. 14, Issue 3 https://doi.org/10.1038/nmat4156	journal	December 2014
Resonant internal quantum transitions and femtosecond radiative decay of excitons in monolayer WSe2 Poellmann, C.; Steinleitner, P.; Leierseder, U. Nature Materials, Vol. 14, Issue 9 https://doi.org/10.1038/nmat4356	journal	July 2015
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
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
Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene Novoselov, K. S.; McCann, E.; Morozov, S. V. Nature Physics, Vol. 2, Issue 3 https://doi.org/10.1038/nphys245	journal	February 2006
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
Optical manipulation of valley pseudospin Ye, Ziliang; Sun, Dezheng; Heinz, Tony F. Nature Physics, Vol. 13, Issue 1 https://doi.org/10.1038/nphys3891	journal	September 2016
Ultrafast transition between exciton phases in van der Waals heterostructures Merkl, P.; Mooshammer, F.; Steinleitner, P. Nature Materials, Vol. 18, Issue 7 https://doi.org/10.1038/s41563-019-0337-0	journal	April 2019
Biexcitonic optical Stark effects in monolayer molybdenum diselenide Yong, Chaw-Keong; Horng, Jason; Shen, Yuxia Nature Physics, Vol. 14, Issue 11 https://doi.org/10.1038/s41567-018-0216-7	journal	July 2018
Stark Effect in Rapidly Varying Fields Autler, S. H.; Townes, C. H. Physical Review, Vol. 100, Issue 2 https://doi.org/10.1103/PhysRev.100.703	journal	October 1955
Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies Hybertsen, Mark S.; Louie, Steven G. Physical Review B, Vol. 34, Issue 8, p. 5390-5413 https://doi.org/10.1103/PhysRevB.34.5390	journal	October 1986
Electron-hole excitations and optical spectra from first principles Rohlfing, Michael; Louie, Steven G. Physical Review B, Vol. 62, Issue 8 https://doi.org/10.1103/PhysRevB.62.4927	journal	August 2000
Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS 2 , Mo S e 2 , WS 2 , and WS e 2 Li, Yilei; Chernikov, Alexey; Zhang, Xian Physical Review B, Vol. 90, Issue 20 https://doi.org/10.1103/PhysRevB.90.205422	journal	November 2014
Exciton band structure of monolayer MoS 2 Wu, Fengcheng; Qu, Fanyao; MacDonald, A. H. Physical Review B, Vol. 91, Issue 7 https://doi.org/10.1103/PhysRevB.91.075310	journal	February 2015
Bright and dark singlet excitons via linear and two-photon spectroscopy in monolayer transition-metal dichalcogenides Berkelbach, Timothy C.; Hybertsen, Mark S.; Reichman, David R. Physical Review B, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevB.92.085413	journal	August 2015
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 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
Quantum Mechanics with a Momentum-Space Artificial Magnetic Field Price, Hannah M.; Ozawa, Tomoki; Carusotto, Iacopo Physical Review Letters, Vol. 113, Issue 19 https://doi.org/10.1103/PhysRevLett.113.190403	journal	November 2014
Giant Enhancement of the Optical Second-Harmonic Emission of WSe 2 Monolayers by Laser Excitation at Exciton Resonances Wang, G.; Marie, X.; Gerber, I. Physical Review Letters, Vol. 114, Issue 9 https://doi.org/10.1103/PhysRevLett.114.097403	journal	March 2015
Signatures of Bloch-Band Geometry on Excitons: Nonhydrogenic Spectra in Transition-Metal Dichalcogenides Srivastava, Ajit; Imamoğlu, Ataç Physical Review Letters, Vol. 115, Issue 16 https://doi.org/10.1103/PhysRevLett.115.166802	journal	October 2015
Berry Phase Modification to the Energy Spectrum of Excitons Zhou, Jianhui; Shan, Wen-Yu; Yao, Wang Physical Review Letters, Vol. 115, Issue 16 https://doi.org/10.1103/PhysRevLett.115.166803	journal	October 2015
Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides Trushin, Maxim; Goerbig, Mark Oliver; Belzig, Wolfgang Physical Review Letters, Vol. 120, Issue 18 https://doi.org/10.1103/PhysRevLett.120.187401	journal	May 2018
Berry Phase, Hyperorbits, and the Hofstadter Spectrum Chang, Ming-Che; Niu, Qian Physical Review Letters, Vol. 75, Issue 7 https://doi.org/10.1103/PhysRevLett.75.1348	journal	August 1995
Valley-Contrasting Physics in Graphene: Magnetic Moment and Topological Transport Xiao, Di; Yao, Wang; Niu, Qian Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236809	journal	December 2007
Berry phase effects on electronic properties Xiao, Di; Chang, Ming-Che; Niu, Qian Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/RevModPhys.82.1959	journal	July 2010
The valley Hall effect in MoS2 transistors Mak, K. F.; McGill, K. L.; Park, J. Science, Vol. 344, Issue 6191 https://doi.org/10.1126/science.1250140	journal	June 2014
Ultrafast generation of pseudo-magnetic field for valley excitons in WSe ₂ monolayers Kim, Jonghwan; Hong, Xiaoping; Jin, Chenhao Science, Vol. 346, Issue 6214 https://doi.org/10.1126/science.1258122	journal	December 2014
Berry phase modification to the energy spectrum of excitons Zhou, Jianhui; Shan, Wen-Yu; Yao, Wang Carnegie Mellon University https://doi.org/10.1184/r1/6506474	text	January 2015
Berry phase modification to the energy spectrum of excitons Zhou, Jianhui; Shan, Wen-Yu; Yao, Wang Figshare https://doi.org/10.1184/r1/6506474.v1	text	January 2018
BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures Deslippe, Jack Mendeley https://doi.org/10.17632/dzk6frrs69	dataset	January 2019
Valley contrasting physics in graphene: magnetic moment and topological transport Xiao, Di; Yao, Wang; Niu, Qian arXiv https://doi.org/10.48550/arxiv.0709.1274	text	January 2007
Probing Excitonic Dark States in Single-layer Tungsten Disulfide Ye, Ziliang; Cao, Ting; O'Brien, Kevin arXiv https://doi.org/10.48550/arxiv.1403.5568	text	January 2014
Valley-selective optical Stark effect in monolayer WS2 Sie, Edbert J.; McIver, James W.; Lee, Yi-Hsien arXiv https://doi.org/10.48550/arxiv.1407.1825	text	January 2014
Ultrafast Generation of Pseudo-magnetic Field for Valley Excitons in WSe2 Monolayers Kim, Jonghwan; Hong, Xiaoping; Jin, Chenhao arXiv https://doi.org/10.48550/arxiv.1407.2347	text	January 2014
Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides Trushin, Maxim; Goerbig, Mark Oliver; Belzig, Wolfgang arXiv https://doi.org/10.48550/arxiv.1708.03638	text	January 2017
Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene Zhang, Yuanbo; Tan, Yan-Wen; Stormer, Horst L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0509355	text	January 2005
Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene Novoselov, K. S.; McCann, E.; Morozov, S. V. arXiv https://doi.org/10.48550/arxiv.cond-mat/0602565	text	January 2006
Berry phase, hyperorbits, and the Hofstadter spectrum Chang, M. C.; Niu, Q. arXiv https://doi.org/10.48550/arxiv.cond-mat/9505021	text	January 1995
Resonant internal Quantum transitions and femtosecond radiative decay of excitons in monolayer WSe2 Pöllmann, Christoph; Steinleitner, Philipp; Leierseder, Ursula Universität Regensburg https://doi.org/10.5283/epub.32244	text	January 2015
Ultrafast transition between exciton phases in van der Waals heterostructures Merkl, Philipp; Mooshammer, Fabian; Steinleitner, Philipp Universität Regensburg https://doi.org/10.5283/epub.41038	text	January 2019

Cited By (2)

Resonant optical Stark effect in monolayer WS2 Cunningham, Paul D.; Hanbicki, Aubrey T.; Reinecke, Thomas L. Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-13501-x	journal	December 2019
Large and controllable spin-valley splitting in two-dimensional W S 2 / h − VN heterostructure Ke, Congming; Wu, Yaping; Yang, Weihuang Physical Review B, Vol. 100, Issue 19 https://doi.org/10.1103/physrevb.100.195435	journal	November 2019