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


The Berry phase of Bloch states can have profound effects on electron dynamics1,2,3 and lead to novel transport phenomena, such as the anomalous Hall effect and the valley Hall effect4,5,6. 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 coupling1,7,8,9,10,11. 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. Our study opens up pathways to coherently manipulate the quantum states and excitonic excitation with infrared radiation in two-dimensional semiconductors.

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Fig. 1: Schematics of exciton spectrum and optical transition in monolayer MoSe2.
Fig. 2: Transient reflection spectra of K-valley exciton transitions.
Fig. 3: Valley-dependent intraexciton optical Stark effect.
Fig. 4: Valley-dependent Autler–Townes splitting.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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This work was primarily supported by the Center for Computational Study of Excited State Phenomena in Energy Materials, which is funded by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-AC02–05CH11231, as part of the Computational Materials Sciences Program, which provided the experimental measurements and GW-BSE calculations. The sample fabrication and linear optical spectroscopy was supported by the US Army Research Office under MURI award W911NF-17-1-0312. The pump–probe setup was supported by the ARO MURI award W911NF-15-1-0447. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562. S.T. acknowledges support from NSF DMR-1552220. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST. E.C.R acknowledges support from the Department of Defense (DoD) through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program. C.-K.Y. and C.S.O. acknowledge useful discussion with A. Srivastava.

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Authors and Affiliations



C.-K.Y. and F.W. conceived the project. C.-K.Y. supervised the project, designed the experiments and carried out optical measurements, assisted by J.H. and H.D. C.-K.Y. and F.W. analysed the data and performed theoretical analysis, assisted by M.I.B.U. C.-K.Y., M.I.B.U., E.C.R. and A.Z. fabricated the devices. C.S.O., T.C. and S.G.L. performed GW-BSE calculations, Y.S, H.C. and S.T. synthesized MoSe2 crystals. K.W. and T.T. synthesized hBN crystals. C.-K.Y. and F.W. wrote the manuscript with inputs from all authors.

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Correspondence to Chaw-Keong Yong or Feng Wang.

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Supplementary Sections 1–5, Figs. 1–5 and refs. 1–18.

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Yong, CK., Utama, M.I.B., Ong, C.S. et al. Valley-dependent exciton fine structure and Autler–Townes doublets from Berry phases in monolayer MoSe2. Nat. Mater. 18, 1065–1070 (2019).

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