Pith. sign in

REVIEW 2 major objections 4 minor 62 references

Coherent Interaction of 2s and 1s Exciton States in Transition-Metal Dichalcogenide Monolayers

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Coherent pump-probe measurements in WSe2 and MoSe2 monolayers show a repulsive 2s-1s exciton interaction nearly as strong as the 1s-1s interaction and reveal a bound 2s-1s biexciton with binding energies of 24.2 meV and 29.7 meV.

desk verdict Careful Stark-shift study of 2s–1s exciton interactions; the interaction-strength ratio is solid, but the 2s–1s biexciton binding energies rely on an undefended two-level assumption. read the letter →

arxiv 2501.12966 v2 pith:4B3NBZ7F submitted 2025-01-22 cond-mat.mes-hall

Max Wegerhoff , Moritz Scharfstädt , Stefan Linden , Andrea Bergschneider This is my paper · ORCID
classification cond-mat.mes-hall PACS 71.35.-y78.47.-p
keywords opticalStarkeffectbiexcitonexciton-excitoninteractiontransition-metaldichalcogenidemonolayersRydbergexcitonssemiconductorBlochequationsWSe2MoSe2
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper uses a pump pulse tuned below the 1s exciton resonance to create a fleeting, virtual population of 1s excitons in WSe2 and MoSe2 monolayers and probes how it shifts the energy of the 2s exciton. In co-circular polarization the shift is a blueshift, showing that same-valley 2s-1s interactions are repulsive and only slightly stronger (about 10–20%) than 1s-1s interactions, as the semiconductor Bloch equations predict. In cross-circular polarization the 2s shift changes sign at a specific pump detuning, which the authors identify as the binding energy of a 2s-1s biexciton: 24.2 meV in WSe2 and 29.7 meV in MoSe2. This gives the first measurement of a 2s-1s biexciton and a benchmark for theories of how Rydberg excitons interact.

What carries the argument

The load-bearing mechanism is the optical Stark effect in the low-intensity limit, decomposed via the semiconductor Bloch equations into an exciton-photon term scaling as $1/\delta$ and an exciton-exciton term scaling as $1/\delta^2$, where $\delta$ is the pump detuning from the 1s state. Fitting the measured 1s and 2s shifts as a function of detuning yields the prefactors $a$ and $b$, whose ratio $b_{2s1s}/b_{1s1s}$ gives the interaction-strength ratio with systematic errors cancelling. In the cross-circular geometry, the pump couples the $\lvert ns\rangle$ exciton to the $\lvert ns,1s'\rangle$ biexciton, and the two-level dressed-state shift changes sign when the detuning equals the biexciton binding energy; the zero-crossing of the 2s shift therefore serves as a direct measure of the 2s-1s biexciton binding energy.

What would settle it

Measure the 2s-1s biexciton binding energy by two-photon absorption; if it disagrees with the detuning at which the 2s Stark shift crosses zero (24.2 meV in WSe2, 29.7 meV in MoSe2), the central claim is wrong.

Watch

Extended reading notes

Core claim

We use the optical Stark effect in the low-intensity limit to show that the shift of the 2s exciton in WSe2 and MoSe2 monolayers separates into an exciton-photon term and an exciton-exciton term, distinguished by their $1/\delta$ and $1/\delta^2$ detuning dependence. Fitting this detuning dependence yields a 2s-1s interaction strength only 19% (WSe2) and 8% (MoSe2) larger than the 1s-1s strength, in agreement with semiconductor Bloch equation calculations based on the Rytova-Keldysh potential. In the cross-circular configuration, the 2s light shift changes sign at a pump detuning that is independent of intensity; we identify this zero-crossing with the transition to a bound 2s-1s biexciton and extract binding energies of 24.2±1.0 meV (WSe2) and 29.7±0.6 meV (MoSe2). To our knowledge this is the first observation of a 2s-1s biexciton, and the non-resonant method isolates the bright-bright intervalley biexciton without populating dark states.

Load-bearing premise

The binding energy of the 2s-1s biexciton is read directly from the detuning at which the 2s optical Stark shift changes sign, which assumes that this shift is dominated by the two-level coupling to the biexciton and that no comparable background shift (for example from the direct ac Stark effect on the 2s state or from other virtual populations) displaces the zero-crossing.

Editorial extensions

If this is right

  • The measured 2s-1s biexciton binding energies (24.2 meV in WSe2, 29.7 meV in MoSe2) become the first benchmarks against which theoretical models of biexcitons in two-dimensional semiconductors must be tested.
  • The near-unity ratio of 2s-1s to 1s-1s interaction strength (1.19 in WSe2, 1.08 in MoSe2) shows that Rydberg-exciton interaction enhancement is modest in these materials, informing proposals for strong optical nonlinearities.
  • The non-resonant cross-circular method isolates the bright-bright intervalley biexciton without populating dark states, and the WSe2 value is close to previously reported bright-dark biexciton binding energies, indicating similar binding for the two configurations.
  • The work opens perspectives for the coherent manipulation of Rydberg polaritons in optical cavities, as the authors state.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same zero-crossing technique could measure 3s-1s and 4s-1s biexciton binding energies, revealing whether the near-equality in MoSe2 (29.7 vs 29.1 meV) is accidental or reflects a weak dependence on principal quantum number.
  • Because the ratio $U_{2s1s}/U_{1s1s}$ is insensitive to the absolute calibration of virtual density (which differs by a factor of three between the two methods discussed in the supplement), future studies of interaction strengths in doped or moiré systems could rely on such ratios rather than absolute values.
  • The discrepancy between theory and experiment for the absolute 1s-1s interaction strength in MoSe2 (theory overestimates by about a factor of three) suggests the approximate 2D hydrogen wave functions used in the semiconductor Bloch equation calculation miss part of the screening physics.
  • A cavity or waveguide geometry that enhances the coherent signal might recover the predicted attractive 2s-2s interaction, which the paper reports was obscured by incoherent absorption in a blue-detuned pump configuration.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This manuscript reports femtosecond pump-probe measurements of the excitonic optical Stark effect on the 1s and 2s exciton resonances in charge-neutral WSe2 and MoSe2 monolayers. In the co-circular configuration, the detuning-dependent shift of each resonance is fitted with a two-parameter form Δλ/I = a/δ + b/δ², yielding the 1s-1s and 2s-1s interaction strengths and their ratio. In the cross-circular configuration, the sign change of the 1s and 2s shifts as a function of pump detuning is interpreted as the signature of biexciton resonances, giving 1s-1s binding energies consistent with literature and 2s-1s binding energies of 24.2 ± 1.0 meV (WSe2) and 29.7 ± 0.6 meV (MoSe2). The authors claim the first observation of a bound 2s-1s biexciton state and report that the repulsive 2s-1s interaction is only slightly larger than the 1s-1s one.

Significance. The co-circular analysis is careful and the ratio U2s1s/U1s1s is a robust quantity: it is formed from two fits that share the same virtual 1s density, so systematic errors largely cancel. The 1s-1s BX binding energies reproduce independent photoluminescence measurements, which is a valuable external check. If the 2s-1s BX interpretation survives closer scrutiny, the observation would be a significant advance for Rydberg-exciton physics in TMDCs and would provide a benchmark for biexciton theory. The authors also make the data openly available on Zenodo and are transparent about the model dependence of absolute U values. The principal weakness is that the central zero-crossing interpretation for the 2s state is not backed by a multilevel calculation.

major comments (2)
  1. [Biexcitonic state / Fig. 4(c)] The central claim of a 2s-1s biexciton rests on the assumption that the cross-circular 2s optical Stark shift is dominated by the two-level coupling |2s⟩ ↔ |2s,1s′⟩, so that the zero-crossing in Fig. 4(c) occurs exactly at δ1s = E_bind(2s-1s). This assumption is not derived: the SM contains the SBE calculation only for the co-circular configuration (Eqs. (15)-(17)), and no multilevel expression is given for the cross-circular case. In the same SBE framework, the pump-induced virtual 1s′ density (∝ 1/δ1s²) interacts attractively with the 2s state and would produce a background redshift that does not change sign, and additional 1/δ terms from coupling to other manifolds (for example |2s,2s′⟩) can contribute as well. Any such background displaces the zero-crossing, and the observed intensity independence does not rule it out because both the biexciton coupling and the background scale linearly with pump intensity. The agreement of the 1s-1s BX values with previous work is reassuring, but it does not transfer quantitatively to the 2s state, which has a different exciton-photon enhancement (a2s1s/a1s1s up to 1.77, Table I) and whose biexciton dipole is not independently calibrated. Please quantify the background shift at δ ≈ E_bind (for example with the measured U and n1s) or include such terms in the fit before claiming the binding energies.
  2. [Supplemental Material, Eq. (8)] The displayed formula for the oscillator strength reads fλ = |dcv|² (2/π)(2n−1)³ (rBλ)^−2, which makes f increase with n and directly contradicts the statement in the main text that the oscillator strength decreases rapidly for higher Rydberg states. The standard 2D-hydrogen result has (2n−1)³ in the denominator. Please correct this equation and confirm that the numerical calculations (Table IV and the virtual-density expressions) use the denominator form; as printed, the formula would invalidate the neglect of higher Rydberg states in Eq. (2).
minor comments (4)
  1. [2s-1s interaction] The heading contains a typo: 'Adressing' should be 'Addressing'.
  2. [Table I and SM 'OBE: Virtual exciton density'] The factor-of-three difference between the SBE and OBE virtual-density calibrations is discussed only in the SM; since Table I presents absolute U1s1s values as benchmarks and the text claims the first measurement of U1s1s in WSe2, a sentence in the main text noting this model dependence would help readers.
  3. [Table I] The experimental ratio U2s1s/U1s1s for MoSe2 (1.08 ± 0.12) and the SBE value (1.40 ± 0.18) differ by more than one combined standard error; the word 'agreement' should be qualified in the discussion.
  4. [Fig. 4(c)] Error bars on the plotted shifts and a description of how the zero-crossing and its uncertainty were obtained would strengthen the central figure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured 2s-1s interaction ratio and biexciton binding energies rest on independent fits, externally sourced theory parameters, and benchmarked models rather than on self-referential inputs.

full rationale

The derivation chain is self-contained rather than circular. The co-circular 2s-1s interaction strength is obtained by fitting Eq. (2) to measured detuning-dependent Stark shifts with only a2s1s and b2s1s as free parameters, and the ratio b2s1s/b1s1s = U2s1s/U1s1s follows from the same virtual 1s density, which cancels systematic prefactors. The theoretical comparison values are not derived from the measured ratios but are computed from semiconductor Bloch equation matrix elements (SM Eq. (17)) using independently published rms exciton radii and screening parameters from Refs. [44,45] (SM Tables III-IV), so the agreement is an external check rather than a fitted prediction. The 1s-1s interaction strengths are benchmarked against prior measurements [5,6,20,43], and the 1s-1s biexciton binding energies are cross-checked against photoluminescence studies [9-12,20,48]. The cross-circular 2s-1s binding energy is read from the sign change of the Stark shift following the two-level biexciton model of Ref. [35] and is validated by applying the same procedure to the well-studied 1s-1s state; this is a model-dependent interpretation, not a self-referential reduction. The only self-citation, Ref. [6], appears in a peripheral literature comparison for MoSe2 and is independently corroborated by Refs. [20,43], so it is not load-bearing. No equation is used as its own input, and no fitted parameter is renamed as a prediction; the skeptic's concern about possible multilevel background shifts is a robustness and correctness issue, not a circularity issue.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claims depend on a few fitted amplitudes (the a and b coefficients in Eq. 2), literature values for exciton radii and screening parameters, and standard SBE-based modeling assumptions. No new physical entities are introduced. The absolute calibration of the virtual density uses the fitted XP amplitude together with a theoretical enhancement factor, which couples the measurement to the model. The ratio U_2s1s/U_1s1s and the BX binding energies are the most model-independent outputs.

free parameters (5)
  • a_1s1s (XP amplitude for 1s) = not stated explicitly; derived dipole moment d_cv = 5.25 Debye (WSe2), 3.54 Debye (MoSe2)
    Fitted as the coefficient of the 1/delta_1s term in Eq. (2) for the 1s light shift. Used to calibrate the virtual exciton density.
  • b_1s1s (XX amplitude for 1s) = not stated explicitly; leads to U_1s1s = 0.43 +/- 0.09 ueV um^2 (WSe2), 0.127 +/- 0.029 ueV um^2 (MoSe2)
    Fitted as the coefficient of the 1/delta_1s^2 term in Eq. (2) for the 1s light shift. Determines the 1s-1s interaction strength after density calibration.
  • a_2s1s (XP amplitude for 2s) = not stated explicitly; ratio a_2s1s/a_1s1s = 1.28 +/- 0.09 (WSe2), 1.77 +/- 0.10 (MoSe2)
    Fitted as the coefficient of the 1/delta_1s term for the 2s light shift. Used to assess the exciton-photon enhancement.
  • b_2s1s (XX amplitude for 2s) = not stated explicitly; ratio b_2s1s/b_1s1s = U_2s1s/U_1s1s = 1.19 +/- 0.09 (WSe2), 1.08 +/- 0.12 (MoSe2)
    Fitted as the coefficient of the 1/delta_1s^2 term for the 2s light shift. The ratio to b_1s1s gives the central 2s-1s interaction strength ratio.
  • MoSe2 2s rms radius estimate = approximately 4.5 nm
    The rms radius of the 2s state in MoSe2 was not explicitly stated in ref [45]; the authors estimate it from the supplemental information of that paper. This value enters the theoretical calculation of U_2s1s and the enhancement ratio, and carries a 20% uncertainty.
assumptions (5)
  • domain assumption The low-intensity SBE expression Eq. (1) truncated to Eq. (2), assuming only the 1s virtual state contributes significantly to the pump-induced polarization and density.
    Invoked in the main text before Eq. (2) with the justification that the detuning to higher Rydberg states is at least twice as large and oscillator strengths decrease rapidly. If higher states contributed, the fitted a and b coefficients would be biased.
  • domain assumption The 2D hydrogen wave functions with variational Bohr radii approximate the real exciton wave functions in TMDC monolayers.
    Used in the Supplemental Material to compute rho_1s1s, rho_2s1s, and U_lambda1s. The Bohr radii are deduced from experimentally measured rms radii in refs [44,45].
  • domain assumption The Rytova-Keldysh potential with parameters r0 and epsilon describes the dielectric screening of the Coulomb interaction.
    Used in the Supplemental Material (Eq. 7) for the theoretical computation of the interaction strengths. The screening length and dielectric constant are taken from literature.
  • domain assumption The zero-crossing of the optical Stark shift as a function of pump detuning equals the biexciton binding energy.
    Invoked in the main text around Fig. 4 and based on ref [35]. The paper validates this assumption by reproducing known 1s-1s BX binding energies.
  • domain assumption The transfer matrix simulation correctly models the device stack, including refractive indices, layer thicknesses, and the exciton as an OBE resonance.
    Used to extract the field enhancement factor f_FEF, the Purcell factor, and the radiative/non-radiative decay rates, which enter the intensity calibration and the OBE cross-check.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Coherent Interaction of 2s and 1s Exciton States in Transition-Metal Dichalcogenide Monolayers." pith.science (2026). https://pith.science/paper/4B3NBZ7F

@misc{pith2026250112966,
  author       = {Pith},
  title        = {Pith review of: Coherent Interaction of 2s and 1s Exciton States in Transition-Metal Dichalcogenide Monolayers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4B3NBZ7F}},
  note         = {Machine review of arXiv:2501.12966}
}
read the original abstract

We use femtosecond pump-probe spectroscopy to study the coherent interaction of excited exciton states in WSe2 and MoSe2 monolayers via the optical Stark effect. For co-circularly polarized pump and probe, we measure a blueshift which points to a repulsive interaction between the 2s and 1s exciton states. The determined 2s-1s interaction strength is on par with that of the 1s-1s, in agreement with the semiconductor Bloch equations. Furthermore, we demonstrate the existence of a 2s-1s biexciton bound state in the cross-circular configuration in both materials and determine their binding energy.

Figures

Figures reproduced from arXiv: 2501.12966 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of the van-der-Waals heterostructure [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Co-circular pump-probe measurements. The pump is [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Determination of the 1s-1s and 2s-1s interaction [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Cross-circular measurements. (a) Energy level dia [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Optical micrograph of the WSe [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Sketch of the confocal pump-probe setup in reflection [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Cross-circular measurements in resonance to the BX [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

62 extracted references · 60 canonical work pages

  1. [1]

    K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically Thin MoS2 : A New Direct-Gap Semiconduc- tor, Physical Review Letters 105, 136805 (2010)

    work page 2010

  2. [2]

    Splendiani, L

    A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, and F. Wang, Emerging Photolumines- cence in Monolayer MoS2, Nano Letters 10, 1271 (2010)

    work page 2010

  3. [3]

    G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Colloquium: Excitons in atomically thin transition metal dichalco- genides, Reviews of Modern Physics 90, 021001 (2018)

    2018

  4. [4]

    E. J. Sie, A. J. Frenzel, Y.-H. Lee, J. Kong, and N. Gedik, Intervalley biexcitons and many-body effects in mono- layer MoS2, Physical Review B 92, 125417 (2015)

    work page 2015

  5. [5]

    Barachati, A

    F. Barachati, A. Fieramosca, S. Hafezian, J. Gu, B. Chakraborty, D. Ballarini, L. Martinu, V. Menon, D. Sanvitto, and S. K´ ena-Cohen, Interacting polariton fluids in a monolayer of tungsten disulfide, Nature Nan- otechnology 13, 906 (2018)

    work page 2018

  6. [6]

    L. B. Tan, O. Cotlet, A. Bergschneider, R. Schmidt, P. Back, Y. Shimazaki, M. Kroner, and A. ˙Imamo˘ glu, Interacting Polaron-Polaritons, Physical Review X 10, 021011 (2020)

    work page 2020

  7. [7]

    K. Wei, Q. Liu, Y. Tang, Y. Ye, Z. Xu, and T. Jiang, Charged biexciton polaritons sustaining strong nonlin- earity in 2D semiconductor-based nanocavities, Nature Communications 14, 5310 (2023)

    work page 2023

  8. [8]

    K. Hao, J. F. Specht, P. Nagler, L. Xu, K. Tran, A. Singh, C. K. Dass, C. Sch¨ uller, T. Korn, M. Richter, A. Knorr, X. Li, and G. Moody, Neutral and charged inter-valley 6 biexcitons in monolayer MoSe2, Nature Communications 8, 15552 (2017)

    work page 2017

Show all 62 references
  1. [9]

    Z. Ye, L. Waldecker, E. Y. Ma, D. Rhodes, A. Antony, B. Kim, X.-X. Zhang, M. Deng, Y. Jiang, Z. Lu, D. Smirnov, K. Watanabe, T. Taniguchi, J. Hone, and T. F. Heinz, Efficient generation of neutral and charged biexcitons in encapsulated WSe 2 monolayers, Nature Communications 9...

    2018

  2. [10]

    Barbone, A

    M. Barbone, A. R.-P. Montblanch, D. M. Kara, C. Palacios-Berraquero, A. R. Cadore, D. De Fazio, B. Pingault, E. Mostaani, H. Li, B. Chen, K. Watan- abe, T. Taniguchi, S. Tongay, G. Wang, A. C. Ferrari, and M. Atat¨ ure, Charge-tuneable biexciton complexes in monolayer WSe 2, N...

    2018

  3. [11]

    Z. Li, T. Wang, Z. Lu, C. Jin, Y. Chen, Y. Meng, Z. Lian, T. Taniguchi, K. Watanabe, S. Zhang, D. Smirnov, and S.-F. Shi, Revealing the biexciton and trion-exciton com- plexes in BN encapsulated WSe 2, Nature Communica- tions 9, 3719 (2018)

    2018

  4. [12]

    S.-Y. Chen, T. Goldstein, T. Taniguchi, K. Watanabe, and J. Yan, Coulomb-bound four- and five-particle inter- valley states in an atomically-thin semiconductor, Nature Communications 9, 3717 (2018)

    2018

  5. [13]

    Steinhoff, M

    A. Steinhoff, M. Florian, A. Singh, K. Tran, M. Ko- larczik, S. Helmrich, A. W. Achtstein, U. Woggon, N. Owschimikow, F. Jahnke, and X. Li, Biexciton fine structure in monolayer transition metal dichalcogenides, Nature Physics 14, 1199 (2018)

    2018

  6. [14]

    Chernikov, T

    A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2, Physical Review Let- ters 113, 076802 (2014)

    2014

  7. [15]

    K. He, N. Kumar, L. Zhao, Z. Wang, K. F. Mak, H. Zhao, and J. Shan, Tightly Bound Excitons in Mono- layer WSe2, Physical Review Letters 113, 026803 (2014)

    2014

  8. [16]

    Walther, R

    V. Walther, R. Johne, and T. Pohl, Giant optical nonlin- earities from Rydberg excitons in semiconductor micro- cavities, Nature Communications 9, 1309 (2018)

    2018

  9. [17]

    J. Gu, V. Walther, L. Waldecker, D. Rhodes, A. Raja, J. C. Hone, T. F. Heinz, S. K´ ena-Cohen, T. Pohl, and V. M. Menon, Enhanced nonlinear interaction of polari- tons via excitonic Rydberg states in monolayer WSe 2, Nature Communications 12, 2269 (2021)

    2021

  10. [18]

    Heck¨ otter, V

    J. Heck¨ otter, V. Walther, S. Scheel, M. Bayer, T. Pohl, and M. Aßmann, Asymmetric Rydberg blockade of giant excitons in Cuprous Oxide, Nature Communications 12, 3556 (2021)

    2021

  11. [19]

    Popert, Y

    A. Popert, Y. Shimazaki, M. Kroner, K. Watanabe, T. Taniguchi, A. ˙Imamo˘ glu, and T. Smole´ nski, Optical Sensing of Fractional Quantum Hall Effect in Graphene, Nano Letters 22, 7363 (2022)

    2022

  12. [20]

    T. Uto, B. Evrard, K. Watanabe, T. Taniguchi, M. Kro- ner, and A. ˙Imamo˘ glu, Interaction-Induced ac Stark Shift of Exciton-Polaron Resonances, Physical Review Letters 132, 056901 (2024)

    2024

  13. [21]

    Evrard, H

    B. Evrard, H. Adlong, A. Ghita, T. Uto, L. Cior- ciaro, K. Watanabe, T. Taniguchi, M. Kroner, and A. ˙Imamo˘ glu, ac Stark Spectroscopy of Interactions be- tween Moir´ e Excitons and Polarons, Physical Review X 15, 021002 (2025)

    2025

  14. [22]

    E. J. Sie, C. H. Lui, Y.-H. Lee, J. Kong, and N. Gedik, Observation of Intervalley Biexcitonic Optical Stark Ef- fect in Monolayer WS 2, Nano Letters 16, 7421 (2016)

    2016

  15. [23]

    C.-K. Yong, J. Horng, Y. Shen, H. Cai, A. Wang, C.-S. Yang, C.-K. Lin, S. Zhao, K. Watanabe, T. Taniguchi, S. Tongay, and F. Wang, Biexcitonic optical Stark effects in monolayer molybdenum diselenide, Nature Physics14, 1092 (2018)

    2018

  16. [24]

    Mysyrowicz, D

    A. Mysyrowicz, D. Hulin, A. Antonetti, A. Migus, W. T. Masselink, and H. Morko¸ c, ”Dressed Excitons” in a Multiple-Quantum-Well Structure: Evidence for an Op- tical Stark Effect with Femtosecond Response Time, Physical Review Letters 56, 2748 (1986)

    1986

  17. [25]

    Von Lehmen, D

    A. Von Lehmen, D. S. Chemla, J. P. Heritage, and J. E. Zucker, Optical Stark effect on excitons in GaAs quan- tum wells, Optics Letters 11, 609 (1986)

    1986

  18. [26]

    Unold, K

    T. Unold, K. Mueller, C. Lienau, T. Elsaesser, and A. D. Wieck, Optical Stark Effect in a Quantum Dot: Ultrafast Control of Single Exciton Polarizations, Physical Review Letters 92, 157401 (2004)

    2004

  19. [27]

    J. Kim, X. Hong, C. Jin, S.-F. Shi, C.-Y. S. Chang, M.- H. Chiu, L.-J. Li, and F. Wang, Ultrafast generation of pseudo-magnetic field for valley excitons in WSe 2 mono- layers, Science 346, 1205 (2014)

    2014

  20. [28]

    E. J. Sie, J. W. McIver, Y.-H. Lee, L. Fu, J. Kong, and N. Gedik, Valley-selective optical Stark effect in mono- layer WS2, Nature Materials 14, 290 (2015)

    2015

  21. [29]

    P. D. Cunningham, A. T. Hanbicki, T. L. Reinecke, K. M. McCreary, and B. T. Jonker, Resonant optical Stark ef- fect in monolayer WS2, Nature Communications 10, 5539 (2019)

    2019

  22. [30]

    A. O. Slobodeniuk, P. Koutensk´ y, M. Bartoˇ s, F. Troj´ anek, P. Mal´ y, T. Novotn´ y, and M. Koz´ ak, Ultra- fast valley-selective coherent optical manipulation with excitons in WSe 2 and MoS2 monolayers, npj 2D Materi- als and Applications 7, 17 (2023)

    2023

  23. [31]

    H. Choi, J. Kim, J. Park, J. Lee, W. Heo, J. Kwon, S.- H. Lee, F. Ahmed, K. Watanabe, T. Taniguchi, Z. Sun, M.-H. Jo, and H. Choi, Ultrafast Floquet engineering of Fermi-polaron resonances in charge-tunable monolayer WSe2 devices, Nature Communications 15, 10852 (2024)

    2024

  24. [32]

    Schmitt-Rink and D

    S. Schmitt-Rink and D. S. Chemla, Collective Excita- tions and the Dynamical Stark Effect in a Coherently Driven Exciton System, Physical Review Letters57, 2752 (1986)

    1986

  25. [33]

    Zimmermann, On the Dynamical Stark Effect of Exci- tons

    R. Zimmermann, On the Dynamical Stark Effect of Exci- tons. The Low-Field Limit, physica status solidi (b) 146, 545 (1988)

    1988

  26. [34]

    Schmitt-Rink, D

    S. Schmitt-Rink, D. Chemla, and D. Miller, Linear and nonlinear optical properties of semiconductor quantum wells, Advances in Physics 38, 89 (1989)

    1989

  27. [35]

    Combescot, Semiconductors in strong laser fields: from polariton to exciton optical Stark effect, Physics Reports 221, 167 (1992)

    M. Combescot, Semiconductors in strong laser fields: from polariton to exciton optical Stark effect, Physics Reports 221, 167 (1992)

    1992

  28. [36]

    Haug and S

    H. Haug and S. W. Koch, Quantum theory of the opti- cal and electronic properties of semiconductors, 4th ed. (World Scientific, New Jersey, NJ, 2005)

    2005

  29. [37]

    See supplemental material for more details on the theory and methods, which includes refs. [50-61]

  30. [38]

    Sidler, P

    M. Sidler, P. Back, O. Cotlet, A. Srivastava, T. Fink, M. Kroner, E. Demler, and A. ˙Imamo˘ glu, Fermi polaron- polaritons in charge-tunable atomically thin semiconduc- tors, Nature Physics 13, 255 (2017)

    2017

  31. [39]

    D. K. Efimkin and A. H. MacDonald, Many-body theory 7 of trion absorption features in two-dimensional semicon- ductors, Physical Review B 95, 035417 (2017)

    2017

  32. [40]

    E. Liu, J. Van Baren, Z. Lu, T. Taniguchi, K. Watanabe, D. Smirnov, Y.-C. Chang, and C. H. Lui, Exciton-polaron Rydberg states in monolayer MoSe 2 and WSe 2, Nature Communications 12, 6131 (2021)

    2021

  33. [41]

    Huang, K

    D. Huang, K. Sampson, Y. Ni, Z. Liu, D. Liang, K. Watanabe, T. Taniguchi, H. Li, E. Martin, J. Levin- sen, M. M. Parish, E. Tutuc, D. K. Efimkin, and X. Li, Quantum Dynamics of Attractive and Repulsive Polarons in a Doped MoSe 2 Monolayer, Physical Review X 13, 011029 (2023)

    2023

  34. [42]

    Tebbe, M

    D. Tebbe, M. Sch¨ utte, K. Watanabe, T. Taniguchi, C. Stampfer, B. Beschoten, and L. Waldecker, Tailor- ing the dielectric screening in WS2–graphene heterostruc- tures, npj 2D Materials and Applications 7, 29 (2023)

    2023

  35. [43]

    Scuri, Y

    G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watan- abe, P. Kim, M. D. Lukin, and H. Park, Large Excitonic Reflectivity of Monolayer MoSe2 Encapsulated in Hexag- onal Boron Nitride, Physical Review Letters 120, 037402 (2018)

    2018

  36. [44]

    Stier, N

    A. Stier, N. Wilson, K. Velizhanin, J. Kono, X. Xu, and S. Crooker, Magnetooptics of Exciton Rydberg States in a Monolayer Semiconductor, Physical Review Letters 120, 057405 (2018)

    2018

  37. [45]

    Goryca, J

    M. Goryca, J. Li, A. V. Stier, T. Taniguchi, K. Watan- abe, E. Courtade, S. Shree, C. Robert, B. Urbaszek, X. Marie, and S. A. Crooker, Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields, Nature Communications 10, 4172 (2019)

    2019

  38. [46]

    Shahnazaryan, I

    V. Shahnazaryan, I. Iorsh, I. A. Shelykh, and O. Kyri- ienko, Exciton-exciton interaction in transition-metal dichalcogenide monolayers, Physical Review B 96, 115409 (2017)

    2017

  39. [47]

    A. O. Slobodeniuk, P. Koutensk´ y, M. Bartoˇ s, F. Troj´ anek, P. Mal´ y, T. Novotn´ y, and M. Koz´ ak, Semi- conductor Bloch equation analysis of optical Stark and Bloch-Siegert shifts in monolayer WSe2 and MoS2, Phys- ical Review B 106, 235304 (2022)

    2022

  40. [48]

    L. B. Tan, O. K. Diessel, A. Popert, R. Schmidt, A. ˙Imamo˘ glu, and M. Kroner, Bose Polaron Interactions in a Cavity-Coupled Monolayer Semiconductor, Physical Review X 13, 031036 (2023)

    2023

  41. [49]

    Wegerhoff, M

    M. Wegerhoff, M. Scharfst¨ adt, S. Linden, and A. Bergschneider, Data set for letter ”Coherent Inter- action of 2s and 1s Exciton States in Transition-Metal Dichalcogenide Monolayers”, 10.5281/zenodo.15166311 (2025)

    2025 doi

  42. [50]

    L. V. Keldysh, Coloumb interaction in thin semiconduc- tor and semimetal films, Journal of Experimental and Theoretical Physics Letters 29, 716 (1979)

    1979

  43. [51]

    Cudazzo, I

    P. Cudazzo, I. V. Tokatly, and A. Rubio, Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane, Physical Re- view B 84, 085406 (2011)

    2011

  44. [52]

    N. S. Rytova, Screened potential of a point charge in a thin film (2020), arXiv:1806.00976

    2020 arXiv

  45. [53]

    J.-L. Uslu, T. Ouaj, D. Tebbe, A. Nekrasov, J. H. Bertram, M. Sch¨ utte, K. Watanabe, T. Taniguchi, B. Beschoten, L. Waldecker, and C. Stampfer, An open- source robust machine learning platform for real-time de- tection and classification of 2D material flakes, Machine Learnin...

    2024

  46. [54]

    P. J. Zomer, M. H. D. Guimar˜ aes, J. C. Brant, N. Tombros, and B. J. Van Wees, Fast pick up technique for high quality heterostructures of bilayer graphene and hexagonal boron nitride, Applied Physics Letters 105, 013101 (2014)

    2014

  47. [55]

    Liu, C.-C

    H.-L. Liu, C.-C. Shen, S.-H. Su, C.-L. Hsu, M.-Y. Li, and L.-J. Li, Optical properties of monolayer transition metal dichalcogenides probed by spectroscopic ellipsom- etry, Applied Physics Letters 105, 201905 (2014)

    2014

  48. [56]

    Y. Zhou, G. Scuri, J. Sung, R. Gelly, D. Wild, K. De Greve, A. Joe, T. Taniguchi, K. Watanabe, P. Kim, M. Lukin, and H. Park, Controlling Excitons in an Atom- ically Thin Membrane with a Mirror, Physical Review Letters 124, 027401 (2020)

    2020

  49. [57]

    D. S. Wild, Algorithms and Platforms for Quantum Sci- ence and Technology, Ph.D. thesis, Harvard University (2020)

    2020

  50. [58]

    S. Lee, T. Jeong, S. Jung, and K. Yee, Refractive In- dex Dispersion of Hexagonal Boron Nitride in the Visible and Near-Infrared, physica status solidi (b) 256, 1800417 (2019)

    2019

  51. [59]

    K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, Plasmonic Films Can Easily Be Better: Rules and Recipes, ACS Photonics 2, 326 (2015)

    2015

  52. [60]

    I. H. Malitson, Interspecimen Comparison of the Refrac- tive Index of Fused Silica, Journal of the Optical Society of America 55, 1205 (1965)

    1965

  53. [61]

    Schinke, P

    C. Schinke, P. Christian Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kr¨ oger, S. Winter, A. Schir- macher, S. Lim, H. T. Nguyen, and D. MacDonald, Un- certainty analysis for the coefficient of band-to-band ab- sorption of crystalline silicon, AIP Advances 5, 06716...

    2015

  54. [62]

    From the rms radii we deduce the Bohr radii rB λ and add a generous error to account for inaccuracies in our theoretical model

    and is our estimate based on the information given in the SM of [45]. From the rms radii we deduce the Bohr radii rB λ and add a generous error to account for inaccuracies in our theoretical model. WSe2 MoSe2 rrms 1s 1.7 nm 1 .1 nm rrms 2s 6.6 nm ≈ 4.5 nm r0 4.5 nm 3 .9 nm ϵ 4...

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.