Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Asymmetric trions in monolayer transition metal dichalcogenides

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Dark-exciton offset dominates the measured trion splitting in WSe2

desk verdict A genuinely new conceptual point about trion spectra—the measured splitting includes the bright-dark exciton binding difference—backed by careful numerics, but the headline WSe2 T3 number leans on a fitted mass ratio. read the letter →

arxiv 2507.16643 v1 pith:R6SBJ3FR submitted 2025-07-22 cond-mat.mes-hall cond-mat.quant-gas

Arthur Christianen , Atac Imamoglu This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.quant-gas
keywords trionsmonolayertransitionmetaldichalcogenidesbright-darkexcitonsplittingtrionbindingenergyexchangeinteractionRytova-KeldyshpotentialWSe2MoSe2
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

The paper argues that the energy difference between the trion peak and the bright exciton peak, routinely read as the trion binding energy, actually contains a second contribution: the binding-energy difference between the dark and bright excitons. Because dark excitons are more strongly bound than bright excitons in monolayer TMDs, the trion wave function becomes asymmetric, with the bright-exciton bond stretched relative to the dark-exciton bond. In WSe2 the model assigns roughly 31 meV of the measured 35 meV splitting to the bright\u2013dark difference and only about 4 meV to true trion binding, making that trion about twice as extended as usually assumed. The same calculation reproduces the measured trion energies in WSe2 and MoSe2 using dielectric screening parameters fixed by independent Rydberg-exciton measurements rather than adjusted to fit the trions. If this is right, optical spectra must be read with the dark exciton as the reference state for trion binding.

What carries the argument

The working object is the variational trion wave function $\psi_T(r_1,r_2,\theta,\alpha)=u(r_1,r_2,\theta)\exp(im\alpha)/\sqrt{2\pi r_1 r_2}$ with $m=0$, where $r_1$ and $r_2$ are the electron\u2013hole distances associated with the bright and dark excitons, $\theta$ is the angle between them, and $u$ is expanded in two-dimensional hydrogenic basis functions. Coulomb interactions are treated with the Rytova\u2013Keldysh potential, and exchange is added as a short-range Gaussian $V_X(r)=c_X\exp(-r^2/\sigma_X^2)$ whose strength follows from density-functional estimates. The mechanism that carries the argument is the additive offset $\Delta E_{\rm BD}$: once exchange and the conduction-band mass difference are included, the two branches of the wave function no longer contribute equally, the dark-exciton branch dominates, and the measured trion\u2013bright-exciton splitting inherits the bright\u2013dark exciton binding difference rather than measuring pure trion binding.

What would settle it

A direct measurement of the upper conduction-band electron mass in WSe2, for example from Landau-level spectroscopy or quantum transport, could pin the mass ratio near the DFT value of 27% rather than the assumed 33%; combined with a measurement of the dark-trion binding energy relative to the dark exciton, this would reveal whether the true T3 binding is really about 4 meV or substantially larger.

Watch

Extended reading notes

Core claim

The central claim is that the measured quantity $\Delta E_{\rm exp}=\omega_{\rm BX}-\omega_{\rm T}$ decomposes as $\Delta E_{\rm exp}=\Delta E_{\rm bind}+\Delta E_{\rm BD}$, where $\Delta E_{\rm bind}$ is the trion binding energy referenced to the dark exciton and $\Delta E_{\rm BD}=E_{\rm DX}-E_{\rm BX}$ is the bright\u2013dark exciton binding-energy difference. Including a short-range exchange interaction on the bright exciton and a 33% mass difference between the upper and lower conduction bands, the authors compute trion energies in WSe2 of $-21.2$, $-26.0$, and $-35.0$ meV for T1, T2, and T3, close to the measured $-21$, $-29$, and $-35$ meV, with the T3 splitting broken into $-30.7$ meV of bright\u2013dark offset and only $-4.2$ meV of actual binding. The resulting wave function for T3 has $\langle r_1\rangle \approx 4.1$ nm for the bright-exciton bond length, roughly twice the size conventionally assumed. In MoSe2 the same framework works with a comparable exchange energy of about 9 meV, but there the genuine trion binding remains the dominant part of the splitting because of the heavier carrier masses.

Load-bearing premise

The load-bearing input is the assumed 33% mass difference between the upper and lower conduction-band electrons in WSe2, chosen to match the T3 trion energy, while the independently predicted value is about 27% and measured masses deviate by 15\u201330% from theory.

Editorial extensions

If this is right

  • Commonly quoted trion binding energies for WSe2 should be revised downward: the T3 trion is bound by about 4 meV relative to the dark exciton, not 35 meV relative to the bright exciton.
  • The spatial size of the WSe2 T3 trion is roughly twice the conventional estimate, so overlap integrals and density estimates that assume a compact symmetric trion will need rescaling.
  • Optical spectra should be analyzed with the dark exciton as the reference state, making $\Delta E_{\rm BD}$ a required input alongside the trion binding energy.
  • The model restores consistency between trion energies and the independently measured dielectric screening constant $\kappa=4.4$, eliminating the need for a downward adjustment of $\kappa$ to fit trions.
  • The correction is material dependent: in MoSe2 the true trion binding still dominates the measured splitting, so the reinterpretation matters most in materials with light carriers such as WSe2.

Reading between the lines

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

  • If the T3 trion is really bound by only about 4 meV, its large bright-exciton bond length makes it unusually sensitive to the dielectric environment, so few-meV shifts between samples could be a natural consequence rather than an inconsistency.
  • The same asymmetry should govern dark trions and the hexciton feature: the paper's computed dark-trion position 41.6 meV below the bright exciton offers a direct, testable prediction for density-dependent photoluminescence.
  • A Landau-level or transport measurement of the WSe2 upper conduction-band mass near the DFT value of 27% would shift the T3 decomposition toward a larger true binding energy, providing a sharp experimental check of the 4 meV number.
  • The framework invites applying the same bright\u2013dark decomposition to charged excitons in other two-dimensional semiconductors and to trions in twisted heterobilayers, where the dark-exciton offset may be comparable to the binding.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This Letter argues that the commonly measured exciton-trion splitting ΔE_exp in monolayer TMDs is not simply the trion binding energy, because dark excitons are more strongly bound than the bright exciton. The authors solve the three-body Schrödinger equation with Rytova-Keldysh potentials, a short-range exchange interaction, and a correlated 2D-hydrogenic basis, and decompose ΔE_exp into a bright-dark exciton binding-energy difference ΔE_BD and a trion binding energy ΔE_bind defined relative to the dark exciton. For WSe2 and MoSe2 they report agreement with measured trion energies, with the WSe2 T3 trion dominated by ΔE_BD (30.7 meV) rather than ΔE_bind (4.2 meV); the associated wavefunction is strongly asymmetric, with the bright-exciton bond length stretched to about twice the commonly assumed trion size.

Significance. The conceptual message is important and likely correct as a matter of definition: the measured splitting contains the bright-dark exciton energy difference, and this contribution can be comparable to or larger than the trion binding contribution. The paper is also transparent: it separates the two contributions in Table I, explains the variational method in the main text and Supplemental Material, and explicitly identifies the mass-ratio assumption used to reproduce the WSe2 T3 energy. These are genuine strengths. The significance is nevertheless conditional, because the quantitative claims currently rely on parameters that are adjusted to match the same experimental values—most notably the WSe2 upper-conduction-band mass ratio and the MoSe2 exchange strength. The framework and mechanism are valuable, but the quantitative explanation is not yet independently constrained.

major comments (2)
  1. [Results (Table I, Fig. 3b)] The headline WSe2 T3 decomposition is calibrated to the experiment rather than predicted from independent inputs. The text states that the 35 meV singlet energy is reproduced by 'assuming a 33% mass difference' between the upper and lower conduction bands, while the independent DFT estimate is about 27% and the manuscript notes that experimentally determined masses deviate 15–30% from theory. Because ΔE_BD = 30.7 meV is about 88% of the 35 meV splitting, the central statement that only about 4 meV is true trion binding—and the related claim that ⟨r1⟩ ≈ 4.11 nm is about twice the usual trion size—is directly proportional to this fitted input. Please report the T2 and T3 results at the DFT mass ratio and across the stated experimental uncertainty, giving ΔE_BD, ΔE_bind, and the wavefunction expectation values, and state explicitly which conclusions survive over that range.
  2. [Results (MoSe2 discussion, Table I)] The MoSe2 column is also fitted: the 9 meV exchange interaction is inferred from the experimental trion energy ('consistent with an exchange interaction on the order of 9 meV'), and the cited 9 meV estimate from Ref. [18] is for MoS2 rather than an independent MoSe2 input. With the exchange strength set to 9 meV, ΔE_BD = 9.0 meV and the total becomes 24.3 meV, so this agreement is a consistency check rather than a quantitative prediction. I ask that IX(MoSe2) be computed with the same DFT-based method as for WSe2, or that a sensitivity scan over IX be provided and the wording adjusted accordingly.
minor comments (5)
  1. [Results, p. 3] The cross-reference 'As shown in Fig. 1b)' appears to be a typo; Fig. 1 has no panel b, and the surrounding text discusses the exchange-strength dependence shown in Fig. 3a.
  2. [Eq. (3) and Eq. (4)] Please state the units and normalization convention for IX and for the Gaussian exchange potential VX(r). As written, Eq. (3) uses IX as if it were an energy, while the contact interaction in 2D has units of energy times area; the calibration of cX relative to IX should be made explicit.
  3. [Table I] For comparison against experiment, please quote the experimental uncertainties from Refs. [7] and [12]; without them, the claimed agreement at the level of 0.2–3 meV has no quantitative benchmark.
  4. [Supplemental Material, Eq. (10)] The punctuation error 'Here. L^{2l}_i' should be corrected to 'Here, L^{2l}_i'.
  5. [Fig. 4 caption] It would be helpful to state explicitly in the caption that r1 is the bright-exciton bond length and r2 is the dark-exciton bond length, since this assignment is otherwise only given in the main text.

Circularity Check

2 steps flagged · score 6.0 of 10

Quantitative agreement for WSe2 T3 and MoSe2 is obtained by parameters tuned to those same experimental trion energies; the headline 'only 4 meV true trion binding' is therefore partly a fit, though T1 and T2 provide partially independent support.

  1. fitted input called prediction [Results section, paragraph after Fig. 3b; Table I (WSe2 T2/T3 rows) and Conclusion]
    "We reproduce the experimental 35 meV electron-trion (singlet) energy by assuming a 33 % mass difference [29] between the upper and lower conduction band electrons, compared to the theoretically predicted value of approximately 27 % [16, 19]."

    The 33% mass ratio is chosen so that the calculation reproduces the 35 meV T3 splitting, and Table I then reports -35.0 for T3 with ΔEBD = -30.7 and ΔEbind = -4.2. Since ΔEBD is the dominant contribution and scales with the mass ratio, the headline claim that 'only about 4 meV' is true trion binding is not an independent prediction: it is obtained from a parameter fit to the very energy it is used to explain. The split between ΔEBD and ΔEbind is an output of the calculation, but the total being matched is an input, and the dominant term is directly controlled by the fitted mass ratio. The T2 value (26 vs 29 meV) is a partly independent check, but the central T3 decomposition is not.

  2. fitted input called prediction [Results section, paragraph after T2/T3 discussion; Table I (MoSe2 T1 row)]
    "In MoSe2 the experimental trion binding energy is consistent with an exchange interaction on the order of 9 meV."

    The exchange strength IX is inferred from the MoSe2 experimental trion binding energy that Table I then presents as reproduced (-24.3 vs -24). Because IX directly determines ΔEBD = -9.0 and the total is ΔEBD + ΔEbind, the numerical agreement for MoSe2 is partly enforced by construction. Independent support from the MoS2 estimate (~9 meV) reduces but does not remove the fitted character of this input.

full rationale

The paper's central identity ΔEexp = ΔEBD + ΔEbind is definitional, not circular: once the trion binding is defined with respect to the dark exciton, the level scheme forces the sum. The independent T1 WSe2 prediction is a genuine test: using the DFT exchange energy of 11.5 meV from Ref. [16] and recalibrating r0 to the measured 1s exciton energy, the model gives 21.2 meV vs the measured 21 meV. The T2 value (26 vs 29 meV) also provides a partially independent check because it uses the same mass ratio but targets a different trion. However, the two load-bearing quantitative agreements are not fully independent: the WSe2 T3 mass ratio is chosen to reproduce the 35 meV splitting, and the MoSe2 exchange strength is inferred from the experimental trion binding energy. Consequently the headline numerical claims—'only ~4 meV true trion binding' and the MoSe2 reproduction—partially reduce to fitted inputs. The conceptual asymmetry mechanism is robust and externally motivated, and the paper is transparent about these choices, but the quantitative central claim is not yet independently constrained. No self-citation chain is load-bearing: Refs. [16], [18], and [19] are external DFT or experimental studies, while self-citations [7] and [20] supply experimental data and a numerical method, not the circular premise.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central conceptual claim (trion asymmetry) does not rest on fitted parameters, but the quantitative agreement with experiment is achieved with several hand-adjusted inputs: the WSe2 conduction band mass ratio, the MoSe2 exchange energy, and renormalized r0 values. The exchange range sigma_X is an ad hoc modeling choice. These parameters are not independently constrained by the trion data, which is why the quantitative 'explanation' is partially circular.

free parameters (5)
  • WSe2 upper conduction band electron mass (me,2) = 0.36 (33% mass difference vs me,1 = 0.54)
    Chosen to reproduce the 35 meV T3 trion energy; theoretical predictions give ~27% (me,2 ~ 0.39). Affects T2 and T3 ΔE_BD and the resulting trion energies.
  • MoSe2 exchange energy (IX_MoSe2) = ~9 meV
    Inferred from the experimental MoSe2 trion binding energy; the paper states the trion energy is consistent with a 9 meV exchange interaction.
  • Effective screening length r0 (WSe2) = 3.85 nm (renormalized from 4.4 nm)
    Adjusted to keep the same 1s exciton binding energy when exchange interactions are added; affects all trion energies.
  • Effective screening length r0 (MoSe2) = 3.64 nm (renormalized from 3.9 nm)
    Same renormalization as for WSe2, to preserve the experimental 1s exciton energy.
  • Exchange Gaussian range sigma_X = 2 Å
    Chosen by hand as a short-range width for the exchange potential; the integrated strength is fixed to DFT values, but the spatial form is an ad hoc modeling choice.
assumptions (6)
  • domain assumption Direct Coulomb interactions are described by the Rytova-Keldysh potential with effective parameters (kappa, r0) extracted from Rydberg exciton fits.
    Used in Eq. (2); the paper explicitly treats r0 as an effective parameter that absorbs short-distance physics (Theory section).
  • domain assumption Electrons and holes have quadratic dispersion.
    Assumed in the Hamiltonian (Eq. 5); valid at low doping and near band edges, excludes band structure effects such as trigonal warping and quantum geometry.
  • domain assumption The trion ground state has zero total angular momentum (m = 0) and the wave function factorizes with u(r1, r2, theta).
    Eqs. (1) and (7); higher partial waves are neglected.
  • ad hoc to paper Exchange interaction between a hole and the same-spin electron is modeled as a short-range Gaussian potential with strength from DFT and range sigma_X = 2 Å.
    Eq. (4); the form and range are chosen by hand, and the paper assumes this captures the exchange physics inside the trion.
  • domain assumption Opposite-spin electron-hole exchange and electron-electron exchange between different valleys are negligible.
    Stated to be an order of magnitude smaller; affects the claimed few-meV accuracy (Theory section).
  • domain assumption In the low-doping regime, many-body dressing of the exciton is small and the trion is an isolated three-body bound state.
    Opening of the Theory section; neglects Fermi sea effects and polaron dressing.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Asymmetric trions in monolayer transition metal dichalcogenides." pith.science (2026). https://pith.science/paper/R6SBJ3FR

@misc{pith2026250716643,
  author       = {Pith},
  title        = {Pith review of: Asymmetric trions in monolayer transition metal dichalcogenides},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R6SBJ3FR}},
  note         = {Machine review of arXiv:2507.16643}
}
read the original abstract

Exciton spectroscopy serves as a sensitive probe of electronic states in two-dimensional semiconductors. A prominent feature in optical spectra is the trion peak arising from the binding of a charge carrier to an exciton. The splitting between the exciton and trion peaks is usually interpreted as the trion binding energy, but we theoretically show that this view is incomplete. Since dark excitons are more strongly bound than the bright exciton, the trion wave function is asymmetric and a large contribution to the measured splitting is the difference between the bright and dark exciton binding energies. Our model quantitatively explains the measured trion energies in MoSe2 and WSe2, demonstrating the importance of the internal structure of the exciton for the interpretation of the optical response of transition metal dichalcogenides.

Figures

Figures reproduced from arXiv: 2507.16643 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic overview of the trion structure and its [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. a) Scheme of optical transitions relevant for trion [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. a) illustrates the effect of introducing electron￾hole exchange interactions. All parameters are fixed to the case of the positively charged trion (T1) in WSe2, and we add a variable-strength exchange interaction to the bright exciton potential. The blue curve shows the trion energy measured with respect to the bright exciton, while the red line shows the trion binding energy. We find that the trion binding energy d… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Wavefunctions [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. ARPES signatures of trions in van der Waals materials

    cond-mat.mes-hall 2025-11 conditional novelty 7.0 of 10

    Trions in doped monolayer TMDs are predicted to show ARPES peaks one electron–exciton binding energy below the conduction-band minimum, with mass-imbalanced trions producing a characteristic double-peak structure.

Reference graph

Works this paper leans on

36 extracted references · 29 canonical work pages · cited by 1 Pith paper

  1. [18]

    Robert, B

    C. Robert, B. Han, P. Kapuscinski, A. Delhomme, C. Faugeras, T. Amand, M. R. Molas, M. Bartos, K. Watanabe, T. Taniguchi, et al., Nat. Comm. 11, 4037 (2020)

    work page 2020

  2. [1]

    Smole´ nski, P

    T. Smole´ nski, P. E. Dolgirev, C. Kuhlenkamp, A. Popert, Y. Shimazaki, P. Back, X. Lu, M. Kroner, K. Watanabe, T. Taniguchi, et al., Nature 595, 53 (2021)

    work page 2021

  3. [2]

    J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, et al., Nature 622, 63 (2023)

    2023

  4. [3]

    F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, et al., Phys. Rev. X 13, 031037 (2023)

    work page 2023

  5. [4]

    Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Kn¨ uppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Nature 622, 69 (2023)

    2023

  6. [5]

    Y. Xia, Z. Han, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Nature 637, 833 (2025)

    2025

  7. [6]

    Y. Guo, J. Pack, J. Swann, L. Holtzman, M. Cothrine, K. Watanabe, T. Taniguchi, D. G. Mandrus, K. Barmak, J. Hone, et al., Nature 637, 839 (2025)

    work page 2025

  8. [7]

    Kiper, H

    N. Kiper, H. S. Adlong, A. Christianen, M. Kroner, K. Watanabe, T. Taniguchi, and A. ˙Imamo˘ glu, Phys. Rev. X 15, 011049 (2025)

    work page 2025

Show all 36 references
  1. [8]

    Van Tuan, S.-F

    D. Van Tuan, S.-F. Shi, X. Xu, S. A. Crooker, and H. Dery, Phys. Rev. Lett. 129, 076801 (2022)

    2022

  2. [9]

    Dijkstra, A

    A. Dijkstra, A. B. Mhenni, D. Van Tuan, E. C ¸ etiner, M. Schur-Wilkens, J. Kim, L. Steiner, K. Watanabe, T. Taniguchi, M. Barbone, et al., arXiv:2505.08923 (2025)

    2025

  3. [10]

    Sidler, P

    M. Sidler, P. Back, O. Cotlet, A. Srivastava, T. Fink, M. Kroner, E. Demler, and A. Imamoglu, Nat. Phys. 13, 255 (2017)

    2017

  4. [11]

    D. K. Efimkin and A. H. MacDonald, Phys. Rev. B 95, 035417 (2017)

    2017

  5. [12]

    Courtade, M

    E. Courtade, M. Semina, M. Manca, M. Glazov, C. Robert, F. Cadiz, G. Wang, T. Taniguchi, K. Watan- abe, M. Pierre, et al., Phys. Rev. B 96, 085302 (2017)

    2017

  6. [13]

    M. M. Glazov, J. Chem. Phys. 153, 10.1063/5.0012475 (2020)

    2020 doi

  7. [14]

    A. V. Stier, N. P. Wilson, K. A. Velizhanin, J. Kono, X. Xu, and S. A. Crooker, Phys. Rev. Lett. 120, 057405 (2018)

    2018

  8. [15]

    Goryca, J

    M. Goryca, J. Li, A. V. Stier, T. Taniguchi, K. Watanabe, E. Courtade, S. Shree, C. Robert, B. Urbaszek, X. Marie, and S. A. Crooker, Nat. Comm. 10, 4172 (2019)

    2019

  9. [16]

    P. Li, C. Robert, D. Van Tuan, L. Ren, M. Yang, X. Marie, and H. Dery, Phys. Rev. B106, 085414 (2022)

    2022

  10. [17]

    Zhang, T

    X.-X. Zhang, T. Cao, Z. Lu, Y.-C. Lin, F. Zhang, Y. Wang, Z. Li, J. C. Hone, J. A. Robinson, D. Smirnov, et al., Nat. Nanotechnol. 12, 883 (2017)

    2017

  11. [19]

    Korm´ anyos, G

    A. Korm´ anyos, G. Burkard, M. Gmitra, J. Fabian, V. Z´ olyomi, N. D. Drummond, and V. Fal’ko, 2D Ma- terials 2, 022001 (2015)

    2015

  12. [20]

    C. Fey, P. Schmelcher, A. Imamoglu, and R. Schmidt, Phys. Rev. B 101, 195417 (2020)

    2020

  13. [21]

    Rytova, Proc

    N. Rytova, Proc. MSU Phys. Astron. 3, 30 (1967)

    1967

  14. [22]

    Keldysh, Pis’ma Zh

    L. Keldysh, Pis’ma Zh. Eksp. Teor. Fiz. 29, 716 (1979)

    1979

  15. [23]

    Srivastava and A

    A. Srivastava and A. m. c. Imamo˘ glu, Phys. Rev. Lett. 115, 166802 (2015)

    2015

  16. [24]

    Liu, W.-Y

    G.-B. Liu, W.-Y. Shan, Y. Yao, W. Yao, and D. Xiao, Phys. Rev. B 88, 085433 (2013)

    2013

  17. [25]

    Dery, Phys

    H. Dery, Phys. Rev. B 94, 075421 (2016)

    2016

  18. [26]

    [15], we we fix κ = 4.4 for both materi- als instead of the value of κ = 4.5 taken for WSe2 in [15]

    Compared to Ref. [15], we we fix κ = 4.4 for both materi- als instead of the value of κ = 4.5 taken for WSe2 in [15]. We change r0 accordingly to keep the exciton binding energy the same

  19. [27]

    (8)], where µ1 and µ2 are the reduced masses of the bright and the dark exciton

    instead of µ1 and µ2 [see Eq. (8)], where µ1 and µ2 are the reduced masses of the bright and the dark exciton. The results are shown in the third column of Table I. 3 K 1 23 K' BX 1 BX b) c) a) ∆Eexp ωBX ωT ωDX ∆Ebind ∆SO ∆EBD FIG. 2. a) Scheme of optical transitions relevant ...

  20. [28]

    M. A. Semina, J. V. Mamedov, and M. M. Glazov, Oxf. Open Mater. Sci. 3, itad004 (2023)

    2023

  21. [29]

    Hichri and S

    A. Hichri and S. Jaziri, Phys. Rev. B 102, 085407 (2020)

    2020

  22. [30]

    Measured with respect to the lower conduction band elec- tron mass

  23. [31]

    B. C. Mulkerin, A. Tiene, F. M. Marchetti, M. M. Parish, and J. Levinsen, Phys. Rev. Lett. 131, 106901 (2023)

    2023

  24. [32]

    Zipfel, K

    J. Zipfel, K. Wagner, J. D. Ziegler, T. Taniguchi, K. Watanabe, M. A. Semina, and A. Chernikov, J. Chem. Phys. 153, 10.1063/5.0012721 (2020). 6

    2020 doi

  25. [33]

    Klein, M

    J. Klein, M. Florian, A. H¨ otger, A. Steinhoff, A. Del- homme, T. Taniguchi, K. Watanabe, F. Jahnke, A. W. Holleitner, M. Potemski, C. Faugeras, A. V. Stier, and J. J. Finley, Phys. Rev. B 105, L041302 (2022)

    2022

  26. [34]

    Massignan, R

    P. Massignan, R. Schmidt, G. E. Astrakharchik, A. ˙Imamoglu, M. Zwierlein, J. J. Arlt, and G. M. Bruun, arXiv:2501.09618 (2025)

    2025 arXiv

  27. [35]

    Al-Marzoug, H

    S. Al-Marzoug, H. Bahlouli, and M. Abdelmonem, arXiv:1110.0958 (2011). SUPPLEMENT AL MA TERIAL For the trion binding calculations, we follow Ref. [20]. In brief: we set ℏ = 1 and assume a quadratic dispersion of the electrons and holes, leading to a Hamiltonian H = − X i=1,2,3...

    2011 arXiv

  28. [36]

    We have chosen basis functions ϕ in the form of 2D-hydrogenic wave functions ϕl,i = ( r λ )l+1/2L2l i ( r λ ) exp(− r 2λ ) s Γ(i + 1) λΓ(i + 2l + 1)

    Due to the mirror symmetry, the even and odd functions in θ decouple, and the ground-state trion lives in the even sector. We have chosen basis functions ϕ in the form of 2D-hydrogenic wave functions ϕl,i = ( r λ )l+1/2L2l i ( r λ ) exp(− r 2λ ) s Γ(i + 1) λΓ(i + 2l + 1). (10)...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.