Pith. sign in

REVIEW 4 major objections 5 minor 74 references

Excitons and trions in CrSBr bilayers

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The trion observed in CrSBr bilayers is the direct intralayer state, with 18–20 meV binding energy.

desk verdict Plausible order-of-magnitude theory for CrSBr trions, with an honest but unresolved short-range screening caveat; deserves review. read the letter →

arxiv 2411.15493 v2 pith:GXIXFIKY submitted 2024-11-23 cond-mat.mes-hall cond-mat.mtrl-scicond-mat.other

M. A. Semina , F. Tabataba-Vakili , A. Rupp , A.S. Baimuratov , A. Högele , M.M. Glazov This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-scicond-mat.other
keywords CrSBrexcitonbindingenergytrionRytova–KeldyshpotentialanisotropiceffectivemassbilayervanderWaalsheterostructureinterlayerFermipolaron
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 asks what Coulomb-bound electron–hole and two-electron–hole complexes look like in a two-dimensional semiconductor whose electron and hole masses are very different along the two in-plane directions, taking CrSBr bilayers as the concrete material. Using an effective-mass Hamiltonian with a screened Rytova–Keldysh interaction generalized to two polarizable layers, it finds a direct intralayer exciton binding energy of about 200 meV and a direct intralayer trion binding energy of 18–20 meV, which it regards as consistent with recent experiments. It also finds that interlayer complexes lose binding energy quickly with separation: the same-layer indirect trion has only about 2–3 meV binding at realistic distances, and the split-layer trion is essentially unbound. The paper concludes that the trion seen in the experiment is the direct intralayer one, and it gives radiative decay rates, exchange-induced anisotropic dispersions, and Fermi-polaron energy shifts for the same model.

What carries the argument

The central object is the bilayer Rytova–Keldysh potential, a screened Coulomb interaction in which each CrSBr layer is a polarizable dielectric sheet; its same-layer and cross-layer Fourier transforms, Eqs. (11a) and (11b), encode the dependence on interlayer distance $d$ and reduce to the monolayer potential as $d\to\infty$. Binding energies come from solving the exciton and trion Schrödinger equations with this potential and strongly anisotropic kinetic terms, using finite-element calculations as a numerical check and a variational envelope—an exponential with separate length parameters along $x$ and $y$, plus a correlation factor for the two identical carriers—for the trions. The mass anisotropy ratio $M=\mu_x/\mu_y\approx20$ is what elongates the exciton wavefunction and controls how steeply indirect binding energies fall with $d$.

What would settle it

A decisive observation would be a gated hBN-encapsulated CrSBr bilayer measurement of the exciton–trion splitting at low electron density: a trion binding energy outside the 14–20 meV range, or the appearance of a second charged-exciton line with a binding energy of several meV at an interlayer distance near 0.8 nm, would contradict the paper's assignment that the observed trion is the direct intralayer $X_d^-$ and that the split-layer trion is essentially unbound.

Watch

Extended reading notes

Core claim

Within a minimum three-band $\mathbf{k}\cdot\mathbf{p}$ model, the paper claims that CrSBr has strongly anisotropic carrier masses ($m_e^x=7.31m_0$, $m_e^y=0.14m_0$; $m_h^x=2.84m_0$, $m_h^y=0.45m_0$), hence a reduced-mass ratio $\mu_x/\mu_y\approx 20$. Solving the relative-motion Schrödinger equation for excitons and trions with the bilayer-screened Rytova–Keldysh potential yields a direct exciton binding energy around 200 meV and a direct trion binding energy of 14–20 meV (quoted as 18–20 meV in the conclusion) for hBN-encapsulated bilayers, in reasonable agreement with measured values. The spatially indirect exciton remains bound at all interlayer distances, but the split-layer trion $X_i^{\prime-}$ loses binding already for $d\gtrsim0.25\,a_B$ and is unlikely to be observable, while the indirect trion with both electrons in one layer has about 2–3 meV binding for $d=0.7$–$0.9$ nm. The central assignment is therefore that the trion observed in Ref. [15] is the direct intralayer trion $X_d^-$.

Load-bearing premise

The load-bearing assumption is that electrons and holes form weakly bound effective-mass particles moving in a smoothly screening dielectric, even though the calculated exciton sizes (about 0.6 nm and 1.8 nm) and the 0.8 nm interlayer distance are comparable to the unit-cell size.

Editorial extensions

If this is right

  • For hBN-encapsulated CrSBr bilayers, the trion line seen in photoluminescence should be assigned to the direct intralayer trion with 18–20 meV binding energy, and no split-layer interlayer trion should appear at realistic interlayer distances.
  • Direct intralayer exciton and trion binding energies increase with interlayer distance because the second layer contributes less screening, while indirect (interlayer) binding energies decrease with distance.
  • The same-layer indirect trion, with both electrons in one layer and the hole in the other, remains weakly bound, about 2–3 meV at $d=0.7$–$0.9$ nm, and is the most plausible interlayer charged state.
  • The bright exciton emits only in $y$ polarization, and at finite momentum its dispersion is anisotropic, with group velocity larger along the magnetic easy $b$-axis, which should be visible in exciton propagation.

Reading between the lines

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

  • Read as a general trend beyond CrSBr, the distance-dependence curves imply that in any strongly anisotropic van der Waals magnet the charged exciton most likely to be observed is the intralayer trion, because interlayer trions lose binding energy rapidly once carriers sit in different layers.
  • The predicted anisotropy of exciton propagation could be tested by time-resolved or spatially resolved photoluminescence of an expanding exciton cloud in monolayer or bilayer CrSBr, independently of the trion assignment.
  • Tuning the interlayer distance with pressure or twist angle should leave the direct trion binding nearly constant while moving the same-layer indirect trion through its few-meV binding window, offering a clean experimental knob to separate intra- and interlayer charged states.
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

4 major / 5 minor

Summary. The paper develops a theory of neutral and charged excitons in anisotropic two-dimensional semiconductors, applied to CrSBr monolayers and bilayers. Using an effective-mass Hamiltonian with Rytova-Keldysh and bilayer-screened Coulomb interactions, the authors compute exciton and trion binding energies variationally and by finite-element methods, obtaining a direct exciton binding energy around 200 meV and a direct intralayer trion binding energy of 18–20 meV for the assumed parameters. They also study indirect (interlayer) excitons and trions, finding X_i^- binding of about 2–3 meV and X_i'^- essentially unbound at realistic interlayer distances. The paper additionally addresses radiative decay, long-range exchange effects on exciton dispersion, and Fermi-polaron/Suris-tetron correlations, and compares the trion binding estimates with the experiments of Ref. [15].

Significance. If the quantitative assignments are correct, the paper resolves the nature of the trion observed in CrSBr bilayers (intralayer X_d^-) and provides a falsifiable prediction that the split-layer trion X_i'^- is unbound. The work is also useful as a general framework for excitons and trions in strongly anisotropic 2D semiconductors. Strengths include the cross-check of variational trion energies against finite-element calculations for isotropic cases, the explicit discussion of the model's limitations, and the analytic treatment of quasi-1D asymptotics and Fermi-polaron correlations. The main quantitative claim, however, rests on a model whose short-range screening and effective-mass description the authors themselves state are not entirely applicable at the relevant length scales, so the specific 18–20 meV assignment and the X_i'^- unbound prediction require additional robustness checks before they can be considered definitive.

major comments (4)
  1. [Sec. III B (paragraph beginning 'We stress that here both the interlayer distance d...')] This paragraph explicitly states that 'the effective mass approximation and macroscopic description of the screening by a dielectric between the layers are not entirely applicable' because d and r0 are on the order of the unit cell. The central quantitative claim—that the trion observed in Ref. [15] is the intralayer X_d^- with 18–20 meV binding and that X_i'^- is unbound—is controlled precisely by the short-range part of the Rytova-Keldysh potential and by small differences of large energies. The manuscript should provide a quantitative robustness test, for example by varying r0 and d over their plausible ranges, by evaluating the anisotropic polarizability case of Eq. (13), or by benchmarking against a microscopic dielectric function. Without such a test, the specific assignment to Ref. [15] is not secured to the precision implied by the conclusion.
  2. [Sec. III A (text following Eq. (19))] The authors state that the variational accuracy of the absolute trion energy is better than 5–10% but that the binding-energy accuracy is only 20–30% because it is a difference of two large energies. For the quoted X_d^- binding of 18–20 meV, this implies an uncertainty of roughly ±4–6 meV. The conclusion that the measured trion in Ref. [15] is compatible with this value, and the contrast with the 2–3 meV X_i^- binding, should be presented with this uncertainty explicitly, for instance as error bars in Fig. 7(b). Without that, the 'reasonable agreement' claim is stronger than the stated numerical accuracy warrants.
  3. [Sec. III A (first paragraph, polarizability anisotropy)] The neglect of the in-plane anisotropy of the CrSBr polarizability is justified only by the assertion that it 'does not change the results much,' citing a factor-of-2 variation of the susceptibility in Ref. [3]. No calculation is shown. Since the trion binding energy is only about 5% of the exciton binding energy and the potential enters in its logarithmic short-range regime (r0≈3.9 nm > rx≈0.6 nm), a factor-of-2 change in r0 along x could shift the 18–20 meV window by an amount comparable to the claimed accuracy. The authors should either perform the anisotropic calculation using Eq. (13) with αx ≠ αy or explicitly bound the resulting shift.
  4. [Sec. III B and Conclusion] The statement that X_i'^- 'is unlikely to be observed in bilayer CrSBr' is categorical, but the calculation finds its binding energy dropping to negligible values for d≳0.25 a_2D^B ≈ 0.28 nm, well below the nominal d≈0.8 nm. Because this near-threshold behavior is controlled by the same short-range potential whose macroscopic description the authors disclaim, the prediction should be reported as an extrapolation with a stated uncertainty rather than as a definitive no-observation statement. A quantitative estimate of how the X_i'^- binding depends on the uncertainty in r0, d, and the anisotropic polarizability is needed to support the conclusion.
minor comments (5)
  1. [Introduction] The phrase 'few-patricle Hamilonian' should read 'few-particle Hamiltonian'.
  2. [Eq. (B5)] The second kinetic term in the denominator is written with k_x^2 but should be k_y^2, consistent with the integration over k_y and with Eq. (B2).
  3. [Fig. 7 caption] The caption refers to 'dashed vertical lines in panels (b) and (d)', but the printed figure contains only panels (a) and (b); please update the caption or the panel layout.
  4. [Sec. IV, Eq. (21)] The condition 'K ⩽ qb' should use the magnitude of the two-dimensional wavevector, e.g., |K| ≤ qb, to avoid ambiguity with the component Ky used in the same equation.
  5. [Fig. 5(a) legend] The legend appears to contain two identical entries for 'μ_x/μ_y = 1, numerical calc.'; please disambiguate which curve corresponds to the finite-element result.

Circularity Check

2 steps flagged · score 2.0 of 10

Core exciton/trion calculation is self-contained; only the experimental-validation loop runs through a co-authored, self-justified citation.

  1. self citation load bearing [Section III B, paragraph following Fig. 7(b)]
    "Since its binding energy is significantly smaller than that reported in Ref. [15], we can conclude, that the most likely type of the trion observed in Ref. [15] is the direct intralayer one with a binding energy in the range 18...20 meV for the relevant interlayer distance d."

    The assignment of the measured trion to the intralayer X_d^- state is made by comparing the calculated indirect-trion binding energy with the value 'reported in Ref. [15]'. Ref. [15] shares multiple authors with the present paper (Tabataba-Vakili, Rupp, Baimuratov, Högele, and Glazov), so the decisive comparison is a self-citation used to choose among the candidate trion species. The comparison is not a definitional identity, since the X_d^- binding energy was computed rather than fitted to that measurement, but it makes the experimental confirmation partially internal to the author group.

  2. self citation load bearing [Appendix B, final sentence]
    "This analysis can be extended to account for the direct and indirect excitons and the corresponding trions, justifying the approach used in Ref. [15]."

    Ref. [15] is simultaneously used as the experimental benchmark for the trion binding energies and described here as an approach that the present paper's Appendix B justifies. This creates a mutual-support loop: the theory validates the experimental paper's analysis, and that same experimental paper is then cited as external confirmation of the theory. The loop is ancillary rather than definitional, because the main variational/finite-element binding-energy results do not depend on Ref. [15] for their derivation.

full rationale

The central derivation is self-contained: the exciton and trion binding energies follow from the effective-mass Hamiltonian (Eq. 5) and the screened Rytova-Keldysh / bilayer potentials (Eqs. 6, 11), with effective masses taken from Ref. [3] and the screening radius r0 calibrated to a monolayer exciton binding energy of about 230 meV. The trion binding energy is not a re-parametrization of that fit; it is a three-body variational/finite-element result, so the fitted-input-called-prediction pattern is not established. The main circularity concern is the experimental-validation chain: the paper identifies the trion of Ref. [15] as the intralayer X_d^- by comparing with a co-authored experimental paper, and Appendix B states that the present theory justifies the approach used in that same Ref. [15]. This is a genuine but mild self-citation loop that does not reduce the central calculation to its inputs. The paper's own caveat that the effective-mass and macroscopic screening assumptions 'are not entirely applicable' at the computed length scales is a model-validity risk, not a circularity, and is excluded from the circularity score under the stated rules. Overall score 2.0: one non-load-bearing-to-the-derivation self-citation loop, with independent content in the binding-energy calculation.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central numbers rest on a small set of model inputs rather than on new physical constants. Most inputs come from prior DFT and experiment; the screening radius is calibrated to the exciton binding energy; the interlayer distance is treated as an effective parameter; and the effective-mass and screening assumptions are explicitly acknowledged as marginal at the relevant length scales.

free parameters (3)
  • screening radius r0 = 3.5 a_2D^B, about 3.9 nm
    Chosen so the monolayer exciton binding energy is about 230 meV (Sec III A); it sets the energy scale for all binding energies, though trion binding is computed relative to the exciton.
  • interlayer distance d = 0.7-0.9 nm for realistic comparison; varied over a wide range
    Treated as an effective, phenomenological quantity because the interlayer distance is on the scale of the unit cell; binding energies of indirect complexes depend strongly on d.
  • exciton-electron short-range interaction V0 = not numerically fixed in the paper
    Introduced in Appendix B to parametrize exciton-electron attraction in the Fermi polaron analysis; binding energy is expressed through V0, but it is not fit to CrSBr data and is not central to the main estimates.
assumptions (5)
  • domain assumption Effective mass approximation with parabolic electronic bands
    Used from Sec II, Eq (5); the paper acknowledges this approximation is not entirely applicable at unit-cell length scales.
  • domain assumption Static Rytova-Keldysh dielectric screening model
    Eqs (6) and (11) ignore dynamical screening and are stated to be valid only for in-plane distances exceeding the lattice constant.
  • domain assumption Spin-layer locking with forbidden interlayer tunneling
    Sec II: antiferromagnetic alignment makes tunneling matrix elements vanish, so bilayer states are independent monolayer copies; if this fails, layer splitting and interlayer oscillator strength appear.
  • domain assumption Neglect of dielectric and polarizability anisotropy
    Sec III: the authors assume isotropic screening for the main calculations, estimating the susceptibility anisotropy factor is about 2 versus the 20-50 mass anisotropy.
  • domain assumption Variational trial wavefunctions accurately capture the ground states
    Sec III A: variational binding energies are stated to be accurate to 20-30 percent, with finite-element checks only for isotropic masses.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Excitons and trions in CrSBr bilayers." pith.science (2026). https://pith.science/paper/GXIXFIKY

@misc{pith2026241115493,
  author       = {Pith},
  title        = {Pith review of: Excitons and trions in CrSBr bilayers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GXIXFIKY}},
  note         = {Machine review of arXiv:2411.15493}
}
read the original abstract

We study theoretically the neutral and charged excitons in two-dimensional semiconductors with anisotropic dispersion of charge carriers. Such a situation is realized in CrSBr-based van der Waals heterostructures. We calculate the binding energies of excitons and trions and explore their dependence on the mass ratio, dielectric screening, and interlayer distance in bilayer structures. We also address the effects of exciton-light coupling, including the radiative decay and long-range electron-hole exchange interaction, and briefly analyze correlations between the excitons and the Fermi sea of resident electrons. The estimates for CrSBr bilayers are in reasonable agreement with recent experiments.

Figures

Figures reproduced from arXiv: 2411.15493 by the authors.

Figure 2
Figure 2. FIG. 2. Energy spectrum of CrSBr monolayer calculated us [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Schematics of spectral lines of the Coulomb complexes [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a) Direct exciton ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Direct trion ( [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Binding energy of spatially indirect exciton [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Binding energies of direct and spatially indirect excitons (a) and trions (b) calculated using the screened Rytova [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

74 extracted references · 62 canonical work pages

  1. [15]

    Tabataba-Vakili, H

    F. Tabataba-Vakili, H. P. G. Nguyen, A. Rupp, K. Mosina, A. Papavasileiou, K. Watanabe, T. Taniguchi, P. Maletinsky, M. M. Glazov, Z. Sofer, A. S. Baimura- tov, and A. H¨ ogele, Doping-control of excitons and mag- netism in few-layer CrSBr, Nature Communications 15, 4735 (2024)

    work page 2024

  2. [3]

    Klein, B

    J. Klein, B. Pingault, M. Florian, M.-C. Heißenb¨ uttel, A. Steinhoff, Z. Song, K. Torres, F. Dirnberger, J. B. Curtis, M. Weile, A. Penn, T. Deilmann, R. Dana, R. Bushati, J. Quan, J. Luxa, Z. Sofer, A. Al` u, V. M. Menon, U. Wurstbauer, M. Rohlfing, P. Narang, M. Lonˇ car, and F. M. Ross, The Bulk van der Waals Lay- ered Magnet CrSBr is a Quasi-1D Mater...

    work page 2023

  3. [1]

    E. J. Telford, A. H. Dismukes, K. Lee, M. Cheng, A. Wi- eteska, A. K. Bartholomew, Y.-S. Chen, X. Xu, A. N. Pasupathy, X. Zhu, C. R. Dean, and X. Roy, Layered Antiferromagnetism Induces Large Negative Magnetore- sistance in the van der Waals Semiconductor CrSBr, Ad- vanced Materials 32, 2003240 (2020)

    work page 2020

  4. [2]

    N. P. Wilson, K. Lee, J. Cenker, K. Xie, A. H. Dismukes, E. J. Telford, J. Fonseca, S. Sivakumar, C. Dean, T. Cao, X. Roy, X. Xu, and X. Zhu, Interlayer electronic coupling on demand in a 2D magnetic semiconductor, Nature Ma- terials 20, 1657 (2021)

    work page 2021

  5. [4]

    Dirnberger, J

    F. Dirnberger, J. Quan, R. Bushati, G. M. Diederich, M. Florian, J. Klein, K. Mosina, Z. Sofer, X. Xu, A. Kamra, F. J. Garc ´ ıa-Vidal, A. Al` u, and V. M. Menon, Magneto-optics in a van der Waals magnet tuned by self- hybridized polaritons, Nature 620, 533 (2023)

    work page 2023

  6. [5]

    Klein and F

    J. Klein and F. M. Ross, Materials beyond monolayers: The magnetic quasi-1D semiconductor CrSBr, Journal of Materials Research 10.1557/s43578-024-01459-6 (2024)

    doi:10.1557/s43578-024-01459-6 2024

  7. [6]

    Smolenski, M

    S. Smolenski, M. Wen, Q. Li, E. Downey, A. Alfrey, W. Liu, A. L. N. Kondusamy, A. Bostwick, C. Jozwiak, E. Rotenberg, L. Zhao, H. Deng, B. Lv, D. Zgid, E. Gull, and N. H. Jo, Large Exciton Binding Energy in the Bulk van der Waals Magnet CrSBr, arXiv:2403.13897 (2024)

    arXiv 2024

  8. [7]

    M. D. Watson, S. Acharya, J. E. Nunn, L. Nagireddy, D. Pashov, M. R¨ osner, M. van Schilfgaarde, N. R. Wil- son, and C. Cacho, Giant exchange splitting in the elec- tronic structure of A-type 2D antiferromagnet CrSBr, npj 2D Materials and Applications 8, 54 (2024)

    work page 2024

Show all 74 references
  1. [8]

    G¨ oser, W

    O. G¨ oser, W. Paul, and H. G. Kahle, Magnetic properties of CrSBr, J. Magn. Magn. Mater. 92, 129 (1990)

    1990

  2. [9]

    Scheie, M

    A. Scheie, M. Ziebel, D. G. Chica, Y. J. Bae, X. Wang, A. I. Kolesnikov, X. Zhu, and X. Roy, Spin Waves and Magnetic Exchange Hamiltonian in CrSBr, Advanced Science 9, 2202467 (2022)

    2022

  3. [10]

    K. Lee, A. H. Dismukes, E. J. Telford, R. A. Wiscons, J. Wang, X. Xu, C. Nuckolls, C. R. Dean, X. Roy, and X. Zhu, Magnetic Order and Symmetry in the 2D Semi- conductor CrSBr, Nano Letters 21, 3511 (2021)

    2021

  4. [11]

    X. Bo, F. Li, X. Xu, X. Wan, and Y. Pu, Calculated mag- netic exchange interactions in the van der Waals layered magnet CrSBr, New J. Phys. 25, 013026 (2023)

    2023

  5. [12]

    Y. J. Bae, J. Wang, A. Scheie, J. Xu, D. G. Chica, G. M. Diederich, J. Cenker, M. E. Ziebel, Y. Bai, H. Ren, C. R. Dean, M. Delor, X. Xu, X. Roy, A. D. Kent, and X. Zhu, Exciton-coupled coherent magnons in a 2D semiconduc- 13 tor, Nature 609, 282 (2022)

    2022

  6. [13]

    G. M. Diederich, J. Cenker, Y. Ren, J. Fonseca, D. G. Chica, Y. J. Bae, X. Zhu, X. Roy, T. Cao, D. Xiao, and X. Xu, Tunable interaction between excitons and hybridized magnons in a layered semiconductor, Nature Nanotechnology 18, 23 (2023)

    2023

  7. [14]

    W. M. Linhart, M. Rybak, M. Birowska, P. Scharoch, K. Mosina, V. Mazanek, D. Kaczorowski, Z. Sofer, and R. Kudrawiec, Optical markers of magnetic phase tran- sition in CrSBr, J. Mater. Chem. C 11, 8423 (2023)

    2023

  8. [16]

    E. L. Ivchenko, Optical spectroscopy of semiconductor nanostructures (Alpha Science, Harrow UK, 2005)

    2005

  9. [17]

    C. F. Klingshirn, Semiconductor Optics (Springer Berlin Heidelberg, 2012)

    2012

  10. [18]

    H. Yu, X. Cui, X. Xu, and W. Yao, Valley excitons in two- dimensional semiconductors, National Science Review 2, 57 (2015)

    2015

  11. [19]

    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, Rev. Mod. Phys. 90, 021001 (2018)

    2018

  12. [20]

    M. V. Durnev and M. M. Glazov, Excitons and trions in two-dimensional semiconductors based on transition metal dichalcogenides, Physics-Uspekhi 61, 825 (2018)

    2018

  13. [21]

    M. A. Semina and R. A. Suris, Localized excitons and tri- ons in semiconductor nanosystems, Physics-Uspekhi 65, 111 (2022)

    2022

  14. [22]

    Bianchi, S

    M. Bianchi, S. Acharya, F. Dirnberger, J. Klein, D. Pashov, K. Mosina, Z. Sofer, A. N. Rudenko, M. I. Katsnelson, M. van Schilfgaarde, M. R¨ osner, and P. Hof- mann, Paramagnetic electronic structure of crsbr: Com- parison between ab initio GW theory and angle-resolved photoem...

    2023

  15. [23]

    Suris, V

    R. Suris, V. Kochereshko, G. Astakhov, D. Yakovlev, W. Ossau, J. N¨ urnberger, W. Faschinger, G. Landwehr, T. Wojtowicz, G. Karczewski, and J. Kossut, Exci- tons and trions modified by interaction with a two- dimensional electron gas, physica status solidi (b) 227, 343 (2001)

    2001

  16. [24]

    A. V. Koudinov, C. Kehl, A. V. Rodina, J. Geurts, D. Wolverson, and G. Karczewski, Suris tetrons: Pos- sible spectroscopic evidence for four-particle optical ex- citations of a two-dimensional electron gas, Phys. Rev. Lett. 112, 147402 (2014)

    2014

  17. [25]

    Sidler, P

    M. Sidler, P. Back, O. Cotlet, A. Srivastava, T. Fink, M. Kroner, E. Demler, and A. Imamoglu, Fermi polaron- polaritons in charge-tunable atomically thin semiconduc- tors, Nature Physics 13, 255 (2016)

    2016

  18. [26]

    Chaves, M

    A. Chaves, M. Z. Mayers, F. M. Peeters, and D. R. Reich- man, Theoretical investigation of electron-hole complexes in anisotropic two-dimensional materials, Phys. Rev. B 93, 115314 (2016)

    2016

  19. [27]

    Van der Donck and F

    M. Van der Donck and F. M. Peeters, Excitonic com- plexes in anisotropic atomically thin two-dimensional materials: Black phosphorus and TiS 3, Phys. Rev. B 98, 235401 (2018)

    2018

  20. [28]

    N. S. Rytova, Screened potential of a point charge in a thin film, Proc. MSU, Phys., Astron. 3, 18 (1967)

    1967

  21. [29]

    L. V. Keldysh, Coulomb interaction in thin semiconduc- tor and semimetal films, JETP Lett. 29, 658 (1979)

    1979

  22. [30]

    Cudazzo, I

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

    2011

  23. [31]

    T. C. Berkelbach, M. S. Hybertsen, and D. R. Reich- man, Theory of neutral and charged excitons in mono- layer transition metal dichalcogenides, Phys. Rev. B 88, 045318 (2013)

    2013

  24. [32]

    M. A. Semina, Excitons and trions in bilayer van der Waals heterostructures, Physics of the Solid State 61, 2218 (2019)

    2019

  25. [33]

    N. A. Asriyan, I. L. Kurbakov, A. K. Fedorov, and Y. E. Lozovik, Optical probing in a bilayer dark-bright conden- sate system, Phys. Rev. B 99, 085108 (2019)

    2019

  26. [34]

    Latini, T

    S. Latini, T. Olsen, and K. S. Thygesen, Excitons in van der Waals heterostructures: The important role of dielec- tric screening, Phys. Rev. B 92, 245123 (2015)

    2015

  27. [35]

    K. S. Thygesen, Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals het- erostructures, 2D Materials 4, 022004 (2017)

    2017

  28. [36]

    Van Tuan, M

    D. Van Tuan, M. Yang, and H. Dery, Coulomb interac- tion in monolayer transition-metal dichalcogenides, Phys. Rev. B 98, 125308 (2018)

    2018

  29. [37]

    M. M. Glazov and A. Chernikov, Breakdown of the static approximation for free carrier screening of excitons in monolayer semiconductors, physica status solidi (b) 255, 1800216 (2018)

    2018

  30. [38]

    Scharf, D

    B. Scharf, D. Van Tuan, I. ˇZuti´ c, and H. Dery, Dynamical screening in monolayer transition-metal dichalcogenides and its manifestations in the exciton spectrum, Journal of Physics: Condensed Matter 31, 203001 (2019)

    2019

  31. [39]

    Courtade, M

    E. Courtade, M. Semina, M. Manca, M. M. Glazov, C. Robert, F. Cadiz, G. Wang, T. Taniguchi, K. Watan- abe, M. Pierre, W. Escoffier, E. L. Ivchenko, P. Renucci, X. Marie, T. Amand, and B. Urbaszek, Charged excitons in monolayer WSe2: Experiment and theory, Phys. Rev. B 96, 0853...

    2017

  32. [40]

    K.-Q. Lin, J. D. Ziegler, M. A. Semina, J. V. Mamedov, K. Watanabe, T. Taniguchi, S. Bange, A. Chernikov, M. M. Glazov, and J. M. Lupton, High-lying valley- polarized trions in 2D semiconductors, Nature Commu- nications 13, 6980 (2022)

    2022

  33. [41]

    M. A. Semina, J. V. Mamedov, and M. M. Glazov, Ex- citons and trions with negative effective masses in two- dimensional semiconductors, Oxford Open Materials Sci- ence 3, itad004 (2023)

    2023

  34. [42]

    Sergeev and R

    R. Sergeev and R. Suris, Ground-state energy of X − and X + trions in a two-dimensional quantum well at an ar- bitrary mass ratio, Physics of the Solid State 43, 746 (2001)

    2001

  35. [43]

    G. V. Astakhov, D. R. Yakovlev, V. V. Rudenkov, P. C. M. Christianen, T. Barrick, S. A. Crooker, A. B. Dzyubenko, W. Ossau, J. C. Maan, G. Karczewski, and T. Wojtowicz, Definitive observation of the dark triplet ground state of charged excitons in high magnetic fields, Phys. R...

    2005

  36. [44]

    M. A. Semina, R. A. Sergeev, and R. A. Suris, The bind- ing energy of excitons and X + and X − trions in one- dimensional systems, Semiconductors 42, 1427 (2008)

    2008

  37. [45]

    Q. Li, X. Xie, A. Alfrey, C. W. Beach, N. McLel- lan, Y. Lu, J. Hu, W. Liu, N. Dhale, B. Lv, L. Zhao, 14 K. Sun, and H. Deng, Magnetic exciton-polariton with strongly coupled atomic and photonic anisotropies, arXiv:2306.11265 (2023)

    2023 arXiv

  38. [46]

    S. S. Kumar, B. C. Mulkerin, A. Tiene, F. M. Marchetti, M. M. Parish, and J. Levinsen, Efficient calculation of trion energies in monolayer transition metal dichalco- genides, Phys. Rev. B 111, 085404 (2025)

    2025

  39. [47]

    A. S. Bracker, E. A. Stinaff, D. Gammon, M. E. Ware, J. G. Tischler, D. Park, D. Gershoni, A. V. Filinov, M. Bonitz, F. Peeters, and C. Riva, Binding energies of positive and negative trions: From quantum wells to quantum dots, Phys. Rev. B 72, 035332 (2005)

    2005

  40. [48]

    Van der Donck, M

    M. Van der Donck, M. Zarenia, and F. M. Peeters, Ex- citons and trions in monolayer transition metal dichalco- genides: A comparative study between the multiband model and the quadratic single-band model, Phys. Rev. B 96, 035131 (2017)

    2017

  41. [49]

    R. A. Sergeev and R. A. Suris, The X + trion in a system with spatial separation of the charge carriers, Semicon- ductors 37, 1205 (2003)

    2003

  42. [50]

    M. A. Semina and R. A. Suris, Coulomb states in nanos- tructures, accidental degeneracy, and the Laplace-Runge- Lenz operator, JETP Letters 94, 574 (2011)

    2011

  43. [51]

    Ossau and R

    W. Ossau and R. Suris, eds., Optical properties of 2d sys- tems with interacting electrons (NATO ASI, 2003) Chap. R. A. Suris, Correlation between trion and hole in Fermi distribution in process of trion photo-excitation in doped QWs

    2003

  44. [52]

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

    2017

  45. [53]

    M. M. Glazov, Optical properties of charged excitons in two-dimensional semiconductors, J. Chem. Phys. 153, 034703 (2020)

    2020

  46. [54]

    Z. A. Iakovlev and M. M. Glazov, Fermi polaron fine structure in strained van der Waals heterostructures, 2D Materials 10, 035034 (2023)

    2023

  47. [55]

    Cotlet ¸, F

    O. Cotlet ¸, F. Pientka, R. Schmidt, G. Zarand, E. Demler, and A. Imamoglu, Transport of neutral optical excita- tions using electric fields, Phys. Rev. X 9, 041019 (2019)

    2019

  48. [56]

    Schmidt, T

    R. Schmidt, T. Enss, V. Pietil¨ a, and E. Demler, Fermi polarons in two dimensions. Phys. Rev. A 85, 021602 (2012)

    2012

  49. [57]

    My´ sliwy and K

    K. My´ sliwy and K. Jachymski, Long-range interacting Fermi polaron, Phys. Rev. B 109, 214208 (2024)

    2024

  50. [58]

    Tiene, B

    A. Tiene, B. C. Mulkerin, J. Levinsen, M. M. Parish, and F. M. Marchetti, Crossover from exciton polarons to trions in doped two-dimensional semiconductors at finite temperature, Phys. Rev. B 108, 125406 (2023)

    2023

  51. [59]

    F. Rana, O. Koksal, and C. Manolatou, Many-body the- ory of the optical conductivity of excitons and trions in two-dimensional materials, Phys. Rev. B 102, 085304 (2020)

    2020

  52. [60]

    Chang, S.-Y

    Y.-C. Chang, S.-Y. Shiau, and M. Combescot, Crossover from trion-hole complex to exciton-polaron in n-doped two-dimensional semiconductor quantum wells, Phys. Rev. B 98, 235203 (2018)

    2018

  53. [61]

    L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Butterworth-Heinemann, Ox- ford, 1977)

    1977

  54. [62]

    J. B. McGuire, Interacting Fermions in One Dimension. II. Attractive Potential, J. Math. Phys. 7, 123 (1966)

    1966

  55. [63]

    Klawunn and A

    M. Klawunn and A. Recati, Fermi polaron in two dimen- sions: Importance of the two-body bound state, Phys. Rev. A 84, 033607 (2011)

    2011

  56. [64]

    For significant V0D a simple expression (B3) for the ex- citon self-energy may not be applicable due to strong interaction of the Fermi sea hole with the exciton

  57. [65]

    Maialle, E

    M. Maialle, E. de Andrada e Silva, and L. Sham, Exciton spin dynamics in quantum wells, Phys. Rev. B 47, 15776 (1993)

    1993

  58. [66]

    S. V. Gupalov, E. L. Ivchenko, and A. V. Kavokin, Fine structure of localized exciton levels in quantum wells, JETP 86, 388 (1998)

    1998

  59. [67]

    Yu, G.-B

    H. Yu, G.-B. Liu, P. Gong, X. Xu, and W. Yao, Dirac cones and Dirac saddle points of bright excitons in mono- layer transition metal dichalcogenides, Nat Commun 5, 3876 (2014)

    2014

  60. [68]

    M. M. Glazov, T. Amand, X. Marie, D. Lagarde, L. Bouet, and B. Urbaszek, Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides, Phys. Rev. B 89, 201302 (2014)

    2014

  61. [69]

    Yu and M

    T. Yu and M. W. Wu, Valley depolarization due to inter- valley and intravalley electron-hole exchange interactions in monolayer MoS2, Phys. Rev. B 89, 205303 (2014)

    2014

  62. [70]

    H. H. Fang, B. Han, C. Robert, M. A. Semina, D. Lagarde, E. Courtade, T. Taniguchi, K. Watanabe, T. Amand, B. Urbaszek, M. M. Glazov, and X. Marie, Control of the Exciton Radiative Lifetime in van der Waals Heterostructures, Phys. Rev. Lett. 123, 067401 (2019)

    2019

  63. [71]

    Z. A. Iakovlev and M. M. Glazov, Longitudinal- transverse splitting and fine structure of Fermi po- larons in two-dimensional semiconductors, J. Lumin. 273, 120700 (2024)

    2024

  64. [72]

    Cohen, J

    G. Cohen, J. B. Haber, J. B. Neaton, D. Y. Qiu, and S. Refaely-Abramson, Phonon-driven femtosecond dy- namics of excitons in crystalline pentacene from first principles, Phys. Rev. Lett. 132, 126902 (2024)

    2024

  65. [73]

    M. M. Glazov and R. A. Suris, Ultrafast exciton trans- port in van der Waals heterostructures, Zh. Exp. Teor. Fiz. 166, 20 (2024)

    2024

  66. [74]

    Loudon, One-Dimensional Hydrogen Atom, American Journal of Physics 27, 649 (1959)

    R. Loudon, One-Dimensional Hydrogen Atom, American Journal of Physics 27, 649 (1959)

    1959

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.