Pith. sign in

REVIEW 3 major objections 4 minor 72 references

Strain-Induced Activation of Symmetry-Forbidden Exciton-Phonon Couplings for Enhanced Phonon-Assisted Photoluminescence in MoS$_2$ Monolayers

T0 review · 3 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 Strain switches on phonon-assisted light emission in MoS2.

desk verdict A clean symmetry argument for strain-activated phonon-assisted PL in MoS2, but the quantitative +1% peak rests on a known phase-mismatch that could reverse the predicted intensity trends. read the letter →

arxiv 2501.01410 v2 pith:SJU32W47 submitted 2025-01-02 cond-mat.mtrl-sci

Rishabh Saraswat , Rekha Verma , Sitangshu Bhattacharya This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords exciton-phononcouplingmonolayerMoS2photoluminescencebiaxialstraindarkexcitonssymmetryselectionrulesBethe-Salpeterequationfirst-principlescalculation
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

Monolayer MoS2 is a bright emitter at room temperature, but its lowest-energy intervalley excitons are momentum-dark and, this paper argues, cannot recombine with the help of phonons at cryogenic temperatures because the only phonons that could supply the momentum belong to a symmetry-forbidden representation (A''). The paper uses finite-momentum Bethe-Salpeter and density-functional perturbation calculations, backed by group-theoretic selection rules, to show that biaxial tensile strain activates the even A' phonon channels. Near +1% strain the phonon-assisted photoluminescence should peak sharply, dominated by a hole-phonon process that scatters the hole from K to K' and recombines there. If correct, this gives a concrete route to making dark excitons radiative in Mo-based dichalcogenides through strain engineering.

What carries the argument

The central object is the exciton-phonon coupling matrix element $G^{\beta\lambda,\nu}(\mathbf{Q},\mathbf{q})$ of Eq. (2), which the paper constructs as a quantum superposition of electron and hole scattering events, each weighted by the exciton wavefunction coefficients from the finite-momentum Bethe-Salpeter equation. Symmetry analysis is the engine: along the M-K line the point group reduces to $C_s(m)$, where the $E'$ exciton of $C_{3h}$ at K becomes $A'$; only the phonon modes that are even under the mirror plane ($A'$) can couple, while the $A''$ modes are forbidden, explaining the absence of phonon-assisted emission in the unstrained crystal. Biaxial strain does not change the symmetry but alters the coupling strengths, and the van Roosbroeck-Shockley relation with phonon sidebands converts those couplings into a predicted PL spectrum. The strain window from -0.5% to +3% is chosen because it is experimentally reachable.

What would settle it

Measure the cryogenic photoluminescence of a MoS2 monolayer under controlled biaxial tensile strain from 0 to +3% with a piezo stage. The central claim is falsified if no doublet of phonon sidebands appears near 50 and 70 meV below the bright exciton as strain approaches +1%, or if the indirect emission does not peak around +1% but instead rises monotonically or stays absent across the whole window.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a symmetry switch: in unstrained 2H-MoS2 the lowest intervalley excitons at K and M are dark, and the A'' phonon modes along the M-K route are forbidden to couple to them, so no phonon-assisted photoluminescence appears at cryogenic temperature. Biaxial tensile strain, while leaving the D3h point group intact, redistributes the exciton-phonon coupling strength so that A' modes become active; in particular an out-of-plane optical mode (mode 8, about 42 meV) and an in-plane acoustic shear mode (mode 3) dominate. The calculation further shows that the corresponding emission is carried mainly by hole-phonon scattering from K to K', producing two phonon replicas about 50 and 70 meV below the bright exciton. The indirect emission is non-monotonic in strain and maximized near +1%.

Load-bearing premise

The load-bearing premise is that the numerical phase mismatch between the phonon and exciton wavefunctions, which the authors explicitly say exists with current codes, does not change the strain-dependent ordering and sign of the A' coupling strengths that produces the +1% peak.

Editorial extensions

If this is right

  • Cryogenic PL of unstrained MoS2 should show only the bright intravalley line; under roughly +1% biaxial tension, two additional replicas should appear about 50 and 70 meV below it.
  • The lower-energy replica is predicted to be dominated by hole-phonon scattering from K to K', which can be tested by comparing spectra under different excitation polarizations or by time-resolved measurements.
  • The indirect PL intensity is predicted to be non-monotonic in strain, peaking near +1%; stretching beyond that should reduce the phonon sidebands even though the direct line redshifts.
  • The same symmetry-based mechanism offers a possible explanation for the non-monotonic strain dependence of PL observed in WSe2, where an exciton-phonon channel would complement the defect-resonance picture.
  • For other Mo-based TMDs, the selection rule says no A''-assisted emission should appear at low temperature; only the even A' modes can be switched on by strain, which narrows the search for brightening dark excitons.

Reading between the lines

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

  • If the strain-activated hole-phonon channel is as strong as predicted, it would compete with spin and valley relaxation channels, so strained MoS2 could also show strain-tunable valley depolarization times; the paper does not discuss this consequence.
  • The phase-mismatch caveat means the quantitative ordering of modes 3 and 8 and the exact optimal strain are the least secure numbers; a consistent gauge between the phonon and exciton calculations might shift the peak by a few tenths of a percent.
  • A direct experimental check could be done on a piezo-strained MoS2 monolayer: monitor the PL doublet separation under strain; if the two replicas move with the phonon energies rather than with the exciton, the assignment to modes 3 and 8 is confirmed.
  • The symmetry argument is generic: any TMD monolayer with a $C_{3h}$ valley and $C_s(m)$ M-K line should show the same A'/A'' dichotomy, so the strain-activation mechanism likely transfers to MoSe2, WS2, and WSe2.
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

3 major / 4 minor

Summary. The manuscript reports first-principles calculations of exciton-phonon coupling and phonon-assisted photoluminescence in monolayer MoS2 under biaxial strain. Using finite-momentum BSE exciton coefficients from Yambo and DFPT electron-phonon matrix elements from Quantum Espresso, the authors compute the exciton-phonon coupling strengths, scattering rates, linewidths, and PL spectra through the van Roosbroeck-Shockley relation. Group-theoretic analysis in D3h and its subgroups identifies A' phonon modes as symmetry-allowed and A'' modes as forbidden for intervalley exciton scattering. The central claim is that unstrained MoS2 has no phonon-assisted PL at cryogenic temperature, while tensile biaxial strain activates A'-mediated channels, mainly hole-phonon scattering by an out-of-plane optical mode (mode 8, about 42 meV), producing a maximum indirect PL near +1% strain. The unstrained linewidth and exciton dispersion are benchmarked against Chan et al. and Wu et al., and the computed direct PL is compared with experimental data.

Significance. If the central result holds, the work would establish a symmetry-based strain-engineering route to brighten dark intervalley excitons in Mo-based TMD monolayers and would offer a plausible explanation for the non-monotonic strain dependence of PL in WSe2. The paper's strengths are its explicit group-theoretic selection argument, its benchmarking against external unstrained calculations (Chan et al. for linewidths, Wu et al. for the exciton dispersion) and experiment, and its falsifiable prediction of a maximum phonon-assisted PL near +1% biaxial strain. However, the admitted wavefunction-phase mismatch between the DFPT and BSE codes is not a peripheral numerical detail: it enters the central coupling matrix element of Eq. (2) and, by the authors' own statement, can reverse intensity trends. The quantitative strain dependence and the assignment of mode 8 as the dominant hole-phonon channel are therefore not yet secure, although the qualitative symmetry selection argument is plausible.

major comments (3)
  1. [Limitations paragraph (before Summary)] The authors explicitly state that Eq. (2) requires the same Kohn-Sham wavefunction phases in the DFPT and BSE steps, that current Quantum Espresso/Yambo interfaces cannot enforce this, and that 'there could be a phase-mismatch which can show an opposite trend in the intensity levels.' Because the central prediction of a +1% strain maximum and the assignment of mode 8 as the dominant hole-phonon channel (Fig. 2(c) and Fig. 6(d)) are based on the magnitudes of the gauge-sensitive complex sums in Eq. (2), the admitted phase mismatch directly undermines the quantitative strain-dependence claim. The anomalous strong coupling near the Gamma point in Fig. 2, attributed by the authors to this mismatch, confirms that the contamination is present in the plotted quantity. The authors should either repeat the calculation with a phase-consistent interface (for example, the YAMBO-PERTURBO route they cite) or provide an explicit gauge-invariance check, such as randomizing wavefunction phases and showing that the couplings and PL spectra are stable.
  2. [Abstract and Fig. 7 discussion] The abstract claims that unstrained MoS2 exhibits no phonon-assisted PL at cryogenic temperatures, but the body reports that 'faint indirect emission is visible near 1.73 eV' under unstrained conditions in the discussion of Fig. 7, and Fig. 7(a) shows a weak indirect feature. This internal inconsistency makes the baseline 'forbidden' claim stronger than the computed result supports. Please state quantitatively whether the unstrained emission is zero, negligible, or merely weak, and adjust the abstract and summary wording accordingly.
  3. [Eqs. (4)-(5) and damping in Eq. (6)] The linewidth curves in Fig. 4 are obtained by fitting Toyozawa and linear-plus-Bose models with fitted parameters (S_A, S_O, E_A, E_O, a, b, gamma0), and the PL calculation uses a hand-set 2 meV damping factor. These auxiliary models are not derived from the ab initio calculation and introduce several free parameters. The authors should test and report the sensitivity of the predicted +1% strain maximum to reasonable variations of these parameters, so that the reader can see that the central strain trend is not an artifact of the fitting choices.
minor comments (4)
  1. [Eq. (6)] The symbols D^±_{beta lambda, q nu}, R_lambda, and the sign conventions in omega ∓ 2 omega_{q mu} are not fully defined in the text; please define all symbols or refer the reader to the relevant equation in the Supplemental Information.
  2. [Fig. 3(a)] The legend labels the curves as 'Exciton 1 & 2', 'Exciton 3 & 4', and 'Exciton 5', while the text says the lowest five excitons are considered; please clarify whether excitons 2 and 4 are exactly degenerate with excitons 1 and 3, respectively, and whether they are omitted from the plot or simply degenerate.
  3. [Eq. (3) and Eq. (6)] The infinitesimal eta appearing in the self-energy and PL expressions is never given a numerical value; please specify the broadening parameter used and state whether the results are converged with respect to it.
  4. [General presentation] The text refers to 'Lechifflart et al.' in the limitations paragraph; the corresponding reference is listed as P. Lechifflart et al., and the spelling should be made consistent throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the strain-activated phonon-assisted PL is computed from first-principles DFPT matrix elements and BSE exciton coefficients, validated against external unstrained benchmarks, and not fitted to the target +1% peak.

full rationale

The central claim is derived, not assumed: electron-phonon matrix elements (Eq. 1) from Quantum Espresso and BSE exciton coefficients from Yambo enter the exciton-phonon coupling (Eq. 2), self-energy (Eq. 3), and van Roosbroeck-Shockley PL formula (Eq. 6), with no parameter fitted to force the +1% strain maximum. The unstrained linewidths are benchmarked against Chan et al., the exciton dispersion against Wu et al., and the direct PL against the experimental inset from Ref. [27]; these are external checks, not self-citations. The A'/A'' selection rule is an independent group-theoretic argument, not an imported uniqueness theorem. The only fitted quantities are the Toyozawa and weak-coupling linewidth parameters in Fig. 4, which are descriptive fits to computed linewidths and do not enter the PL intensity calculation that produces the strain dependence. The authors' admitted phase-mismatch limitation between QE g-elements and Yambo A-coefficients, which 'can show an opposite trend in the intensity levels,' is a serious quantitative caveat and is explicitly weighted here, but it is a correctness risk rather than a circular reduction: the computed couplings and the admitted error are not definitions of the target result. The abstract's 'no phonon-assisted PL' statement is internally inconsistent with the body's 'faint indirect emission is visible near 1.73 eV' under unstrained conditions, but that is a consistency issue, not circularity. No load-bearing self-citation chain exists in this manuscript.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central prediction uses standard GW-BSE and DFPT frameworks; no new particles, forces, or dimensions are introduced. The only truly free numbers are line-shape fit constants and a phenomenological damping factor. The most fragile input is the assumed phase/gauge consistency across the two codes, which the authors explicitly flag as a limitation.

free parameters (8)
  • PL damping factor = 2 meV
    Added to the PL spectrum to account for exciton-phonon self-energy; chosen by hand rather than derived.
  • Toyozawa acoustic coupling S_A for exciton 1 = 2.27 meV
    Fit to the computed linewidth of exciton 1 using Toyozawa's strong-coupling model.
  • Toyozawa optical coupling S_O for exciton 1 = 0.1 meV
    Fit to the computed linewidth of exciton 1.
  • Mean acoustic phonon energy E_A for exciton 1 = 25 meV
    Fit parameter in the Toyozawa linewidth model.
  • Mean optical phonon energy E_O for exciton 1 = 48.1 meV
    Fit parameter in the Toyozawa linewidth model.
  • Acoustic linewidth coefficient a for exciton 5 = 2 meV/K
    Fit to the computed linewidth of exciton 5.
  • Optical linewidth coefficient b for exciton 5 = 35 meV
    Fit to the computed linewidth of exciton 5.
  • Temperature-independent offset gamma0 for exciton 5 = 35.1 meV
    Fit to the computed linewidth of exciton 5.
assumptions (5)
  • domain assumption G0W0 quasiparticle energies and finite-momentum BSE describe the low-energy exciton manifold of MoS2 accurately.
    All exciton energies, couplings, and PL spectra rely on this; convergence is asserted but only partly documented in the inaccessible SI.
  • domain assumption D3h point group symmetry and compatibility relations determine allowed exciton-phonon channels, and biaxial strain does not change the point group.
    Used to classify A' versus A'' modes and to forbid or allow couplings; the authors state that strain preserves the symmetry.
  • standard math Fermi's golden rule and the van Roosbroeck-Shockley relation with a first-order exciton-phonon self-energy capture the PL spectrum.
    Equations (3) and (6) rely on standard many-body perturbation theory, but the calculation neglects dynamical phonon effects and excitonic occupation factors.
  • domain assumption Only the top valence band contributes to the ground-state exciton and the hole-phonon scattering process.
    Stated in the Fig. 1 caption: only the top valence band is considered for holes. Deeper valence bands could add scattering channels.
  • ad hoc to paper The same Kohn-Sham wavefunction phase set must be used in the DFPT and BSE steps for gauge-invariant exciton-phonon coupling, and the computation satisfies this closely enough.
    The authors acknowledge that current QE and Yambo codes cannot guarantee this, and they attribute anomalous coupling near Gamma to the resulting phase mismatch.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Strain-Induced Activation of Symmetry-Forbidden Exciton-Phonon Couplings for Enhanced Phonon-Assisted Photoluminescence in MoS$_2$ Monolayers." pith.science (2026). https://pith.science/paper/SJU32W47

@misc{pith2026250101410,
  author       = {Pith},
  title        = {Pith review of: Strain-Induced Activation of Symmetry-Forbidden Exciton-Phonon Couplings for Enhanced Phonon-Assisted Photoluminescence in MoS$_2$ Monolayers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SJU32W47}},
  note         = {Machine review of arXiv:2501.01410}
}
abstract

Phonon-assisted photoluminescence (PL) in molybdenum-based two-dimensional dichalcogenides is typically weak due to the dormant phonon coupling with optically inactive momentum-dark (intervalley) excitons, unlike in tungsten-based dichalcogenides where such processes are more prominent. Despite this inefficiency, we revisit excitons in MoS$_2$ using rigorous finite-momentum Bethe-Salpeter equation calculations to identify ways to enhance phonon-assisted recombination channels. Our ab-initio results, complemented by group-theoretic analyses, reveal that while unstrained MoS$_2$ exhibits no phonon-assisted PL emissions at cryogenic temperatures due to forbidden A$^{\prime\prime}$ phonon modes, biaxial strain opens a pathway to significantly intensify this emission by activating hole-phonon A$^{\prime}$-mediated scattering channels. By calculating allowed exciton-phonon matrix elements and scattering rates, we demonstrate how strain redistributes oscillator strengths toward radiative recombination. These findings provide a promising route to improving PL emission efficiency in various metal dichalcogenide monolayers through strain engineering and offer valuable insights for further exploration of exciton-phonon dynamics, including time-resolved spectroscopic studies.

Figures

Figures reproduced from arXiv: 2501.01410 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a)-(c): Phonon mode A [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (a) Relaxation time at [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Linewidth for exciton 1 and 5 at [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Lowest energy phonon replicas at 10 K for various [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: PL intensities with increasing [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Normalized PL intensities with varying temperatures at unstrained and [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

72 extracted references · 69 canonical work pages

  1. [1]

    Paramshivay

    The in-plane (two-dimensional) components, x and y, transform as the E′ representation, enabling mixing and transitions al- lowed by symmetry. The out-of-plane z component trans- forms as A′ 1, allowing additional transitions. Consequently, the overall transformation of the dipole operator can be ex- pressed as E′ x, y + A′ 1 [z]. This implies that when a...

    work page 2023

  2. [2]

    P. T. Landsberg, in Recombination in Semiconductors (Cam- bridge University Press, 1992)

    work page 1992

  3. [3]

    Knox, Theory of Excitons, Sup , 5 (1963) p

    R. Knox, Theory of Excitons, Sup , 5 (1963) p. 100

    work page 1963

  4. [4]

    Cassabois, P

    G. Cassabois, P. Valvin, and B. Gil, Hexagonal boron nitride is an indirect bandgap semiconductor, Nat. Photon. 10, 262 (2016)

    work page 2016

  5. [5]

    M. S. Dresselhaus, G. Dresselhaus, and A. Jorio, Group the- ory: Application to the Physics of Condensed Matter , 1st ed. (Springer-Verlag Berlin Heidelberg, Germany, 2008)

    work page 2008

  6. [6]

    W. Yao, D. Xiao, and Q. Niu, Coupled spin and valley physics in monolayers of MoS2 and other group-vi dichalcogenides, Phys. Rev. B 77, 235406 (2008)

    work page 2008

  7. [7]

    Schué, L

    L. Schué, L. Sponza, A. Plaud, H. Bensalah, K. Watanabe, T. Taniguchi, F. Ducastelle, A. Loiseau, and J. Barjon, Bright luminescence from indirect and strongly bound excitons in h- BN, Phys. Rev. Lett. 122, 067401 (2019)

    work page 2019

  8. [8]

    T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu, and J. Feng, Valley-selective circular dichro- ism of monolayer molybdenum disulphide, Nat. Commun. 3, 887 (2012)

    work page 2012

Show all 72 references
  1. [9]

    Xiao, G.-B

    D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Valley- dependent optoelectronics from inversion symmetry breaking, Phys. Rev. Lett. 108, 196802 (2012)

    2012

  2. [10]

    K. F. Mak, K. He, J. Shan, and T. F. Heinz, Control of valley polarization in monolayer MoS 2 by optical helicity, Nat. Nan- otechnol. 7, 494–498 (2012)

    2012

  3. [11]

    H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, Valley polariza- tion in MoS 2 monolayers by optical pumping, Nat. Nanotech- nol. 7, 490–493 (2012)

    2012

  4. [12]

    Srivastava, M

    A. Srivastava, M. Sidler, A. V . Allain, D. S. Lembke, A. Kis, and A. Imamo ˘glu, Valley zeeman effect in elementary optical excitations of monolayer WSe2, Nat. Phys. 11, 141–147 (2015)

    2015

  5. [13]

    A. M. Jones, H. Yu, N. J. Ghimire, S. Wu, G. Aivazian, J. S. Ross, B. Zhao, J. Yan, D. G. Mandrus, D. Xiao, W. Yao, and X. Xu, Optical generation of excitonic valley coherence in monolayer WSe2, Nat. Nanotechnol. 8, 634–638 (2013)

    2013

  6. [14]

    Deilmann and K

    T. Deilmann and K. S. Thygesen, Dark excitations in monolayer transition metal dichalcogenides, Phys. Rev. B 96, 201113(R) (2017)

    2017

  7. [15]

    J. P. Echeverry, B. Urbaszek, T. Amand, X. Marie, and I. C. Gerber, Splitting between bright and dark excitons in transition metal dichalcogenide monolayers, Phys. Rev. B 93, 121107(R) (2016)

    2016

  8. [16]

    G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Colloquium: Excitons in atom- ically thin transition metal dichalcogenides, Phys. Rev. B 90, 021001 (2018)

    2018

  9. [17]

    Malic, M

    E. Malic, M. Selig, M. Feierabend, S. Brem, D. Christiansen, F. Wendler, A. Knorr, and G. Berghäuser, Dark excitons in tran- sition metal dichalcogenides, Phys. Rev. Lett.2, 014002 (2018)

    2018

  10. [18]

    Splendiani, L

    A. Splendiani, L. Sun, Y . Zhang, T. Li, J. Kim, C.-Y . Chim, G. Galli, and F. Wang, Emerging photoluminescence in mono- layer MoS2, Nano Lett. 10, 1271–1275 (2010)

    2010

  11. [19]

    Mueller and E

    T. Mueller and E. Malic, Exciton physics and device applica- tion of two-dimensional transition metal dichalcogenide semi- conductors, NPJ 2D Mater. Appl. 2, 29 (2018)

    2018

  12. [20]

    Robert, R

    C. Robert, R. Picard, D. Lagarde, G. Wang, J. P. Echeverry, F. Cadiz, P. Renucci, A. Högele, T. Amand, and X. M. et al. , Excitonic properties of semiconducting monolayer and bilayer MoTe2, Phys. Rev. B 94, 155425 (2016)

    2016

  13. [21]

    M. R. Molas, C. Faugeras, A. O. Slobodeniuk, K. Nogajew- ski, M. Bartos, D. M. Basko, and M. Potemski, Brightening of dark excitons in monolayers of semiconducting transition metal dichalcogenides, 2D Materials 4, 021003 (2017)

    2017

  14. [22]

    Zhang, T.-R

    Y . Zhang, T.-R. Chang, B. Zhou, Y .-T. Cui, H. Yan, Z. Liu, F. Schmitt, J. Lee, R. Moore, and Y . C.et al., Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2, Nat. Nanotechnol. 9, 111 (2014)

    2014

  15. [23]

    H. R. Gutiérrez, N. Perea-López, A. L. Elías, A. Berkdemir, B. Wang, R. Lv, F. López-Urías, V . H. Crespi, H. Terrones, and M. Terrones, Extraordinary room-temperature photolumines- cence in triangular WS2 monolayers, Nano Lett. 13, 3447–3454 (2013)

    2013

  16. [24]

    K. He, N. Kumar, L. Zhao, Z. Wang, K. F. Mak, H. Zhao, and J. Shan, Tightly bound excitons in monolayer WSe2, Phys. Rev. Lett. 113, 026803 (2014)

    2014

  17. [25]

    Palummo, M

    M. Palummo, M. Bernardi, and J. C. Grossman, Exciton ra- diative lifetimes in two-dimensional transition metal dichalco- genides, Nano Lett. 5, 2794 (2015)

    2015

  18. [26]

    Y . Zhou, G. Scuri, D. S. Wild, A. A. High, A. Dibos, L. A. Jauregui, C. Shu, K. D. Greve, K. Pistunova, A. Y . Joe, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, Probing dark excitons in atomically thin semiconductors via near-field coupling to surface plasmon ...

    2017

  19. [27]

    Zhang, Y

    X.-X. Zhang, Y . You, S. Y . F. Zhao, and T. F. Heinz, Experi- mental evidence for dark excitons in monolayer WSe 2, Phys. Rev. Lett. 115, 257403 (2015). 9

    2015

  20. [28]

    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, S. G. Louie, and T. F. Heinz, Magnetic brightening and control of dark excitons in monolayer WSe2, Nat. Nanotechnol. 12, 883–888 (2017)

    2017

  21. [29]

    Robert, B

    C. Robert, B. Han, P. Kapuscinski, A. Delhomme, C. Faugeras, T. Amand, M. R. Molas, M. Bartos, K. Watanabe, T. Taniguchi, B. Urbaszek, M. Potemski, and X. Marie, Measurement of the spin-forbidden dark excitons in mos 2 and mose 2 monolayers, Nat. Commun. 11, 4037 (2020)

    2020

  22. [30]

    Z. Wang, A. Molina-Sánchez, P. Altmann, D. Sangalli, D. D. Fazio, G. Soavi, U. Sassi, F. Bottegoni, F. Ciccacci, M. Finazzi, L. Wirtz, A. C. Ferrari, A. Marini, G. Cerullo, and S. D. Conte, Intravalley spin–flip relaxation dynamics in single-layer WS 2, Nano Lett. 18, 6882 (2018)

    2018

  23. [31]

    Yu and M

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

    2014

  24. [32]

    C. M. Chow, H. Yu, A. M. Jones, J. R. Schaibley, M. Koehler, D. G. Mandrus, R. Merlin, W. Yao, and X. Xu, Phonon-assisted oscillatory exciton dynamics in monolayer MoSe 2, NPJ 2D Mater. Appl. 1, 33 (2017)

    2017

  25. [33]

    S. Brem, A. Ekman, D. Christiansen, F. Katsch, M. Selig, C. Robert, X. Marie, B. Urbaszek, A. Knorr, and E. Malic, Phonon-assisted photoluminescence from indirect excitons in monolayers of transition-metal dichalcogenides, Nano Lett. 20, 2849 (2020)

    2020

  26. [34]

    Zheng, J.-K

    S. Zheng, J.-K. So, F. Liu, Z. Liu, N. Zheludev, and H. J. Fan, Giant enhancement of cathodoluminescence of monolayer tran- sitional metal dichalcogenides semiconductors, Nano Lett. 17, 6475–6480 (2017)

    2017

  27. [35]

    D. Li, C. Trovatello, S. D. Conte, M. Nuß, G. Soavi, G. Wang, A. C. Ferrari, G. Cerullo, and T. Brixner, Exciton–phonon cou- pling strength in single-layer MoSe2 at room temperature, Nat. Commun. 12, 954 (2021)

    2021

  28. [36]

    Miyauchi, S

    Y . Miyauchi, S. Konabe, F. Wang, W. Zhang, A. Hwang, Y . Hasegawa, L. Zhou, S. Mouri, M. Toh, G. Eda, and K. Mat- suda, Evidence for line width and carrier screening e ffects on excitonic valley relaxation in 2D semiconductors, Nat. Com- mun. 9, 2598 (2018)

    2018

  29. [37]

    Chellappan, A

    V . Chellappan, A. L. C. Pang, S. Sarkar, Z. E. Ooi, and K. E. J. Goh, Effect of phonons on valley depolarization in monolayer WSe2, Electron. Mater. Lett. 14, 766 (2018)

    2018

  30. [38]

    V . Funk, K. Wagner, E. Wietek, J. D. Ziegler, J. Förste, J. Lind- lau, M. Förg, K. Watanabe, T. Taniguchi, A. Chernikov, and A. Högele, Spectral asymmetry of phonon sideband lumines- cence in monolayer and bilayer WSe 2, Phys. Rev. Res. 3, L042019 (2021)

    2021

  31. [39]

    Jeong, S

    T.-Y . Jeong, S. Bae, S.-Y . Lee, S. Jung, Y .-H. Kim, and K.- J. Yee, Valley depolarization in monolayer transition-metal dichalcogenides with zone-corner acoustic phonons, Nanoscale 12, 22487 (2020)

    2020

  32. [40]

    H. Li, A. W. Contryman, X. Qian, S. M. Ardakani, Y . Gong, X. Wang, J. M. Weisse, C. H. Lee, J. Zhao, P. M. Ajayan, J. Li, H. C. Manoharan, and X. Zheng, Optoelectronic crystal of ar- tificial atoms in strain-textured molybdenum disulphide, Nat. Commun. 6, 7381 (2015)

    2015

  33. [41]

    H.-Y . Chen, D. Sangalli, and M. Bernardi, First-principles ultra- fast exciton dynamics and time-domain spectroscopies: Dark- exciton mediated valley depolarization in monolayer WSe 2, Phys. Rev. Res. 4, 043203 (2022)

    2022

  34. [42]

    D. R. Hamann, Optimized norm-conserving Vanderbilt pseu- dopotentials, Phys. Rev. B 88, 085117 (2013)

    2013

  35. [43]

    P. H. López, S. Heeg, C. Schattauer, S. Kovalchuk, A. Kumar, D. J. Bock, J. N. Kirchhof, B. Höfer, K. Greben, D. Yagodkin, L. Linhart, F. Libisch, and K. I. Bolotin, Strain control of hy- bridization between dark and localized excitons in a 2D semi- conductor, Nat. Commun. 13,...

    2022

  36. [44]

    Sangalli, A

    D. Sangalli, A. Ferretti, H. Miranda, C. Attaccalite, I. Marri, E. Cannuccia, P. Melo, M. Marsili, F. Paleari, A. Marrazzo, et al. , Many-body perturbation theory calculations using the Y AMBO code, J. Condens. Matter Phys.31, 325902 (2019)

    2019

  37. [45]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, and M. C. et al., Advanced capabilities for materials modelling with quantum ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017)

    2017

  38. [46]

    accurately reproduces excitonic energies within exper- imental ranges. Electron-phonon matrix elements (includ- ing self-energies [47] with Debye-Waller corrections [48]), and exc-ph matrix elements were computed on a converged 3 (a) mode 3 (b) mode 3 (c) mode 3 (d) mode 3 0% ...

  39. [47]

    See Supplemental Information at http://-/supplemental/ for nec- essary convergence and supporting figures

  40. [48]

    Guandalini, P

    A. Guandalini, P. D’Amico, A. Ferretti, and D. Varsano, E ffi- cient GW calculations in two dimensional materials through a stochastic integration of the screened potential, NPJ Comput. Mater. 9, 44 (2023)

    2023

  41. [49]

    H. Y . Fan, Temperature dependence of the energy gap in monatomic semiconductors, Phys. Rev. 6, 808 (1950)

    1950

  42. [50]

    Cannuccia and A

    E. Cannuccia and A. Marini, E ffect of the quantum zero-point atomic motion on the optical and electronic properties of di- amond and trans-polyacetylene, Phys. Rev. lett. 107, 255501 (2011)

    2011

  43. [51]

    Zanfrognini, A

    M. Zanfrognini, A. Plaud, I. Stenger, F. Fossard, L. Sponza, L. Schué, F. Paleari, E. Molinari, D. Varsano, L. Wirtz, F. m. c. Ducastelle, A. Loiseau, and J. Barjon, Distinguishing di fferent stackings in layered materials via luminescence spectroscopy, Phys. Rev. Lett. 131, 2...

    2023

  44. [52]

    Paleari, H

    F. Paleari, H. P. Miranda, A. Molina-Sánchez, and L. Wirtz, Exciton-phonon coupling in the ultraviolet absorption and emission spectra of bulk hexagonal boron nitride, Phys. Rev. Lett. 122, 187401 (2019)

    2019

  45. [53]

    T. Q. P. Vuong, G. Cassabois, P. Valvin, V . Jacques, A. V . D. Lee, A. Zobelli, K. Watanabe, T. Taniguchi, and B. Gil, Phonon symmetries in hexagonal boron nitride probed by incoherent light emission, 2D Mater. 4, 011004 (2016)

    2016

  46. [54]

    Pan and F

    Y . Pan and F. Caruso, Strain-induced activation of chiral- phonon emission in monolayer WS 2, NPJ 2D Mater. Appl. 8, 42 (2024)

    2024

  47. [55]

    Chowdhury, S

    T. Chowdhury, S. Chatterjee, D. Das, I. Timokhin, P. D. Núñez, M. A. Gokul, S. Chatterjee, K. Majumdar, P. Ghosh, A. Mishchenko, and A. Rahman, Strain-induced activation of chiral-phonon emission in monolayer WS 2, Phys. Rev. B 110, L081405 (2024)

    2024

  48. [56]

    O. B. Aslan, M. Deng, and T. F. Heinz, Strain tuning of excitons in monolayer WSe2, Phys. Rev. B 98, 115308 (2018)

    2018

  49. [57]

    Giustino, Electron-phonon interactions from first principles, Rev

    F. Giustino, Electron-phonon interactions from first principles, Rev. Mod. Phys. 89, 015003 (2017)

    2017

  50. [58]

    Lechifflart, F

    P. Lechifflart, F. Paleari, D. Sangalli, and C. Attaccalite, First- principles study of luminescence in hexagonal boron nitride single layer: Exciton-phonon coupling and the role of substrate, Phys. Rev. Mater. 7, 024006 (2023)

    2023

  51. [59]

    Marini, M

    G. Marini, M. Calandra, and P. Cudazzo, Optical absorption and photoluminescence of single-layer boron nitride from a first- principles cumulant approach, Nano Lett. 24, 6017 (2024)

    2024

  52. [60]

    Paleari, First-principles approaches to the description of indirect absorption and luminescence spectroscopy: exciton- 10 phonon coupling in hexagonal boron nitride, Ph.D

    F. Paleari, First-principles approaches to the description of indirect absorption and luminescence spectroscopy: exciton- 10 phonon coupling in hexagonal boron nitride, Ph.D. thesis, Uni- versité du Luxembourg (2019)

    2019

  53. [61]

    H.-Y . Chen, D. Sangalli, and M. Bernardi, Exciton-phonon in- teraction and relaxation times from first principles, Phys. Rev. Lett. 125, 107401 (2020)

    2020

  54. [62]

    Y .-h. Chan, J. B. Haber, M. H. Naik, J. B. Neaton, D. Y . Qiu, F. H. da Jornada, and S. G. Louie, Exciton lifetime and optical line width profile via exciton–phonon interactions: Theory and first-principles calculations for monolayer mos2, Nano Lett.23, 3971 (2023)

    2023

  55. [63]

    Toyozawa, Theory of line-shapes of the exciton absorption bands, Prog

    Y . Toyozawa, Theory of line-shapes of the exciton absorption bands, Prog. Theor. Phys. 20, 53 (1958)

    1958

  56. [64]

    T. Q. P. Vuong, G. Cassabois, P. Valvin, S. Liu, J. H. Edgar, and B. Gil1, Exciton-phonon interaction in the strong-coupling regime in hexagonal boron nitride, Phys. Rev. B95, 201202(R) (2017)

    2017

  57. [65]

    G. D. Mahan, Many-Particle Physics, 3rd ed. (Springer Interna- tional Edition, New York, United States of America, 2014)

    2014

  58. [66]

    F. Wu, F. Qu, and A. H. MacDonald, Exciton band structure of monolayer MoS2, Phys. Rev. B 9, 075310 (2015)

    2015

  59. [67]

    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. Watan- abe, T. Taniguchi, J. Hone, and T. F. Heinz, Efficient generation of neutral and charged biexcitons in encapsulated WSe2 mono- layers, Nat. Commun. 9, 37...

    2018

  60. [68]

    Z. Li, T. Wang, C. Jin, Z. Lu, Z. Lian, Y . Meng, M. Blei, S. Gao, T. Taniguchi, K. Watanabe, T. Ren, S. Tongay, L. Yang, D. Smirnov, T. Cao, and S.-F. Shi, Emerging photolumines- cence from the dark-exciton phonon replica in monolayer WSe2, Nat. Commun. 10, 2469 (2019)

    2019

  61. [69]

    Courtade, M

    E. Courtade, M. Semina, M. Manca, M. M. Glazov, C. Robert, F. Cadiz, G. Wang, T. Taniguchi, K. Watanabe, M. Pierre, W. Escoffier, E. L. Ivchenko, P. Renucci, X. Marie, T. Amand, and B. Urbaszek, Charged excitons in monolayer wse2: Exper- iment and theory, Phys. Rev. B96, 085302 (2017)

    2017

  62. [70]

    Lindlau, C

    J. Lindlau, C. Robert, V . Funk, J. Forste, M. Forg, L. Colombier, A. Neumann, E. Courtade, S. Shree, T. Taniguchi, K. Watanabe, M. M. Glazov, X. Marie, B. Urbaszek, and A. Hogele, Identi- fying optical signatures of momentum-dark excitons in transi- tion metal dichalcogenide ...

    2017

  63. [71]

    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. Watanabe, T. Taniguchi, S. Ton- gay, G. Wang, A. C. Ferrari, and M. Atatüre, Charge-tuneable biexciton complexes in monolayer WSe 2, Na...

    2018

  64. [72]

    J.-J. Zhou, J. Park, I.-T. Lu, I. Maliyov, X. Tong, and M. Bernardi, Perturbo: A software package for ab initio electron-phonon interactions, charge transport and ultrafast dy- namics, Comput. Phys. Commun. , 107970 (2021)

    2021

Pith tools

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