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REVIEW 3 major objections 4 minor 89 references

Excitonic effects in phonons: reshaping the graphene Kohn anomalies and lifetimes

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper finds that excitonic electron-hole interactions red-shift graphene's K-point TO phonon by ~150 cm⁻¹, raise its group velocity tenfold, and quintuple its linewidth via a 26x enhancement of the electron-phonon coupling.

desk verdict Genuinely new framework for excitonic effects in phonons, with a plausible central physics but a load-bearing approximation (dropped double-counting term) that the paper does not quantify, so the headline numbers remain conditional. read the letter →

arxiv 2504.13715 v2 pith:NXHANXAP submitted 2025-04-18 cond-mat.mtrl-sci cond-mat.mes-hall

Alberto Guandalini , Francesco Macheda , Giovanni Caldarelli , Francesco Mauri This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hall
keywords excitoniceffectsphononself-energyKohnanomalygrapheneelectron-phononcouplingBethe-SalpeterequationgeneralizedKohn-Shamlinewidth
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 develops a first-principles framework that puts excitonic (electron-hole) interactions into the phonon self-energy, and applies it to graphene's optical phonons. It claims that near the Brillouin-zone corner K these interactions dramatically reshape the Kohn anomaly: the transverse optical phonon red-shifts by ~150 cm⁻¹, its group velocity increases tenfold, and its linewidth grows about fivefold, driven by a 26-fold increase in the squared electron-phonon matrix element. Near the zone center Γ the excitonic corrections are minor, because at long wavelengths the electron-phonon coupling acts as a gauge field that merely shifts the Dirac cone. If the claim is right, standard DFT phonon calculations miss the dominant physics of the K-point phonons and of graphene's intrinsic resistivity.

What carries the argument

The central object is the electron-hole ladder propagator $L_W$ (solution of the Bethe-Salpeter equation with static $W$), contracted to the density-density response $\chi_W$, which enters the phonon self-energy as $\Delta C = V_{\mathrm{DFT}} (\chi_W - \chi_0) V_{\mathrm{DFT}}$. The paper also uses the exact generalized Fermi golden rule from the variational formulation to extract effective dressed electron-phonon matrix elements, and the gauge-field argument that at $\Gamma$ an atomic displacement merely shifts the Dirac cone, protecting the phonon linewidth.

What would settle it

Recompute the K-point TO phonon self-energy including the double-counting correction (nonzero $\Delta f_{Hxc}$ and full GDFT vertex) within the same tight-binding model; if the ~150 cm$^{-1}$ red-shift and ~5x FWHM enhancement are not reproduced, the excitonic claim rests on the neglected term.

Watch

Extended reading notes

Core claim

Working in a generalized Kohn-Sham (GDFT) framework, the authors compute the phonon dynamical matrix from the interacting electron density-density response $\chi_W(z)$ that includes the full Bethe-Salpeter ladder of electron-hole interactions with a static screened Coulomb interaction $W$, evaluated in a tight-binding model fitted to DFT. The phonon correction takes the differential form $\Delta C = V(\chi_W - \chi_0)V$, so that all deviation from DFT comes from the difference between the interacting and bare responses. They find that at the K point the excitonic ladder reverses the self-energy-driven blue-shift and produces a substantial red-shift of the TO phonon (~150 cm$^{-1}$ for the dynamical phonon), a tenfold increase of the group velocity, and a fivefold increase of the full-width at half-maximum (from ~20 to ~100 cm$^{-1}$), which they attribute to a 26-fold increase in the effective electron-phonon coupling squared. These effects persist while $2E_F < \hbar\omega_{ph}$ and are quenched at higher doping. At $\Gamma$, the linewidth is protected because the electron-phonon coupling renormalizes the Fermi velocity, leaving the ratio $v_g/v_\phi$ nearly unchanged, a 'gauge-field protection' that requires the full ladder series to be respected.

Load-bearing premise

The entire claimed effect is computed while neglecting the double-counting correction required by the theory, using a model interaction fitted to DFT; if that neglected correction or the fitted interaction materially changes the result, the predicted redshift and linewidth enhancement would change.

Editorial extensions

If this is right

  • At K, the TO phonon frequency in freestanding graphene is about 150 cm⁻¹ lower than DFT predicts, and its group velocity is about ten times larger, which should show up in the dispersion of the 2D Raman mode.
  • The K-point FWHM grows from ~20 to ~100 cm⁻¹, meaning phonon lifetimes are shortened about fivefold by excitonic effects.
  • The squared electron-phonon matrix element at K is enhanced by a factor ~26, which the paper argues makes K-point phonons the likely dominant source of the intrinsic electrical resistivity of graphene at room temperature.
  • The excitonic enhancement survives up to doping $2E_F < \hbar\omega_{ph}$ and is quenched at higher doping, so it is most relevant in undoped or lightly doped graphene.
  • Near Γ, the phonon frequency and linewidth are essentially unchanged by excitonic effects, because the coupling acts as a gauge field; the full ladder sum is required to recover this cancellation.

Reading between the lines

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

  • A quantitative transport calculation built on the enhanced $|g_K|^2$ would likely show that DFT-based estimates of phonon-limited resistivity in graphene systematically underestimate the K-point contribution; the paper hints at this but does not compute the resistivity.
  • The strong monolayer-vs-graphite contrast suggests that screening by a substrate (for example hBN encapsulation or multilayer stacking) would suppress the excitonic redshift and linewidth broadening, a testable difference between suspended and supported graphene.
  • A direct measurement of the TO branch near K in suspended graphene, via momentum-resolved EELS or high-resolution Raman of the 2D mode as a function of doping, could verify the predicted ~150 cm⁻¹ red-shift and ~100 cm⁻¹ FWHM, and should show quenching when $2E_F$ exceeds $\hbar\omega_{ph}$.
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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 paper develops a generalized Kohn-Sham (GDFT) framework for phonon dispersions and linewidths that includes electron-hole (excitonic) interactions, and applies it to graphene. The formal part expresses the phonon dynamical matrix as a DFT contribution plus a correction built from the BSE-ladder susceptibility χW and the GDFT vertex. Numerically, the correction is evaluated in a five-nearest-neighbor π-band tight-binding model fitted to DFT, with the double-counting term ΔfHxc set to zero and with a static screened interaction W. The central claims near K are a TO-phonon redshift of about 150 cm^-1, a tenfold group-velocity enhancement, a fivefold FWHM increase, and a 26-fold enhancement of |g|^2; near Γ the excitonic effects are claimed to be small due to a gauge-field protection. The validation compares the computed dispersion with graphite data over most of the Brillouin zone and with a single freestanding-graphene Raman dataset (Ref. 13) shifted rigidly by 20 cm^-1.

Significance. If the central claims are correct, the paper would reshape the standard DFT picture of the K-point Kohn anomaly and identify zone-boundary phonons as the dominant source of intrinsic resistivity in graphene at room temperature. The formal framework is a useful extension of the variational formulation of Ref. 23, and the ladder-convergence analysis in Fig. 5 plus the gauge-field consistency check are valuable methodological contributions. However, the numerical predictions are conditional on the untested neglect of the double-counting term and on the fitting/validation choices, so the result is a promising but not yet fully established quantitative claim.

major comments (3)
  1. [Eq. (8) and SM Sec. VIII] The central numerical claim rests on setting ΔfHxc=0. Equation (4) defines the GDFT functional with a double-counting term \bar E_xc that cancels the Fock-like term in the uniform limit; its second density derivative enters Eq. (8) explicitly and modifies the GDFT vertex in Eq. (9). SM Sec. VIII states that this term is neglected because of the reduced tight-binding Hilbert space. The only in-paper justification is the 'excellent agreement' with experiment, but Fig. 1 compares mostly graphite data and Fig. 2(b) uses a single freestanding-graphene dataset (Ref. 13) shifted by 20 cm^-1. No estimate or bound on \bar E_xc near K is provided. Since Fig. 5 shows that self-energy and ladder contributions have opposite signs and nearly cancel at Γ, an omitted term of similar scale could change the 150 cm^-1 redshift and the fivefold linewidth materially. Please compute or bound this term, or otherwise demonstrate that it is negligible at K.
  2. [SM Sec. VIII, spectral function] The linewidth claim is not reproducible as written. The SM states that the 0+ limit in the phonon Green's function is replaced by a finite damping η=10 meV. Inserting η=10 meV into G^-1=ω^2-D(ω+iη) adds a Lorentzian broadening of roughly 2η≈160 cm^-1 to every spectral function, yet Fig. 3(e) reports a DFT FWHM of order 10 cm^-1 at Γ. Either the FWHMs are extracted after deconvolving or subtracting this broadening, or η is used only in the electronic response and not in the final phonon Green's function. The present wording is contradictory and needs clarification, because the fivefold enhancement near K is a headline result.
  3. [Figs. 1-2, validation] The experimental validation is weaker than the text claims. The 'excellent agreement' that justifies neglecting \bar E_xc is obtained by comparing the graphene calculation with graphite data over most of the Brillouin zone (Refs. 58-60), and the only freestanding-graphene data near K are the Ref. 13 Raman points, which are rigidly shifted by 20 cm^-1 before comparison. A rigid shift applied to the reference data cannot validate a momentum-dependent 150 cm^-1 redshift, and graphite data cannot constrain monolayer-specific excitonic effects. Please provide a quantitative comparison with residuals and error bars, either for the unshifted graphene data or after a clearly stated and justified shift.
minor comments (4)
  1. [Main text before Eq. (5)] The phrase 'partially-screen partially-screen formulation' appears to be a duplicated phrase and should read 'partially screened formulation'.
  2. [Acknowledgments] The word 'programe' should be 'program'.
  3. [Fig. 1] The x-axis label 'K M0' is unclear; the momentum path should be labeled consistently with the high-symmetry points used in the text.
  4. [SM Table I] The columns labeled ℏΓ_Γ and ℏΓ_K are reported in cm^-1; the symbol ℏΓ suggests an energy, so the units should be stated explicitly and the notation made consistent.

Circularity Check

0 steps flagged · score 2.0 of 10

No constructional circularity: the excitonic phonon prediction is a genuine BSE ladder calculation, though validation and numerical machinery lean substantially on the authors' own prior work.

full rationale

The central claims (about 150 cm^-1 redshift near K, 5x linewidth enhancement, 26x increase of electron-phonon matrix elements) are obtained from Eqs. (7)-(8) by evaluating the dynamical correction Delta C = V_DFT (chi_W - chi0_DFT) V_DFT after setting Delta f_Hxc = 0. The target observables, i.e., the Kohn anomaly frequencies and linewidths, are not used as fitting parameters. The prediction therefore does not reduce to its inputs by construction. The manuscript is transparent about the dropped double-counting term: it explicitly states in the Supplemental Material that 'in our procedure we neglect the contribution of the double counting of the Fock-like term. Thus, ~V_GDFT = V_KS and Delta f_Hxc = 0.' The only justification offered for this neglect is a posteriori agreement with experiment, and the freestanding-graphene validation point comes from the authors' own Raman measurement (Ref. [13]) after a rigid 20 cm^-1 shift; the remaining experimental comparison is to graphite data. This is a genuine correctness risk, but it is not circularity, because the numerical value of the K-point redshift is not fitted to that experiment. The tight-binding model, the self-consistent screened W, the variational phonon-response formulation, and the generalized Fermi golden rule are taken from self-citations Refs. [22] and [23], but these are explicit, parameterized derivations rather than unverified uniqueness theorems or ansatze smuggled in solely by citation. The 26x enhancement is also consistent with the independent analytical predictions of Refs. [25,26]. Overall, the derivation is self-contained as a many-body calculation; the self-reliance is in the underlying model and in the post hoc validation, not in a definitional equivalence between input and output. Hence a low circularity score of 2 is appropriate.

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

The central numerical claims rest on a tight-binding model fitted to DFT and on a screened W from the same group's prior work; the formal functional's double-counting term is dropped. These fitted and auxiliary quantities, not the physics of graphene alone, set the magnitude of the reported excitonic enhancement.

free parameters (5)
  • Tight-binding model parameters (five nearest-neighbor π-band model) = Not tabulated in this paper (see Ref 22)
    All excitonic/dynamical corrections are computed with this model; parameters are fitted to ab initio DFT band structure, so the quantitative predictions inherit this fit.
  • Screened interaction W reciprocal-space cutoff = 4.5 Å^-1
    Chosen cutoff for W in the tight-binding calculation; controls the strength of the ladder interaction.
  • Real-space range-separation cutoff r_c for W = Interatomic distance (not quantified)
    W is smoothly reduced below r_c to mitigate static screening artifacts; value is chosen by hand.
  • Finite damping η in the phonon Green's function = 10 meV
    Replaces the 0+ limit to handle finite k grids; affects the computed linewidths and is not varied in a published convergence test.
  • Rigid shift of experimental Raman data = 20 cm^-1
    Applied to Ref 13 data before comparison as a post-hoc alignment based on the known G-peak offset; not derived from the theory.
assumptions (6)
  • domain assumption The induced density of the GDFT functional is approximated by the static DFT induced density (ρ_GDFT ≈ ρ_DFT), neglecting O(|Δρ|^2) terms in the force constants.
    Invoked after Eq. (6) in the main text; this is the key approximation that makes the differential correction computationally cheap.
  • ad hoc to paper The double-counting exchange-correlation term ¯Exc is neglected in the numerical implementation (ΔfHxc = 0).
    Main text 'Computational approach' and SM Sec VIII state the double counting is dropped, despite Eq. (4) requiring it for the jellium limit.
  • domain assumption The screened interaction W is static and modeled with Dirac-cone RPA screening, self-consistently with the band structure.
    Used throughout for the GDFT functional and the BSE; dynamic screening is not included.
  • domain assumption Only π and π* bands are included in the tight-binding response calculation; contributions from other bands to χ_W - χ0_DFT are neglected.
    SM Sec VIII states the model includes only π/π* bands with parameters fitted to the ab initio band structure.
  • domain assumption The gauge-field protection argument assumes the electron-electron interaction depends only on |k - K(u)| and the low-energy model is cylindrically isotropic.
    SM Sec VI states these hypotheses are 'not exact for realistic models, but expected to be satisfied for very small u'.
  • standard math Migdal's theorem justifies neglecting phonon vertex corrections in the electronic dynamics.
    Main text, paragraph on phonon Green's function; standard in electron-phonon theory.

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Pith. "Pith review of Excitonic effects in phonons: reshaping the graphene Kohn anomalies and lifetimes." pith.science (2026). https://pith.science/paper/NXHANXAP

@misc{pith2026250413715,
  author       = {Pith},
  title        = {Pith review of: Excitonic effects in phonons: reshaping the graphene Kohn anomalies and lifetimes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NXHANXAP}},
  note         = {Machine review of arXiv:2504.13715}
}
abstract

We develop an ab initio framework that captures the impact of electron-electron and electron-hole interactions on phonon properties. This enables the inclusion of excitonic effects in the optical phonon dispersions and lifetimes of graphene, both near the center ($\Gamma$) and at the border (K) of the Brillouin zone, at phonon momenta relevant for Raman scattering and for the onset of the intrinsic electrical resistivity. Near K, we find a phonon red-shift of ~150 $cm^{-1}$ and a 10x enhancement of the group velocity, together with a 5x increase in linewidths due to a 26x increase of the electron-phonon matrix elements. These effects persist for doping $2E_{F} < {\hbar}{\omega}_{ph}$ and are quenched at higher dopings. Near $\Gamma$, the excitonic effects are minor because of the gauge field nature of the electron-phonon coupling at small phonon momentum.

Figures

Figures reproduced from arXiv: 2504.13715 by the authors.

Figure 1
Figure 1. FIG. 1: Theoretical static phonon dispersion of graphene [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Dispersion of the static phonons of graphene near [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Top and bottom panels [(a)-(b)-(g)-(h)]: regions [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: FIG. 5: Impact of the number of electronic ladder diagrams [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 1
Figure 1. Figure 1: FIG. 1: Impact of temperature on phonon frequency, phonon velocity and FWHM at [PITH_FULL_IMAGE:figures/full_fig_p010_1.png]
Figure 2
Figure 2. Figure 2: FIG. 2: Joint density of states in GDFT (a)-(b) and in DFT (g)-(h). The static phonon dispersion of the LO/TO mode [PITH_FULL_IMAGE:figures/full_fig_p011_2.png]
Figure 3
Figure 3. Figure 3: FIG. 3: Sketch of Feynman diagrams included in our calculations. In particular, (a) the quasi-particle Dyson equation with [PITH_FULL_IMAGE:figures/full_fig_p015_3.png]
Figure 4
Figure 4. Figure 4: FIG. 4: Top left: static inverse dielectric functions in the random phase approximation used to calculate the static screened [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]

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Works this paper leans on

89 extracted references · 66 canonical work pages

  1. [1]

    = 1 /ϵ∞, where ϵ∞ is the electronic static dielectric constant. In this work, we consider the following Hartree- exchange-correlation (Hxc) functional EGDFT Hxc [n]=EDFT Hxc [ρ]− 1 2 |n(r1, r2)|2W(r1, r2)+ ¯Exc[ρ, W] , (4) wheren(r, r′)= ∑ ifiψi(r)ψ∗ i (r′) is the (one-body) elec- tronic density matrix, while fi and ψi are Kohn-Sham occupations and orbita...

  2. [2]

    Density response with excitonic effects— The eval- uation of Eq

    is shown in the SM [ 30]. Density response with excitonic effects— The eval- uation of Eq. ( 2) requires the density-density response function χ, obtained e.g. with Hedin’s equations [ 19] and linear response theory. However, practical schemes require approximations for the electronic interaction. GW+BSE approaches accurately describe excitonic ef- fects o...

  3. [4]

    23 to include excitonic and dy- namical corrections in a differential form (see SM [ 30])

    Now we take advantage of the partially-screen partially-screen formulation of the electronic response of Ref. 23 to include excitonic and dy- namical corrections in a differential form (see SM [ 30]). The force constants associated to the GDFT functional are rewritten as Csα,rβ (z) = V (sα) GDFT(r1, −z)χW (r1, r2,z )V (rβ) GDFT(r2,z ) −ρ(sα) GDFT(r1, −z)f ...

  4. [5]

    with W=0], and ∆Csα,rβ (z) = ˜V (sα) GDFT(r1)χW (r1, r2,z ) ˜V (rβ) GDFT(r2) −V (sα) DFT (r1)χ0 DFT(r1, r2)V (rβ) DFT(r2) −ρ(sα) DFT(r1)∆fHxc(r1, r2)ρ(rβ) DFT(r2) (8) is a dynamical correction that includes excitonic effects though χW . χ0 DFT is the static bare susceptibility eval- uated with DFT orbitals, energies and occupations (see SM [ 30]), while ˜V...

  5. [7]

    of the ¯Exc contribution. We cal- culate the phonon frequency and full-width half maxi- mum (FWHM) from the peak position and width of the spectral function A(ω) = − ∑ sα Im [ ω πGsα,sα(ω) ] (10) (details in SM [ 30]). Application to neutral graphene— In Fig. 1, we show the static phonon dispersion of graphene obtained by set- ting ω=0 in Eq. ( 7). We do ...

  6. [8]

    Note that, if ∆fHxc is set to zero in Eqs

    can be trivially evaluated. Note that, if ∆fHxc is set to zero in Eqs. ( 8)-(9), ˜VGDFT=VDFT and the correction of the force constant matrix ∆C(z) consist in the difference between χW (z) andχ0 DFT. From such difference, it is explicit how ∆C(z) contains both dynamical and excitonic effects missed in standard DFT. Computational approach— The static DFT dynam...

  7. [9]

    Al-Jishi and G

    R. Al-Jishi and G. Dresselhaus, Phys. Rev. B 26, 4514 (1982)

    1982

  8. [10]

    Aizawa, R

    T. Aizawa, R. Souda, S. Otani, Y. Ishizawa, and C. Os- hima, Phys. Rev. B 42, 11469 (1990)

    1990

Show all 89 references
  1. [11]

    This strong enhancement of gK is in accordance with the an- alytical prediction of Refs

    and the values re- ported in the SM, we find |gK,GDFT|2∼26|gK,DFT|2. This strong enhancement of gK is in accordance with the an- alytical prediction of Refs. [ 25, 26], where a logarithmic divergence of the electron-phonon coupling at K is ex- pected at T =0K for undoped graphe...

    2020

  2. [13]

    Saito, A

    R. Saito, A. Jorio, A. G. Souza Filho, G. Dresselhaus, M. S. Dresselhaus, and M. A. Pimenta, Phys. Rev. Lett. 88, 027401 (2001)

    2001

  3. [14]

    Graziotto, F

    L. Graziotto, F. Macheda, T. Venanzi, G. Marchese, S. Sotgiu, T. Ouaj, E. Stellino, C. Fasolato, P. Postorino, M. Metzelaars, P. Kögerler, B. Beschoten, M. Calandra, M. Ortolani, C. Stampfer, F. Mauri, and L. Baldassarre, Nano Lett. 24, 1867 (2024)

    2024

  4. [15]

    Lazzeri, C

    M. Lazzeri, C. Attaccalite, L. Wirtz, and F. Mauri, Phys. Rev. B 78, 081406 (2008)

    2008

  5. [16]

    Attaccalite and A

    C. Attaccalite and A. Rubio, Physica Status Solidi (b) 246, 2523 (2009)

    2009

  6. [18]

    Strinati, H

    G. Strinati, H. J. Mattausch, and W. Hanke, Phys. Rev. B 25, 2867 (1982)

    1982

  7. [19]

    M. S. Hybertsen and S. G. Louie, Phys. Rev. B 34, 5390 (1986). 6

    1986

  8. [20]

    R. W. Godby, M. Schlüter, and L. J. Sham, Phys. Rev. B 37, 10159 (1988)

    1988

  9. [21]

    Venanzi, L

    T. Venanzi, L. Graziotto, F. Macheda, S. Sotgiu, T. Ouaj, E. Stellino, C. Fasolato, P. Postorino, V. Mišeikis, M. Metzelaars, P. Kögerler, B. Beschoten, C. Coletti, S. Roddaro, M. Calandra, M. Ortolani, C. Stampfer, F. Mauri, and L. Baldassarre, Phys. Rev. Lett. 130, 256901 (2023)

    2023

  10. [22]

    Guandalini, G

    A. Guandalini, G. Caldarelli, F. Macheda, and F. Mauri, Phys. Rev. B 111, 075118 (2025)

    2025

  11. [23]

    Physical observables are obtained in the limit η→0+, to be considered after the thermodynamical limit [ 31]

    We ex- press the analytic continuation of Fourier transforms of retarded quantities in complex frequency z=ω+iη. Physical observables are obtained in the limit η→0+, to be considered after the thermodynamical limit [ 31]. All the information about phonons is encoded in the (ma...

    2025 arXiv

  12. [24]

    Graziotto, F

    L. Graziotto, F. Macheda, T. Sohier, M. Calandra, and F. Mauri, Phys. Rev. B 109, 075420 (2024)

    2024

  13. [25]

    Bauernschmitt and R

    R. Bauernschmitt and R. Ahlrichs, Chemical Physics Let- ters 256, 454 (1996)

    1996

  14. [26]

    Rocca, R

    D. Rocca, R. Gebauer, Y. Saad, and S. Baroni, The Journal of Chemical Physics 128 (2008)

    2008

  15. [27]

    Baer and L

    R. Baer and L. Kronik, The European Physical Journal B 91, 170 (2018)

    2018

  16. [28]

    Hedin, Phys

    L. Hedin, Phys. Rev. 139, A796 (1965)

    1965

  17. [29]

    Strinati, La Rivista del Nuovo Cimento (1978-1999) 11, 1 (1988)

    G. Strinati, La Rivista del Nuovo Cimento (1978-1999) 11, 1 (1988)

    1988

  18. [30]

    Onida, L

    G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002)

    2002

  19. [31]

    Caldarelli, A

    G. Caldarelli, A. Guandalini, F. Macheda, and F. Mauri, Phys. Rev. B 111, 075137 (2025)

    2025

  20. [32]

    Z. Li, G. Antonius, M. Wu, F. H. da Jornada, and S. G. Louie, Phys. Rev. Lett. 122, 186402 (2019)

    2019

  21. [33]

    D. M. Basko and I. L. Aleiner, Phys. Rev. B 77, 041409 (2008)

    2008

  22. [34]

    D. M. Basko, Phys. Rev. B 78, 125418 (2008)

    2008

  23. [35]

    Electron-phonon coupling using many- body perturbation theory: Implementation in the ques- taal electronic structure suite,

    S. Laricchia, C. Eichstaedt, D. Pashov, and M. van Schilfgaarde, “Electron-phonon coupling using many- body perturbation theory: Implementation in the ques- taal electronic structure suite,” (2024), arXiv:2404.02902 [cond-mat.mtrl-sci]

    2024 arXiv

  24. [36]

    Lazzeri and F

    M. Lazzeri and F. Mauri, Phys. Rev. Lett. 97, 266407 (2006)

    2006

  25. [37]

    V. N. Popov and P. Lambin, Phys. Rev. B 82, 045406 (2010)

    2010

  26. [38]

    See Supplemental Material for detailed information about additional theoretical derivations and phonon life- times of doped graphene around the Γ point

  27. [39]

    R. Kubo, M. Toda, and N. Hashitsume, Statistical physics II: nonequilibrium statistical mechanics, Vol. 31 (Springer Science & Business Media, 2012)

    2012

  28. [40]

    E. G. Maximov, Sov. Phys.-JETP 42, 1138 (1975)

    1975

  29. [41]

    W. H. Buttler, F. J. Pinski, and P. B. Allen, Physical Review B 19, 3708 (1979)

    1979

  30. [42]

    Dynamical properties of solids vol 3: Metals, superconductors, magnetic materials, liquids,

    P. Allen, “Dynamical properties of solids vol 3: Metals, superconductors, magnetic materials, liquids,” (North- Holland Publishing Company, Amsterdam, 1980) Chap. Phonons and the Superconducting Transition Tempera- ture

    1980

  31. [43]

    Giustino, Rev

    F. Giustino, Rev. Mod. Phys. 89, 015003 (2017)

    2017

  32. [44]

    Stefanucci, R

    G. Stefanucci, R. van Leeuwen, and E. Perfetto, Phys. Rev. X 13, 031026 (2023)

    2023

  33. [45]

    A. B. Migdal, Sov. Phys.-JETP 6, 996 (1958)

    1958

  34. [46]

    Calandra, G

    M. Calandra, G. Profeta, and F. Mauri, Phys. Rev. B 82, 165111 (2010)

    2010

  35. [47]

    R. M. Martin, L. Reining, and D. M. Ceperley, Interacting Electrons: Theory and Computational Approaches (Cambridge University Press, 2016)

    2016

  36. [48]

    L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 103, 186802 (2009)

    2009

  37. [49]

    Guandalini, R

    A. Guandalini, R. Senga, Y.-C. Lin, K. Suenaga, A. Fer- retti, D. Varsano, A. Recchia, P. Barone, F. Mauri, T. Pichler, and C. Kramberger, Nano Letters 23, 11835 (2023), pMID: 38088831

    2023

  38. [50]

    Guandalini, D

    A. Guandalini, D. A. Leon, P. D’Amico, C. Cardoso, A. Ferretti, M. Rontani, and D. Varsano, Phys. Rev. B 109, 075120 (2024)

    2024

  39. [51]

    A. H. Søndersted, M. Kuisma, J. K. Svaneborg, M. K. Svendsen, and K. S. Thygesen, Phys. Rev. Lett. 133, 026403 (2024)

    2024

  40. [52]

    Yoshinobu and T.-n

    A. Yoshinobu and T.-n. Seiichiro, Chemical Physics Let- ters 462, 348 (2008)

    2008

  41. [53]

    Seth and T

    M. Seth and T. Ziegler, Journal of Chemical Theory and Computation 8, 901 (2012), pMID: 26593352

    2012

  42. [54]

    J. Zhan, M. Govoni, and G. Galli, Journal of Chem- ical Theory and Computation 19, 5851 (2023) , pMID: 37591004, https://doi.org/10.1021/acs.jctc.3c00580

    2023 doi

  43. [55]

    C. A. Jiménez-Hoyos, B. G. Janesko, and G. E. Scuseria, Physical Chemistry Chemical Physics 10, 6621 (2008)

    2008

  44. [56]

    J. Yang, S. Falletta, and A. Pasquarello, npj Computa- tional Materials 9, 108 (2023)

    2023

  45. [57]

    Gygi and A

    F. Gygi and A. Baldereschi, Phys. Rev. Lett. 62, 2160 (1989)

    1989

  46. [58]

    Massidda, A

    S. Massidda, A. Continenza, M. Posternak, and A. Baldereschi, Phys. Rev. Lett. 74, 2323 (1995)

    1995

  47. [59]

    Rohlfing, Phys

    M. Rohlfing, Phys. Rev. B 82, 205127 (2010)

    2010

  48. [60]

    J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)

    1981

  49. [61]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    1996

  50. [62]

    X. Ge, S. J. Binnie, D. Rocca, R. Gebauer, and S. Baroni, Computer Physics Communications 185, 2080 (2014)

    2014

  51. [63]

    Paleari and A

    F. Paleari and A. Marini, Phys. Rev. B 106, 125403 (2022)

    2022

  52. [64]

    Berges, N

    J. Berges, N. Girotto, T. Wehling, N. Marzari, and S. Poncé, Phys. Rev. X 13, 041009 (2023)

    2023

  53. [65]

    Giannozzi, O

    P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. de Gironcoli, P. Delugas, F. Ferrari Ruffino, A. Ferretti, N. Marzari, I. Timrov, A. Urru, and S. Baroni, J. Chem. Phys. 152, 154105 (2020)

    2020

  54. [66]

    Maultzsch, S

    J. Maultzsch, S. Reich, C. Thomsen, H. Requardt, and P. Ordejón, Phys. Rev. Lett. 92, 075501 (2004)

    2004

  55. [67]

    M. Mohr, J. Maultzsch, E. Dobardžić, S. Reich, I. Miloše- vić, M. Damnjanović, A. Bosak, M. Krisch, and C. Thomsen, Phys. Rev. B 76, 035439 (2007)

    2007

  56. [68]

    Grüneis, J

    A. Grüneis, J. Serrano, A. Bosak, M. Lazzeri, S. L. Molodtsov, L. Wirtz, C. Attaccalite, M. Krisch, A. Ru- bio, F. Mauri, and T. Pichler, Phys. Rev. B 80, 085423 (2009)

    2009

  57. [69]

    Piscanec, M

    S. Piscanec, M. Lazzeri, F. Mauri, A. C. Ferrari, and J. Robertson, Phys. Rev. Lett. 93, 185503 (2004)

    2004

  58. [70]

    Venezuela, M

    P. Venezuela, M. Lazzeri, and F. Mauri, Phys. Rev. B 84, 035433 (2011)

    2011

  59. [71]

    J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, Phys. Rev. Lett. 98, 166802 (2007)

    2007

  60. [72]

    Froehlicher and S

    G. Froehlicher and S. Berciaud, Phys. Rev. B 91, 205413 (2015)

    2015

  61. [73]

    Sonntag, K

    J. Sonntag, K. Watanabe, T. Taniguchi, B. Beschoten, 7 and C. Stampfer, Phys. Rev. B 107, 075420 (2023)

    2023

  62. [74]

    P. E. Trevisanutto, C. Giorgetti, L. Reining, M. Ladisa, and V. Olevano, Phys. Rev. Lett. 101, 226405 (2008)

    2008

  63. [75]

    D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Mo- rozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, Nat. Phys. 7, 701 (2011)

    2011

  64. [76]

    Sonntag, S

    J. Sonntag, S. Reichardt, L. Wirtz, B. Beschoten, M. I. Katsnelson, F. Libisch, and C. Stampfer, Phys. Rev. Lett. 120, 187701 (2018)

    2018

  65. [77]

    C.-H. Park, N. Bonini, T. Sohier, G. Samsonidze, B. Kozinsky, M. Calandra, F. Mauri, and N. Marzari, Nano Letters 14, 1113 (2014)

    2014

  66. [78]

    Z. Yin, A. Kutepov, and G. Kotliar, Physical Review X 3, 021011 (2013)

    2013

  67. [79]

    Calandra, P

    M. Calandra, P. Zoccante, and F. Mauri, Physical Re- view Letters 114, 077001 (2015)

    2015

  68. [80]

    Romanin, L

    D. Romanin, L. Monacelli, R. Bianco, I. Errea, F. Mauri, and M. Calandra, The Journal of Physical Chemistry Letters 12, 10339 (2021)

    2021

  69. [81]

    S. P. Villani, M. Campetella, P. Barone, and F. Mauri, npj Computational Materials 10, 81 (2024)

    2024

  70. [82]

    Sonntag, K

    J. Sonntag, K. Watanabe, T. Taniguchi, B. Beschoten, and C. Stampfer, Phys. Rev. B 107, 075420 (2023) . 8 End matter Doping effects — We present in Fig. 4 the ef- fect of doping in the FWHM and regions where the joint density of states is different from zero near K for two differ...

    2023

  71. [83]

    In order to distinguish the two contributions, we plot in Fig

    (self-energy corrections); (ii) the presence of electron-hole interaction diagrams in χW (ladder corrections). In order to distinguish the two contributions, we plot in Fig. 5 the phonon frequencies (a)-(d) and FWHM (e)-(f) of phonons around Γ (left panels) and K (right panels...

  72. [84]

    ( 16), ( 18), ( 19) and ( 20) are solved self-consistently to include electron-electron interaction in χ0

    Eqs. ( 16), ( 18), ( 19) and ( 20) are solved self-consistently to include electron-electron interaction in χ0. This is not always a good choice, but it is appropriate for graphene 7. Eq. ( 19) is equivalent to W (r, r′) = ϵ−1(r, r1)v(r1, r′), where ϵ−1 is the inverse dielectr...

  73. [85]

    with DFT wavefunctions, energies and occu- pations. Eq. ( 21) is represented diagramatically in Fig. 3(c) and it is equivalent to Eq. (10) of the main text, as ρ(sα) DFT(r) = χ0 DFT(r, r2)V (sα) DFT (r2). Excitonic effects are included in the electron-hole propagator LW , obtai...

  74. [86]

    orbital approximation

    In Eq. (30), q is the phonon quasimomentum commensurate with a Born-Von Karman supercell of dimensions N Ω. Using 7 (30) in Eq. 7 of the main text, we get Csα,rβ (q,z ) = C DFT sα,rβ (q) + ∆Crα,sβ (q,z ). (31) We express the response functions on the representation of the Bloc...

  75. [87]

    ( 2), ˆU (rβ,q) ext are cell-periodic potentials, and the sum over R runs over the full crystal

    is defined as 1 ˆV (sα,−q) ext = ∑ R e−iq·(R+τs) ∂ ˆVext ∂u(R)sα = ˆU (sα,−q) ext e−iq·ˆr, (33) where ˆVext was defined in Schrodinger representation in Eq. ( 2), ˆU (rβ,q) ext are cell-periodic potentials, and the sum over R runs over the full crystal. The DFT induced density i...

  76. [88]

    The second term in Eq

    the Hartree-exchange correlation kernel in reciprocal space is defined as [ f DFT Hxc ] nk+q,mk pk′+q,lk′ =N ∫ N Ω drψ(0) nk+q(r)∗ψ(0) mk(r)f DFT Hxc (r, r1)ψ(0) pk′+q(r1)ψ(0) lk′ (r1)∗ (37) where the expression of the kernel in real space f DFT Hxc (r, r′) depends on the appro...

  77. [89]

    In the remainder, we focus in the calculation of the first term

    is trivial to compute. In the remainder, we focus in the calculation of the first term. The interacting electron-hole propagator LW , required to obtain its contracted counterpart χW , satisfies the fol- lowing BSE in reciprocal space [LW ]nk+q,mk pk′+q,lk′ (z) = L0 pk′+q,lk′ (z...

  78. [90]

    (43) We solve Eq

    can be written in terms of the density with excitonic effects as ∑ knm ⟨ ψ(0) mk ⏐ ⏐ ⏐ˆV (sα,−q) DFT ⏐ ⏐ ⏐ψ(0) nk+q ⟩ χW nk+q,mk(z) ⟨ ψ(0) nk+q ⏐ ⏐ ⏐ˆV (rβ,q) DFT ⏐ ⏐ ⏐ψ(0) mk ⟩ = ∑ knm ⟨ ψ(0) mk ⏐ ⏐ ⏐ˆV (sα,−q) DFT ⏐ ⏐ ⏐ψ(0) nk+q ⟩⟨ ψ(0) nk+q ⏐ ⏐ ⏐ˆρ(rβ,q)(z) ⏐ ⏐ ⏐ψ(0) mk ⟩ . ...

  79. [91]

    We iterate until convergence of Eq

    iteratively using ρ (1) start = χ(0)V (1) ext as a starting guess. We iterate until convergence of Eq. ( 43). Between different iterations, we use a linear mixing procedure to update the density matrix 1,7. Using Eq. ( 32) and Eq. ( 38) in Eq. ( 31), we obtain Csα,rβ (q,z ) as ...

  80. [92]

    Though, under proper hypothesis, it can be extended to the case where the band velocity is renormalized by the electron-electron interaction

    is shown for the case of constant Fermi velocity. Though, under proper hypothesis, it can be extended to the case where the band velocity is renormalized by the electron-electron interaction. In this case, the full Hamiltonian reads Hk =H 0 k +H e-ph k +H e-e k , H0 = ℏvF (kx,...

  81. [93]

    The screened matrix elements VDFT are computed with a first nearest-neighbor tight-binding model with parameters fitted over a DFPT ab-initio calculation, as explained in Ref

    Doping effects are included both in the occupation factors and the screened interaction W. The screened matrix elements VDFT are computed with a first nearest-neighbor tight-binding model with parameters fitted over a DFPT ab-initio calculation, as explained in Ref. 15. The matri...

    2025

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