Light-Enhanced Electron-Phonon Coupling in Photoexcited Graphene

The study investigates how ultrafast optical excitation modifies electron–phonon coupling (EPC) and energy transport between photoexcited carriers and phonons in graphene. It addresses whether and how nonequilibrium photocarrier distributions enhance EPC, how this manifests in carrier relaxation, phonon dynamics, and Raman spectral features, and how EPC can be quantified and tracked in real time from macroscopic observables. The work is motivated by the central role of EPC in thermalization, transport, and emergent phases, and by experimental indications of light-modulated EPC in graphene and related materials.

Prior works established EPC as key to electron thermal relaxation and transport in graphene and other materials (Allen 1987; Tse & Das Sarma 2009; Viljas & Heikkilä 2010). Raman studies reported doping-dependent phonon anomalies and EPC tuning (Pisana et al. 2007; Yan et al. 2007, 2008; Ando 2006; Piscanec et al. 2004). Ultrafast spectroscopies revealed nonthermal photocarrier dynamics, carrier cooling and EPC-related phenomena (Gierz et al. 2013, 2015; Rohde et al. 2018; Jensen et al. 2014; Winnerl et al. 2011). Fano resonances indicating electron–phonon interference were observed in graphene and Weyl semimetals. Theoretical frameworks (Green’s functions, Eliashberg) relate macroscopic energy transfer rates to microscopic EPC strength, while standard DFPT can miss non-adiabatic effects at high doping.

Real-time time-dependent density functional theory (TDDFT) simulations were performed using the TDAP implementation in SIESTA. Numerical atomic orbitals (double zeta polarization) were used with a Γ-centered 144×144×1 k-mesh. Electron–ion interactions employed norm-conserving pseudopotentials within LDA and a 200 Ry cutoff. A Gaussian laser pulse F=F0 cos(ωt) exp[−(t−t0)^2/(2σ^2)] with wavelength 800 nm (ħω=1.55 eV), polarization along zigzag (x) direction, peak at t0=20 fs, and full width at half maximum (FWHM) ≈7 fs was applied. Coherent E2g optical phonons (ħωph≈0.2 eV) were included by an initial 1–2% C–C bond stretch. Doping was modeled by shifting the Fermi level EF relative to the Dirac point ED (±(EF−ED)), controlling carrier concentration. Carrier population nki(t), band energies εki(t), and total carrier energy Eki(t)=nki(t)εki(t) were tracked to compute the energy transport rate P(t)=Σk,i dEki(t)/dt. Time-averaged P at ≈50 fs was evaluated with and without illumination, over doping. EPC strength λ was extracted from P using a Green-function-based relation (Eq. 1): λ=α ρ/(πρ NB) with parameters defined from EF, EF−ED, ħωph, Fermi velocity vF, carrier density n, phonon number NB=Mu^2 ωph^2/(2ħωph), and Fermi–Dirac occupation n1; details in Supplementary Note 2. The effective EPC matrix element ⟨g^2⟩ was obtained via Eliashberg relation (Eq. 2): λ=2⟨g^2⟩ NF/ħωph, where NF is the DOS near EF for the Dirac cone. Raman spectra were simulated to analyze Fano lineshapes and extract Fano factors. Time-resolved EPC was tracked by evaluating λ(t) and ⟨g^2⟩(t) during and after the pulse, and compared with values reconstructed from experimental tr-ARPES carrier distributions.

• Carrier relaxation shows a biexponential decay in the presence of phonons with time constants T1≈7 fs (pulse-width-limited) and T2≈650 fs (hot-carrier cooling via optical phonons), matching experimental ranges (100 fs–1 ps). Without phonons, carrier population remains nearly constant after excitation due to missing decay channels.
• Photocarrier population oscillates at the E2g phonon frequency (≈0.2 eV) and its second harmonic (≈0.4 eV), evidencing strong EPC.
• Simulated Raman spectra display asymmetric E2g phonon peaks (Fano resonance). Extracted Fano factors: g_harmonic≈0.04 at 0.2 eV and g_anharmonic≈1.3 at 0.4 eV, indicating strong EPC in photoexcited graphene.
• In the ground state (no illumination), the energy transport rate P versus doping shows a logarithmic anomaly at |EF−ED|=ħωph/2≈0.1 eV, tied to phonon-induced vertical interband e–h excitations; P increases with doping up to this point and decreases beyond due to Pauli blocking.
• Under ≈4 μJ·cm−2 illumination (effective Te≈2500 K), the singularity in P is washed out by Fermi-level broadening and P is strongly enhanced in magnitude relative to ground state.
• EPC strength λ extracted from P increases with doping. Ground-state λ(EF−ED) agrees with DFPT at low-to-moderate doping; deviations at high |EF−ED| are attributed to non-adiabatic effects absent in DFPT but captured here.
• Effective EPC matrix element ⟨g^2⟩ (from Eq. 2): ground state ⟨g^2⟩≈0.05 eV^2 (consistent with DFPT ≈0.043 eV^2 and experiments 0.043–0.047 eV^2). In the excited state (averaged around 50 fs), λ is enhanced ≈3× and fitted ⟨g^2⟩≈0.15 eV^2, in good agreement with tr-ARPES indications.
• Energy-resolved analysis shows that without illumination, low-energy carriers (E−EF<0.6 eV) excited by phonons dominate λ; with illumination, nonthermal high-energy photocarriers (peaked near E−EF≈0.8 eV ≈ ħω/2) dominate the λ enhancement. As doping increases, excited-carrier population decreases due to Pauli blocking.
• Phonon-assisted intraband transitions (PAITs) enabled by broadened nonthermal photocarrier distributions contribute ≈80% of additional EPC channels, explaining light-induced EPC enhancement; mechanisms include electronic broadening (process I) and intervalley/ik scattering (process II).
• Real-time dynamics: During the pulse (t≤30 fs), carriers at E−EF≈1.0 eV and their broadened distribution lead to a 2–3 orders-of-magnitude enhancement of effective EPC (⟨g^2⟩>1 eV^2). After the pulse, as carriers cool and thermalize towards an F–D distribution, the enhanced EPC decays towards the equilibrium value (~0.05 eV^2) within picoseconds. The reconstructed time evolution of EPC from tr-ARPES carrier distributions agrees with experiments.

The findings demonstrate that light can substantially and dynamically enhance EPC in graphene by creating broad, nonthermal photocarrier distributions that open additional phonon-assisted intraband scattering channels. This enhancement increases carrier–phonon energy transfer P and modifies Raman phonon lineshapes via Fano interference. The doping dependence of P and λ, and the disappearance of the ground-state singularity under illumination, are explained by the interplay of phonon-induced interband transitions and Pauli blocking, with photoexcitation-induced Fermi broadening removing phase-space constraints. Quantitative extraction of EPC (λ and ⟨g^2⟩) from macroscopic P links ultrafast thermodynamics to microscopic coupling, validated against DFPT and tr-ARPES. The ability to track EPC in real time, and its sensitivity to photocarrier distributions, suggests routes to optically modulate EPC by tailoring pump fluence, pulse width, and wavelength, and by suppressing competing relaxation channels (e.g., electron–electron scattering).

This work establishes a dynamic framework to evaluate and track nonequilibrium EPC in graphene under ultrafast photoexcitation. It reveals that nonthermal photocarriers drive a ≈3× increase in effective EPC (⟨g^2⟩ from ≈0.05 to ≈0.15 eV^2 on average at ~50 fs) and even transient enhancements by orders of magnitude during the pulse. The mechanism is dominated by phonon-assisted intraband transitions afforded by broadened photocarrier distributions. The methodology connects macroscopic energy transport to microscopic EPC and is corroborated by Raman and tr-ARPES experiments. Beyond graphene, the approach should be applicable to other quantum materials (Dirac/Weyl semimetals, TMDs, metals) where nonequilibrium carrier distributions can enable additional EPC channels. Future work may leverage coherent control to manipulate EPC in real time and explore implications for superconductivity, gap dynamics, and light-driven phase transitions.

• The simulations emphasize the dominant E2g optical phonon mode; contributions from other phonon modes are not explicitly detailed and may affect quantitative EPC under some conditions.
• TDDFT within LDA and chosen pseudopotentials/basis entail approximations; electron–electron scattering and many-body effects beyond TDDFT may influence ultrafast dynamics.
• Doping is modeled via Fermi-level shifts; real experimental doping environments may introduce disorder or substrate effects not captured.
• Extracted excited-state EPC values are averaged at specific times (e.g., ~50 fs); instantaneous values are highly dynamic and depend on pump parameters.
• Comparisons with DFPT highlight non-adiabatic effects at high doping; standard DFPT lacks these, potentially limiting ground-state benchmarks at high |EF−ED|.
• Real-time EPC reconstruction from experiments relies on accurate carrier distributions from tr-ARPES; experimental resolution and assumptions in analysis can introduce uncertainties.