Nonequilibrium Photocarrier and Phonon Dynamics from First Principles: a Unified Treatment of Carrier-Carrier, Carrier-Phonon, and Phonon-Phonon Scattering

TL;DR

The paper develops a first-principles, real-time framework that unifies nonequilibrium photocarrier and phonon dynamics in semiconductors by explicitly including carrier–carrier, carrier–phonon, and phonon–phonon scattering on an equal footing. It combines ab initio light–matter coupling with a GW/COHSEX dressing scheme, Fan–Migdal electron–phonon self-energies, and phonon-phonon anharmonicity, all solved in a maximally localized Wannier basis for ultradense Brillouin-zone sampling. The method yields time-dependent quasiparticle and phonon renormalizations, hot-phonon dynamics, coherent lattice motion, and light-induced screening, enabling direct comparisons to pump–probe experiments and coupling to constrained DFT for long-time structural transitions. Applications to MoS$_2$ and h-BN monolayers demonstrate rapid carrier relaxation, two-stage energy transfer to the lattice, and fluence-dependent screening and exciton behavior, establishing a versatile, predictive platform for ultrafast phenomena in 2D semiconductors.

Abstract

We develop a first-principles many-body framework to describe the dynamics of photocarriers and phonons in semiconductors following ultrafast excitation. Our approach incorporates explicit ab initio light-matter coupling and first-principles collision integrals for carrier-carrier, carrier-phonon, and phonon-phonon scattering. It also yields time-dependent quasiparticle and phonon frequency renormalizations, along with light-induced coherent atomic motion. The equations of motion are solved in a maximally localized Wannier basis, ensuring gauge-consistent scattering integrals and ultradense momentum sampling, thereby enabling direct comparison with pump-probe experiments. The method can be coupled to constrained density-functional theory to access light-induced structural phase transitions at longer times after the light pulse. We showcase the capabilities and predictive power of this framework on MoS$_2$ and h-BN monolayers. For MoS$_2$, we resolve photoinduced renormalizations of electronic and lattice properties, ultrafast carrier relaxation, hot-phonon dynamics, and displacive coherent atomic motion. Including carrier-carrier scattering is crucial to obtain realistic photocarrier equilibration times, while omitting phonon-phonon scattering leads to incorrect long-time lattice thermalization and a factor of two larger A$_{1g}$ coherent phonon damping time. For h-BN, we quantify photoinduced changes in the electronic, optical, and lattice responses in quasi-equilibrium, demonstrating a fluence-dependent enhancement of screening and melting of excitonic features.

Figures (12)

• Figure 1: Real-time dynamics of selected electronic and lattice observables in monolayer MoS$_2$ after above-gap excitation (fluence $\approx 0.85$ mJ/cm$^{-2}$). (a) Occupation of the lowest conduction band at $K$. (b) Effective temperature of the $A_{1g}$ phonon; inset: long-time cooling (2–5 ps). (c) Coherent amplitude of the $A_{1g}$ mode. Solid curves include the full interaction set: (a) carrier--carrier + carrier–phonon; (b,c) carrier–phonon + phonon–phonon, while dashed curves include only carrier–phonon. Discrepancies in timescales and amplitudes highlight the necessity of treating all interactions on equal footing.
• Figure 2: (a) Dyson equations for the interacting electron (straight line) and phonon (curly line) propagators. Bold lines denote interacting propagators; thin lines, noninteracting ones. (b,c) Electron and phonon self-energy diagrams included in the present approximation. (d) Conventions for the bare and screened Coulomb interactions $v$ and $W_s$, electron–phonon couplings $\bar{g}$ and $g$, and third-order anharmonic coupling $\Phi^{(3)}$.
• Figure 3: Pictorial representation of the collisions considered in the dynamics. The labels $i_{n}$ and $f_{n}$ denote the initial and final states, respectively. (a) Carrier–phonon processes where a phonon is absorbed or emitted by an incoming electron. (b) Phonon–phonon processes where a phonon is absorbed or emitted by an incoming phonon. (c) Carrier-carrier processes involving two-electron collisions.
• Figure 4: Full set of dynamical EOMs of the coupled electron–phonon system. This is naturally divided into three main blocks, each one describing the coupled electron, phonon, and ion dynamics.
• Figure 5: The workflow comprises four main stages: (i) Ab initio DFT and DFPT calculations on coarse $\vb{k}$ and $\vb{q}$ grids. These yield Kohn–Sham orbitals and eigenvalues (from DFT), along with the dynamical matrix, deformation potential, and third-order anharmonic matrix (from DFPT). (ii) Maximally localized Wannier functions (MLWF) construction, GW correction within many-body perturbation theory (MBPT), and (optional) anharmonic SSCHA calculation. Kohn–Sham orbitals are employed to compute MLWFs, static screening, and GW eigenvalues, while harmonic dynamical-matrix and total-energy calculations are used to estimate the nonperturbative anharmonic matrix and SSCHA frequencies. (iii) Preparation of matrix elements on dense $\vb{k}$ and $\vb{q}$ grids. MLWF matrices and phonon eigenvalues are employed to transform the matrix elements into the optimally smooth subspace and normal-mode basis, followed by interpolation onto dense grids. (iv) Explicit time integration of the EOMs. The time derivatives of occupations, polarization, atomic displacements, and momenta are evaluated through the EOMs (see Fig. \ref{['fig:EOM']}). The dynamical variables are evolved and observables computed at each step. The cycle continues until quasi-equilibrium is achieved. The steps (iii) and (iv), represented by light yellow blocks in the workflow, are all performed within the epiq code