The critical role of hot carrier cooling in optically excited structural transitions

The study investigates how hot carrier cooling influences photoinduced phase transitions (PIPTs), a mechanism often neglected in simulations that focus solely on non-equilibrium carrier populations immediately after photoexcitation. Prior explanations attribute PIPTs to transient modifications of potential energy surfaces or excitation of soft phonon modes due to photoexcited carriers. However, the rapid relaxation of carriers to lower energy states within the first hundred femtoseconds can alter occupations, forces, and energy transfer to the lattice. Using IrTe₂, a quasi-2D metallic system exhibiting Ir–Ir dimerization in its low-temperature phase, the authors aim to elucidate the role of hot carrier cooling in triggering dimer dissolution and subsequent recovery, thereby clarifying the atomic-scale dynamics and reconciling ultrafast diffraction observations with microscopic mechanisms.

The paper situates its work within extensive ultrafast studies showing optical control of structural phases in 1D, 2D, and 3D materials using time-resolved diffraction and photoemission. Two prevalent pictures have been used: (i) photoexcited carriers transiently reshape potential energy surfaces, stabilizing phases different from the ground state; (ii) soft phonon mode excitation drives coherent nuclear motion to a new phase. Prior rt-TDDFT simulations often used fixed excited occupations or high electronic temperatures and lacked carrier cooling due to Ehrenfest dynamics limitations. Experiments on IrTe₂ (Ideta et al.; Monney et al.) suggested roles for carrier recombination and lattice heating following carrier cooling, but the atomistic mechanism and interplay of forces and kinetic energy remained unclear. The authors’ previous work tied driving forces to occupations of Ir–Ir dimer bonding/antibonding states, motivating inclusion of realistic carrier cooling in simulations.

The authors perform real-time time-dependent density functional theory (rt-TDDFT) simulations with a Gaussian-envelope laser field to mimic photoexcitation and incorporate hot carrier cooling via a Boltzmann-factor-based scheme that restores detailed balance among electronic transitions. Key computational details: plane-wave DFT with PBE exchange-correlation and norm-conserving pseudopotentials (PWmat code); plane-wave cutoff 45 Ry; 128-atom supercell of IrTe₂; Γ-point sampling; time step 0.1 fs using a linear time-dependent Hamiltonian approach. The pump is modeled as E(t)=E0 cos(ωt) exp[-(t−t0)²/(2σ²)] with E0=0.2 V/Å, ω=3.1 eV (≈400 nm), t0=60 fs, and 2σ=25 fs. Photoexcitation results in ≈3% valence electrons promoted, as in experiments. Hot carrier cooling is introduced through a Boltzmann correlation with decoherence time τ=20 fs (tested to be not sensitive within reasonable ranges), modifying the time-dependent coefficients and changing total energy; the energy change is added to the transition degree of freedom in an NVE ensemble to capture electron–phonon energy transfer and coherent lattice kinetic energy gain. A comparative NVT setup is also used, keeping total lattice kinetic energy constant to mimic rapid heat dissipation, to isolate the role of kinetic energy enhancement. Partial density of states (PDOS) is tracked for Ir–Ir dimer antibonding d-orbitals (≈0.3–1.0 eV above EF), and a time-dependent occupation metric N_dimer is defined by integrating the occupation in this window. The evolution of Ir–Ir bond lengths quantifies dimer dissolution/recovery. Simulated diffraction intensity changes ΔI/I are computed via the Debye–Waller relation I(t)=exp(-Q²⟨u²(t)⟩/3). For comparison with purely thermal processes, ground-state Born–Oppenheimer MD (BOMD) is run at ≈1000 K (NVE), using the same 128-atom supercell and Γ-point, to assess the timescale of thermally driven dimer dissolution without photoexcitation.

• Without hot carrier cooling (standard rt-TDDFT/Ehrenfest-like), immediately after excitation only ~40% of Ir–Ir dimer antibonding states are occupied at 120 fs; photoelectrons largely populate higher-energy, more delocalized states. Lattice remains near 200 K; no significant energy transfer or Ir–Ir dimer dissolution is observed over 1.2 ps (no LT→HT transition).
• Including hot carrier cooling via the Boltzmann factor yields rapid re-distribution of carriers from higher-energy states into localized Ir–Ir antibonding states (0.3–1.0 eV above EF), increasing N_dimer. After an initial slight decline from 120–150 fs (electron–electron dominated cooling), a pronounced bump in N_dimer from 150–210 fs signifies phonon-assisted cooling.
• Concurrently, the Ir–Ir dimer atomic kinetic energy rises markedly (150–300 fs), evidencing electron-to-lattice energy transfer. The combination of enhanced antibonding occupation (stronger driving forces) and increased kinetic energy enables ultrafast Ir–Ir dimer dissociation at ≈300 fs—faster than half a lattice vibrational period (~1.2 THz LO mode), indicating a deterministic kinetic transition.
• The simulated femtosecond electron diffraction (FED) ΔI/I with cooling quantitatively matches experiment, showing a minimum at ~750 fs. The LT→HT structural transition completes at ~300 fs, while the diffraction intensity minimum is delayed to ~750 fs due to displacive coherent motions plus phonon-induced disorder.
• As cooling proceeds further, excited electrons relax past EF to recombine nonradiatively with holes (onset ~210 fs), reducing the dimer-dissolving forces. With residual coherent velocities, Ir atoms re-form dimers at new locations, accounting for the sub-picosecond recovery of dimerization even at elevated lattice temperatures (~900 K, well above Ts=280 K).
• Control simulations: In NVT (no net kinetic energy gain), increased antibonding occupation alone is insufficient to dissociate dimers, highlighting the essential role of kinetic energy enhancement. Ground-state BOMD at ~1000 K shows purely thermal dimer dissolution occurs at ~6.5 ps, an order of magnitude slower than the hot-carrier-driven process.
• Overall, the hot carrier cooling enables both force enhancement and coherent lattice kinetic energy, jointly reproducing experimental time-resolved diffraction and elucidating ultrafast dissolution and recovery dynamics.

The results directly address whether and how hot carrier cooling governs PIPTs in a metallic system without a bandgap. Cooling funnels electrons into localized Ir–Ir antibonding states, amplifying bond-weakening forces, while simultaneously transferring energy to coherent lattice motions that help overcome barriers on sub-phonon-cycle timescales. Subsequent continued cooling across EF enables nonradiative electron–hole recombination in the absence of a bandgap, removing the dissociative forces and facilitating rapid dimer reformation driven by residual coherent motion. This cohesive picture reconciles ultrafast diffraction observations of both rapid suppression and sub-picosecond recovery of dimerization in IrTe₂. It underscores that accounting for detailed-balance-respecting carrier relaxation is crucial for predictive simulations of light-induced structural dynamics. The mechanistic insights—force localization via selective state occupation plus coherent kinetic energy—are likely relevant to other systems with bond-centered order parameters (e.g., VO₂ vanadium dimers, CDW materials such as 1T-TaS₂, 1T-TiSe₂, and LaTe₃), providing a framework to design excitation protocols that tailor carrier distributions and maximize desired structural responses.

By augmenting rt-TDDFT with a Boltzmann-factor scheme to include hot carrier cooling, the study reveals that ultrafast Ir–Ir dimer dissolution in IrTe₂ arises from two synergistic effects of cooling: increased occupation of dimer antibonding states (enhanced driving forces) and coherent lattice kinetic energy growth (barrier crossing). The simulations reproduce experimental FED transients, capture LT→HT transition completion at ~300 fs, and explain sub-picosecond dimer recovery via nonradiative recombination and coherent motion, even at high lattice temperatures. Comparisons to NVT and high-temperature BOMD highlight the distinct, faster kinetic pathway enabled by carrier cooling versus slower thermally driven transitions (~6.5 ps). Future work could extend the approach to other correlated and dimerized materials, explore pulse shaping and state-selective excitation to control structural outcomes, and refine electron–phonon coupling treatments beyond effective Boltzmann schemes for quantitative generalization.