Self-amplified photo-induced gap quenching in a correlated electron material

Abstract

Capturing the dynamic electronic band structure of a correlated material presents a powerful capability for uncovering the complex couplings between the electronic and structural degrees of freedom. When combined with ultrafast laser excitation, new phases of matter can result, since far-from-equilibrium excited states are instantaneously populated. Here, we elucidate a general relation between ultrafast non-equilibrium electron dynamics and the size of the characteristic energy gap in a correlated electron material. We show that carrier multiplication via impact ionization can be one of the most important processes in a gapped material, and that the speed of carrier multiplication critically depends on the size of the energy gap. In the case of the charge-density wave material 1T-TiSe₂, our data indicate that carrier multiplication and gap dynamics mutually amplify each other, which explains-on a microscopic level-the extremely fast response of this material to ultrafast optical excitation.

Figure 1. Spectra of the transient electronic dynamics of photoexcited 1T-TiSe₂.

(a–f) Photoemission maps of the electronic response of the backfolded Se 4p states (blue area), and the hot-electron dynamics in the Ti 3d band (red area) at different times. The absorbed fluence of the 1.6 eV, 32 fs, p-polarized pump pulses was 0.47 mJ cm⁻². The polarization of the 22 eV XUV pulses was p. (g) Suppression of the spectral weight of the backfolded Se 4p states (blue data points and line), which is indicative of the quenching of the CDW. This curve is obtained by mirroring the spectral-weight dynamics at the x axis, so that the timescales can be compared with the electron accumulation in the Ti 3d band (red data points and line). The black data and line shows the cross-correlation from pump and probe pulse, extracted from the laser-assisted photoelectric effect, LAPE (Supplementary Fig. 1). (h) Summary of the extracted CDW quenching times τ_{Se 4p} as a function of absorbed pump fluence in comparison to our previous data set. The fit curves for the extraction of τ_{Se 4p} are shown in Fig. 4c as lines. The error bars for τ_{Se 4p} are obtained from the fits, while the error bars of the absorbed pump fluence originate from the measuring inaccuracy of average power and spot size of the pump pulse.

Figure 2. Hot-electron dynamics in the Ti 3d band.

(a) ARPES map of TiSe₂ at t=200 fs after excitation with an absorbed fluence of 0.47 mJ cm⁻². (b) Spectral weight in the Ti 3d band as a function of time in comparison to the quenching of CDW. (c–e) Possible electron–electron scattering processes: intraband scattering (c), and interband impact ionization scattering (d) as well as the reverse process, Auger recombination (e). Note that the phase space for impact ionization scattering is increased for smaller gap sizes, where more scattering processes with smaller energy transfer become possible.

Figure 3. Computed dependence of carrier dynamics on the size of the gap.

(a,e) Band lineup for small gap (10 meV, grey lines), intermediate gap (50 meV, red lines), and large gap (100 meV, blue lines). Note that the holes that have been created in the optical excitation process far below the Fermi-level (between E–E_F≈−0.9 and −1.5 eV) are not included. (b–d) Computed dynamical electron distributions in the valence band and (f–h) computed electron distributions in the conduction band (right, six times amplified in comparison to b–d), broadened with the experimental energy resolution: initial distributions (b,f) and results after 100 fs (c,g) and 200 fs (d,h). At a 200 fs delay, the dynamical electron distribution in the conduction band in the case of a small gap (solid grey line) is already very close to a quasi-equlibrium distribution (dashed grey line), as the low energy states in the conduction band are filled by additional carriers created via impact ionization. In contrast, the dynamical electron distribution for the large gap case (blue lines) prevents efficient relaxation via impact ionization between the conduction and valence bands toward a quasi-equilibrium distribution on femtosecond timescales.

Figure 4. Non-equilibrium electron dynamics drive the ultrafast quenching of the CDW in TiSe₂.

(a) Measured energy distribution curves (EDC) of the Ti 3d band as a function of time in 20 fs steps from −100 to 200 fs for an absorbed fluence of 0.47 mJ cm⁻² (red to blue lines, k_||-integration from 0.23 to 1.05 Å⁻¹). First, the optically induced non-equilibrium electron distribution relaxes via electron–electron scattering processes to a hot Fermi-Dirac quasi-equilibrium in the Ti 3d band, which is reached after ≈200 fs. This non-equilibrium to quasi-equilibrium thermalization process is illustrated in the data by a fast change of the slope Δ(dI/dE) of the distribution at E−E_F=0.4 eV (black dashed double arrows). (b) Subsequently, the system cools via electron–phonon scattering and recombination, which is visible in the 200–500 fs data in 100 fs steps by a subsequent, slower change of the slope (that is, temperature), and an energetic lowering of the elevated quasi Fermi-level. Note that the EDC peaks are at a higher energy above E_F in comparison to the theoretical result in Fig. 3, because the computed carrier dynamics have been plotted for the fixed band structures in Fig. 3e to highlight the different relaxation dynamics for the different gap sizes. (c) Comparison of hot-electron thermalization (analysed via extracting the change of the slope of the electron distribution Δ(dI/dE), open circles) and suppression of backfolding intensity from the backfolded Se 4p bands (filled circles), which are indicative of the quenching of the CDW, as a function of time for different pump fluencies. The lines are exponential decay fits to the CDW quenching (the respective time constants are shown in Fig. 1h).