Enhanced optical conductivity and many-body effects in strongly-driven photo-excited semi-metallic graphite

Abstract

The excitation of quasi-particles near the extrema of the electronic band structure is a gateway to electronic phase transitions in condensed matter. In a many-body system, quasi-particle dynamics are strongly influenced by the electronic single-particle structure and have been extensively studied in the weak optical excitation regime. Yet, under strong optical excitation, where light fields coherently drive carriers, the dynamics of many-body interactions that can lead to new quantum phases remain largely unresolved. Here, we induce such a highly non-equilibrium many-body state through strong optical excitation of charge carriers near the van Hove singularity in graphite. We investigate the system's evolution into a strongly-driven photo-excited state with attosecond soft X-ray core-level spectroscopy. We find an enhancement of the optical conductivity of nearly ten times the quantum conductivity and pinpoint it to carrier excitations in flat bands. This interaction regime is robust against carrier-carrier interaction with coherent optical phonons acting as an attractive force reminiscent of superconductivity. The strongly-driven non-equilibrium state is markedly different from the single-particle structure and macroscopic conductivity and is a consequence of the non-adiabatic many-body state.

Fig. 1. Signatures of the electronic structure in time-resolved XAFS.

a Single-particle electronic band structure of AB stacked highly pyrolytic graphite (HOPG) calculated with Wien2K. The energy is referenced to the K-point. The inset shows graphite’s hexagonal unit cell with the path for which the band structure is presented. The near-infrared beam excites carriers around the Fermi energy (${\mathrm{E}}_{\mathrm{F}}$), and the soft X-ray beam probes changes in the carrier occupation by promoting 1 s core-electrons that are bound by 284.2 eV into free electronic states around ${\mathrm{E}}_{\mathrm{F}}$ (horizontal line). b Retrieved density of states from the fit for the unpumped case (light blue line) and pumped case, 15 fs after near-infrared excitation with 81.4 $\pm$ 5 mJ/cm² (light red line). Symbols are the measured XAFS with (red squares) and without (blue circles) near-infrared excitation and the corresponding fits (solid lines). c $\mathrm{\Delta }\mathrm{A}$ for excitation with 81.4 $\pm$ 5 mJ/cm² (high fluence case). The black line indicates the position of the static Fermi energy at 285.1 eV, as retrieved from the fit. The red (blue) line at 287.6 eV (282.2 eV) marks the upper (lower) energy limit for the lineouts in (d). d ${\mathrm{\Sigma }}_{\mathrm{i}}\mathrm{\Delta }\mathrm{A}\left(E_{\mathrm{i}}\right)$ above (negative) and below (positive) the static ${\mathrm{E}}_{\mathrm{F}}$ from (c) for the three measured fluences and the corresponding decay times from exponential fits (solid lines). The error bars are the relative error of the mean of $\mathrm{\Delta }\mathrm{A}\left(E_{\mathrm{i}}\right)$ in the corresponding electron and hole energy range. Source data are provided as a Source Data file.

Fig. 2. Carrier thermalization rates after optical excitation.

Carrier thermalization rate $1/{\tau }_{th}$ from an exponential fit to $\mathrm{\Delta }A$ for all three measured fluences (symbols) for electrons a–c, holes e–g, and from the fitted absorption spectra (solid lines). The energy axis is referenced to the static Fermi energy. The horizontal lines in (e–g) indicate the position of the K-point. The gray lines indicate the slope of $1/\tau$ in the apparent energy region (colored boxes), highlighting the dimensionality of the carrier system. The spectral resolution determines the error bars along the energy axis and the error in the thermalization rate is derived from the exponential fit to the measured and retrieved ΔA. d, h The renormalized density of states retrieved from the model at the delay time at which the carrier temperature becomes maximal. Source data are provided as a Source Data file.

Fig. 3. Optical conductivity and mass enhancement.

a–c Mass enhancement factor $\lambda \left(E\right)$ and optical conductivity $\sigma \left(E\right)$ (d–f) retrieved from the relaxation rate, $1/\tau \left(E\right)$, using a Kramers-Kronig transformation of the experimental data (symbols) and the model (lines). The vertical line in (d-f) marks the universal optical conductivity of a single graphene layer at $\pi G_0/4$. The light line in (d–f) is the Drude conductivity. The error bars along the energy axis are determined by the spectral resolution. The error in the optical conductivity is determined by the propagated error of the thermalization rate from Fig. 2. Source data are provided as a Source Data file.