Plasmon-driven exciton formation in a non-equilibrium Fermi liquid

Abstract

Collective modes in Fermi liquids are usually regarded as dissipation channels that relax electronic excitations through Landau damping. Whether such modes can instead mediate the formation of correlated electronic states under non-equilibrium conditions remains an open question. Here we show that, under optical photo-doping, a bulk plasmon can drive correlated inter-band transfer within a transient electronic continuum. Using time- and angle-resolved photoemission spectroscopy (Tr-ARPES) on EuCd$_2$As$_2$ supported by electronic structure calculations, we observe that at high excitation density, plasmons transfer energy from a weakly dispersing bulk band into unoccupied surface states. This bulk-to-surface redistribution stabilizes a long-lived, energy-localized spectral feature consistent with a Mahan exciton. Our results uncover a non-equilibrium regime of Fermi-liquid physics in which collective modes do not merely dissipate energy, but also stabilize correlated bound states.

Figures (12)

• Figure 1: Excitations of a Fermi liquid at and away from equilibrium:(a) Schematic depiction of the excitations of a Fermi liquid at equilibrium, represented as scattering processes along the occupied and unoccupied band dispersions ($E$ vs $k$) (left) and as a spectrum showing the excitation energy $\omega$ as a function of the excitation wave vector $q$ (right). In (a), $E_F$ and $k_F$ indicate the Fermi level and Fermi momentum, respectively. $E_{CBM}$ indicates the energy minimum of the lower conduction band, measured relative to $E_F$, and $\omega_p$ denotes the energy of the plasmon. (b) Schematic depiction of the excitations of a Fermi liquid with a secondary chemical potential ($\mu_{NE}$) photo-doped into a conduction band. In (b), $\mu_{NE}$ is measured relative to the bottom of the subset of photo-doped bands.
• Figure 2: Unoccupied band structure of EuCd2As2:(a)$(001)$-surface spectral function of EuCd2As2, obtained from ab initio density-functional theory (DFT) calculations in the paramagnetic (PM) state (Supplementary Information \ref{['siDFT']}). The spectrum in (a), plotted in the blue shaded $(001)$-surface Brillouin zone (BZ) in the right schematic, consists of a nearly doubly degenerate pair of surface bands that coexist with the surface projections of the bulk conduction manifold; the surface band minimum lies at an energy that we denote as $\widetilde{E}$. (b) Schematic of the time- and angle-resolved photoemission spectroscopy (Tr-ARPES) experiment. The UV probe and IR pump are incident along the $(x,z)$- and $(y,z)$-planes of the lab frame, both at 45 to the sample normal (the $(001)$-surface) and are p-polarized. In (b), the sample is aligned with $\overline{\Gamma}-\overline{\textrm{M}}$ along $k_x$. This measurement geometry probes both the $(001)$-surface and the bulk electronic structure at $k_{z}\approx 0$. (c) Time-integrated ($t-t_0\in[\qty{0}{ps},\qty{2}{ps}]$) ARPES spectrum ($E$ vs $k_y$) showing the occupied and unoccupied band structure of EuCd2As2, with light gray lines showing the bulk band structure at $k_{z}=0$ along $\Gamma-\mathrm{K}$ from the PM-state DFT calculation, and with dark gray horizontal rules indicating where different scans were truncated to render the composite figure. Above the Fermi level $E_{F}$ in (c), we observe a set of surface states whose dispersion closely matches the DFT-obtained surface states in (a) and whose minimum approximately lies at $E_0\approx E_F+\qty{0.8}{eV}$ (Supplementary Information \ref{['sislabgreens']}). Just below $E_{0}$ lies a bulk conduction band that is nondispersing at $\Gamma$ to leading order (yellow triangle in (c)) in which exciton holes form. (d) A constant-energy cut of circular dichroism (CD-) ARPES measurements of the $(001)$-surface states taken along the dashed line in (c) ($E_{0} + 0.23$ eV, $\pm$30meV integration window) at $t_0$, with a hue given by the difference between the ARPES intensities for opposite circular probe photon polarizations and a saturation set by the polarization-integrated photoemission intensity. (e) A constant-energy cut of the local atomic orbital angular momentum (OAM) of the $(001)$-surface states in the PM-phase DFT calculation in (a), taken at $\widetilde{E} + 0.23$ eV (the dashed line in (a)) and projected along the incident axis of the probe ($\langle L_{xz}\rangle$, angled 45 between the bulk line $\Gamma-\textrm{A}$ and the surface and bulk line $\overline{\Gamma}-\overline{\textrm{M}}$ in the BZ in (a), see Supplementary Information \ref{['sispintext']}). The Tr-ARPES measurements in this figure were taken at 20K, below $T_C\approx\qty{25}{K}$ for the ferromagnetic phase, using 1.2eV excitation of low fluence (15 J/cm^2). Importantly, to facilitate comparison with the DFT calculations, we also performed the same measurements in the PM phase at 42K, and observed qualitatively identical (CD-) ARPES spectra (Supplementary Information \ref{['CD_temp_SI']}).
• Figure 3: Population dynamics of the unoccupied surface states at representative excitation densities: (a) ARPES spectra of the unoccupied band structure of EuCd2As2 at selected temporal delays after low-fluence (top row) and high-fluence (bottom row) excitation. (b) Energy distribution curves at various temporal delays after photo-excitation for low (15 J/cm^2, left) and high (55 J/cm^2, right) fluence photo-excitation, where the shaded region at $E_{X}$ in the right panel is a guide to the eye. For the experimental data in this figure, the Tr-ARPES measurements were taken at 9.5K using 1.5eV excitation.
• Figure 4: Electron-plasmon coupling in the unoccupied conduction states:(a) The imaginary part of the self energy $\text{Im }\Sigma(E)$ of the unoccupied band structure, measured at various lattice temperatures under low fluence excitation (15 J/cm^2) by 1.2eV photons. The shaded colored regions in (a) indicate error bars for Lorentzian fits, and represent a 68% confidence interval. The blue triangles in (a) are guides to the eye to highlight the temperature dependence of the kink (derivative discontinuity). To generate (a), ARPES cuts were integrated over $t-t_0\in[\qty{0}{ps},\qty{2}{ps}]$, and vertical offsets were added for clarity. (b) The momentum-integrated spectrum obtained from electron energy loss spectroscopy (EELS) at room temperature, showing a broad plasmon peak at 0.12eV (purple triangle).
• Figure 5: Plasmon-mediated exciton formation: (a) Schematic of the dynamics of electrons excited into unoccupied surface states, showing the plasmon-mediated formation of Mahan excitons. (b) Difference between time traces for high (55 J/cm^2) and low (15 J/cm^2) excitation fluences, with the maximum intensity at each energy level for both fluences (reached approximately at $t_0$) normalized to 1. The superimposed arrow in (b) indicates the formation of holes and electrons associated with the exciton. (c) Theoretical calculation of plasmon-mediated exciton formation using a rate equation (Supplementary Information \ref{['RateEq_SI']}). (d) Decay rates at $E_X$ for different excitation fluences; the yellow shaded region is a guide to the eye. The error bars in (d) represent a 68% confidence interval for exponential decay fits.