First-principles modeling of plasmons in aluminum under ambient and extreme conditions

The theoretical understanding of plasmon behavior is crucial for an accurate interpretation of inelastic scattering diagnostics in many experiments. We highlight the utility of linear response time-dependent density functional theory (LR-TDDFT) as a first-principles framework for consistently modeling plasmon properties. We provide a comprehensive analysis of plasmons in aluminum from ambient to warm dense matter conditions and assess typical properties such as the dynamical structure factor, the plasmon dispersion, and the plasmon lifetime. We compare our results with scattering measurements and with other TDDFT results as well as models such as the random phase approximation, the Mermin approach, and the dielectric function obtained using static local field corrections of the uniform electron gas parametrized from path-integral Monte Carlo simulations. We conclude that results for the plasmon dispersion and lifetime are inconsistent between experiment and theories and that the common practice of extracting and studying plasmon dispersion relations is an insufficient procedure to capture the complicated physics contained in the dynamic structure factor in its full breadth.

Figure 1

Static LFC of aluminum ($r_s=2.07$) at four different temperatures. The data have been obtained from the machine-learning representation from Ref. [41].

Figure 2

DSF for aluminum in atomic units under ambient conditions at (a) 1.08, (b) 1.48, (c) 1.75, and (d) 1.88 (${\AA }^{-1}$). Experimental data (in black) stem from Refs. [51, 86, 87]. Theoretical data (in red) stem from Ref. [51]. TDDFT-RPA/TDDFT-XC/TDDFT-LFC/RPA/RPA-LFC results of this work are shown in blue. The scattering parameter $\alpha =\kappa /q$, with $\kappa$ being the inverse screening length, is unity for $q=2.04/\AA$, collective effects dominate for $\alpha \ll 1$ [36, 59].

Figure 3

Aluminum plasmon dispersion under ambient conditions. The critical and the Fermi wave numbers are indicated by the vertical lines. Experimental data shown in black symbols stems from Refs. [51, 96, 97, 98]. Theoretical data shown in red symbols are taken from Refs. [51, 99, 100, 101]. TDDFT-RPA/TDDFT-XC/TDDFT-LFC/RPA-LFC/RPA results of this work are indicated with blue symbols.

Figure 4

Aluminum plasmon peak FWHM under ambient conditions. The critical wave number is indicated by the vertical line. Experimental and theoretical data shown in black symbols stems from Refs. [65, 97, 107, 108, 109, 110]. TDDFT-RPA/TDDFT-XC/TDDFT-LFC results of this work are indicated with blue symbols.

Figure 5

Aluminum plasmon dispersion under extreme conditions ($T=0.3$ eV) for densities of $2.7\mathrm{g}/{\text{cm}}^3$ (uncompressed) and $3.5\mathrm{g}/{\text{cm}}^3$ (compressed). The Fermi wave number is indicated by the vertical line. Experimental and theoretical data for RPA, MA, $\mathrm{RPA}+\mathrm{LFC}$ (in green) stems from Refs. [48, 112]. TDDFT-RPA, TDDFT-XC, and TDDFT-LFC results of this work are indicated with blue and red symbols.

Figure 6

Aluminum plasmon peak FWHM under extreme conditions for $\rho =2.7{\text{g/cm}}^3$ at $T=0.3$ eV (above) and $T=6$ eV (below). The Fermi wave number is indicated by the vertical line. Experimental and theoretical data for RPA, MA (in green) stems from Refs. [48, 114]. TDDFT-RPA, TDDFT-XC, and TDDFT-LFC results of this work are indicated with blue and red symbols.

Figure 7

DSF for aluminum in atomic units for (a) 0.47, (b) 0.94, and (c) $1.42\left({\AA }^{-1}\right)$ at various temperatures. The TDDFT-RPA results are shown only at 12 eV. The TDDFT-XC results are shown from 1 to 12 eV in the blue area (black curves for 1 and 12 eV) and are broadening with temperature. The purple and green dashed lines are the RPA and $\mathrm{RPA}+\mathrm{T}$-LFC results at 1 eV, respectively. The RPA results are normalized with respect to the TDDFT-XC results at 12 eV to allow plotting them at the same scale.

Figure 8

Static structure factor for aluminum ($r_s=2.07$) computed using PIMC and RPA including LFCs at $\mathrm{\Theta }=0.75$ ($T=8.77$ eV). The ESA results are shown for $\mathrm{\Theta }=0, \mathrm{\Theta }=0.68$ ($T=8$ eV), and $\mathrm{\Theta }=1.03$ ($T=12$ eV). The TDDFT-XC results are shown from ambient to $T=12\text{eV}$ for $q/q_F$ up to $\sim 1.0$.

Figure 9

DSF for aluminum ($\rho =2.7{\text{g/cm}}^3$) in atomic units at $T=2$ and 6 eV with respect to $k$ points and the number of electrons considered in the pseudopotential. AE refers to the use of an all-electron pseudopotential (11 electrons ignoring the $1s^2$ core) compared to the 3 valence electrons otherwise.