Evolution of a strongly correlated liquid with electronic density

Systems created by dissolving elemental metals in liquid ammonia are strongly correlated liquid metals where the electronic correlation strength can be easily changed by altering the electronic density. We study the plasmon in the lithium ammonia system as a function of electronic density using nonresonant inelastic x-ray scattering and use this to determine the long wavelength plasmon energy $E_0$ and the plasmon dispersion $\alpha$ as a function of electronic density. These parameters show the increasing influence of electronic correlations as we go to lower concentrations. The plasmon width is found to increase as we go to lower concentration. The implications of these results are discussed.

Figure 1

(Color online) (a) Phase diagram for liquid lithium ammonia mixtures. Samples discussed in the text are indicated by the dots on the diagram. (b) Energy dispersion and electron-hole continuum RPA calculation for a plasmon with the electronic density seen at 20 MPM. At the cutoff momentum transfer $q_c$, the plasmon decays to electron-hole excitation.

Figure 2

(Color online) Structure factor for lithium ammonia solutions (Ref. 17). The first peak is related to the distance between the lithium atoms. It is near $10{\text{nm}}^{-1}$ for the concentrated solution and moves to lower $q$ values as the lithium concentration is reduced. The second peak near $20{\text{nm}}^{-1}$ is related to the distance between the nitrogen in the ammonia molecules. At low concentrations, elastic scattering is larger at the $q$ values where the plasmon exists.

Figure 3

(Color online) The plasmon at 16 MPM. The peak disperses to higher energies at higher $q$ values as expected. In addition, the width of the peak increases. Above the cutoff vector $q_c\sim 0.61{\text{nm}}^{-1}$ the plasmon can decay into electron-hole pairs and it broadens rapidly.

Figure 4

(Color online) Plasmon data for (a) 10 MPM lithium ammonia solution and (b) 11 MPM lithium ammonia solutions. Insets show the data in the region of the plasmon with the elastic background subtracted. Fits to the data are the solid lines in the figures. The peaks are quite broad everywhere they are visible.

Figure 5

Plasmon at $3.6{\text{nm}}^{-1}$ in an 8 MPM solution. The region of the plasmon is circled and enlarged, showing a small deviation from the background. A peak is more visible in the inset which shows the current-current correlation function. The small rise above 2.6 eV is an instrumental artifact which occurs with the strip detector for the points near the end of a scan.

Figure 6

(Color online) (a) Dispersion of plasmon energy for different concentration lithium ammonia solutions. The solid lines are the best fits to Eq. (4) to quadratic order. The fit lines are drawn only out to the points which were fit, that is, to $q_c$. (b) Plasmon energy vs electron density. In addition to our data, data from previous work [Eq. (9)] are included. The top solid curve is the prediction for the plasmon energy from RPA. The lower solid curve has the RPA functional dependence but that starts from the measured data point at 20 MPM. Both these curves have the same functional dependence and assume that the dielectric constant and effective mass remain constant. (c) Dispersion coefficients compared to RPA prediction. The black squares with error bars are the data for different electron concentrations. The dashed line is the best fit of experimental data to a power law dependence. Note the strong deviation from RPA.

Figure 7

(Color online) Plasmon width as a function of $q$. The plasmon width increases as the electronic concentration is reduced.