Charge density waves in a quantum plasma

We analyze the instability of an unpolarized uniform quantum plasma consisting of two oppositely charged fermionic components with varying mass ratios against charge and spin density waves. Using density functional theory, we treat each component with the local spin density approximation and a rescaled exchange-correlation functional. Interactions between different components are treated with a mean-field approximation. In both two and three dimensions, we find leading unstable charge density wave modes in the second-order expansion of the energy functional, which would induce the transition to quantum liquid crystals. The transition point and the length of the wave vector are computed numerically. Discontinuous ranges of the wave vector are found for different mass ratios between the two components, indicating exotic quantum phase transitions. Phase diagrams are obtained, and a scaling relation is proposed to generalize the results to two-component fermionic plasmas with any mass scale. We discuss the implications of our results and directions for further improvement in treating quantum plasmas.

Figure 1

The energy response in three dimensions to the eigenmode with the smallest eigenenergy, for a mass ratio $\gamma$ of (a) 24, (b) 240, (c) 2400, (d) 5.012, (e) 5.022, and (f) 5.032. The response shown is properly normalized by the total number of particles $N$ and plotted in units of heavier particles' Fermi energy $E_F=\frac{k_F^2}{2m_{*}}$. The dashed lines mark the global minima of the spectra.

Figure 2

The same as in Fig. 1, but for the two-dimensional case, with $\gamma$ equal to (a) 9.12, (b) 91.2, and (c) 912.

Figure 3

(a) The first unstable CDW wave vector $q_c$ when decreasing density for different mass ratios and (b) the phase diagram of the plasma in three dimensions. The solid line in (b) is the exact critical $r_s-\gamma$ relation, normalized by the mass scale $m^{*}$. The dashed lines are conjectured from the $r_s$ dependence of the energy spectra.

Figure 4

The same as in Fig. 3, but for two dimensions.