Collective modes in two-dimensional binary Yukawa systems

We analyze via theoretical approaches and molecular dynamics simulations the collective mode structure of strongly coupled two-dimensional binary Yukawa systems, for selected density, mass, and charge ratios, both in the liquid and crystalline solid phases. Theoretically, the liquid phase is described through the quasilocalized charge approximation (QLCA) approach, while in the crystalline phase we study the centered honeycomb and the staggered rectangular crystal structures through the standard harmonic phonon approximation. We identify “longitudinal” and “transverse” acoustic and optic modes and find that the longitudinal acoustic mode evolves from its weakly coupled counterpart in a discontinuous nonperturbative fashion. The low-frequency acoustic excitations are governed by the oscillation frequency of the average atom, while the high-frequency optic excitation frequencies are related to the Einstein frequencies of the systems.

Figure 1

Liquid state: QLCA gap ($•$) and Einstein (■) frequencies vs $\Gamma$. The arrows indicate the positions of the corresponding gaps in the lattice. The inset shows the $\Gamma$ dependence of the correlation integral $F_{12}$ (symbols), which does not vary with the mass ratio. (a) $n_2=n_1/2$; (b) $n_2=n_1$.

Figure 2

Liquid state: Longitudinal sound speeds. ($•$), MD; line, QLCA; gray shaded area and line, lattice value. For $\Gamma =1$ and $\Gamma =5$ the RPA (Vlasov-equation-based) values of the sound speeds are also indicated (■). (a) $n_2=n_1/2$; (b) $n_2=n_1$.

Figure 3

Liquid state: Effective masses for $Z_1=Z_2$ vs $\Gamma$. (a), (b) $n_2=n_1/2$; (c), (d) $n_2=n_1$. The arrows indicate the mass average $\langle m\rangle =(n_1{m}_1+n_2{Z}_2)/(n_1+n_2)$. The error bars represent 5% (10%) uncertainty in the measurement of the MD sound speed for $M=5$ (20).

Figure 4

Liquid state: Examples of the $g\left(r\right)$ pair distribution functions at $\Gamma =120$ (a), (c), (e) $n_2=n_1/2$; (b), (d), (f) $n_2=n_1$. Note that for $Z_1=Z_2$ we obtain $g_{11}=g_{22}=g_{12}$, irrespective of the density ratios.

Figure 5

Liquid state: Examples for the longitudinal current fluctuation spectra. (a) left column, $n_2=n_1/2$, $Z_2=2Z_1$; (b) right column, $n_2=n_1$, $Z_2=1.4Z_1$.

Figure 6

Liquid state: Current fluctuation spectra from MD simulation [color map (grayscale)] compared with QLCA-calculated dispersion (black lines) for $\Gamma =120$. (a) $n_2=n_1/2$; (b) $n_2=n_1$.

Figure 7

Principal lattice structures: staggered rectangular (a), and honeycomb (b). Primitive cells are shown with dashed lines. In (b) the positions $1^{\prime }$ and $1^{\prime \prime }$ are distinguished.

Figure 8

SR lattice: polarizations of the gap frequencies versus propagation angle for $Z_2=Z_1$.

Figure 9

Mass and charge ratio dependence of the gap frequencies. The QLCA and MD results are also shown. (a) HC lattice; note the portrayal of the invariant mode in the right ($Z=\mathrm{const}$) panels. (b) SR lattice.

Figure 10

The dependence of the lattice sums on the Yukawa screening parameter ($\kappa$). (a) HC lattice; (b) SR lattice.

Figure 11

Calculated mode dispersions for different propagation angles. (a) HC lattice; note that the invariant mode frequency at $k=0$ (pointed at by the arrows) remains invariant for any $M=m_2/m_1$ and any angle; (b) SR lattice.

Figure 12

Current fluctuation spectra from MD simulation at ${\Gamma }_1=10000$ (color map) compared with dispersion from lattice calculations (black lines). (a) HC lattice; (b) SR lattice.

Figure 13

HC lattice: Mode polarizations for 0${}^{\circ }$ propagation. $Z=0.7$, $M=5$, $\alpha =0^{\circ }$ ($k\parallel x$), $ka=0.5$ in the panels, particle “2” is the heavy one (see Fig. 7).

Figure 14

HC lattice: Mode polarizations for 90${}^{\circ }$ propagation. $Z=0.7$, $M=5$, $\alpha ={90}^{\circ }$ ($k\parallel y$), $ka=0.5$ in the panels.

Figure 15

SR lattice: Mode polarizations for 0${}^{\circ }$ propagation. $Z=0.7$, $M=5$, $\alpha =0^{\circ }$ ($k\parallel x$), $ka=0.2$ in the panels, and particle 2 belongs to species 2.

Figure 16

SR lattice: Mode polarizations for 10${}^{\circ }$ propagation. $Z=0.7$, $M=5$, $\alpha ={10}^{\circ }$, $ka=0.5$ in the panels, and particle 2 belongs to species 2. Note the $L-T$ and 1-2 polarization mixings.

Figure 17

The dependence of the HC lattice dispersions on the Yukawa screening parameter ($\kappa$) at $m_2=5m_1$ and $Z_2=0.7Z_1$.