Emergence and Evolution of the $k$ Gap in Spectra of Liquid and Supercritical States

Fundamental understanding of strongly interacting systems necessarily involves collective modes, but their nature and evolution is not generally understood in dynamically disordered and strongly interacting systems such as liquids and supercritical fluids. We report the results of extensive molecular dynamics simulations and provide direct evidence that liquids develop a gap in a solidlike transverse spectrum in the reciprocal space, with no propagating modes between zero and a threshold value. In addition to the liquid state, this result importantly applies to the supercritical state of matter. We show that the emerging gap increases with the inverse of liquid relaxation time and discuss how the gap affects properties of liquid and supercritical states.

Figure 1

Intensity maps of $C(k,\omega )$ for supercritical Ar at (top panel) 250 K, (middle panel) 350 K, and (bottom panel) 450 K and supercritical ${\mathrm{CO}}_2$ at (top panel) 300 K, (middle panel) 400 K, and (bottom panel) 500 K. The maximal intensity corresponds to the middle points of the dark red areas and reduces away from them.

Figure 2

Phonon dispersion curves of (top panel) supercritical Ar at 200–500 K and 550 K, (middle panel) subcritical liquid Ar at 85–120 K, and (bottom panel) supercritical ${\mathrm{CO}}_2$ at 300–600 K. The temperature increment is 30, 5, and 30 K for supercritical Ar, subcritical liquid Ar, and supercritical ${\mathrm{CO}}_2$, respectively. The deviation from linearity (the curving over) of dispersion curves at large $k$ is related to probing the effects comparable to interatomic separations (in the solid, this corresponds to the curving over of $\omega \propto \sin ck$ at large $k$). This effect is not accounted for in the theory leading to the gap in Eqs. (2) and (3) because the theory is formulated in the continuous medium [20] and therefore describes the $k$ gap in the linear part of the dispersion law. We show $k$ in the range slightly extending the first pseudo zone boundary (FPZB) at low temperature. As volume and interatomic separation increase with temperature, FPZB shrinks, resulting in a decrease of $\omega \propto \sin ck$ at large $k$ beyond the FPZB. This effect is unrelated to the $k$ gap.

Figure 3

The width of the $k$ gap vs $1/\tau$ for subcritical liquid Ar in the range 85–115 K, supercritical Ar in the range 200–500 K, and supercritical ${\mathrm{CO}}_2$ in the range 300–600 K.