Figure 1

(a) Schematic band structure in phononic crystals of elastic soft colloids [2, 5] (BG, Bragg gap; HG, hybridization gap). (b) Exemplary spectra for polycrystalline colloidal suspensions of close-packed ${\mathrm{SiO}}_2$ spheres in SR256 and PMMA spheres in decaline-tetraline, of diameter $d$, at $qd\approx 3.7$ [vertical arrow in band diagram (c)]. The solid lines on the anti-Stokes side of the spectra show the fits of a double Lorentzian. (c) Reduced phononic band diagram deduced from BLS experiments on the two systems and three different $d$ for ${\mathrm{SiO}}_2/\mathrm{SR}256$. For the largest $d$, the dashed line represents the first Bloch harmonic intersecting the abscissa at $qd\approx 8$. The positions of the resonant $l$th multipole modes of the single ${\mathrm{SiO}}_2$ (solid arrows) and PMMA (dashed arrows) spheres immersed in the corresponding liquid matrices are indicated on the right margin.Reuse & Permissions

Figure 2

Phononic band structure (only nondegenerate bands are shown) of a fcc crystal of closely packed ${\mathrm{SiO}}_2$ spheres in SR256 along its [111] and [001] directions. The triangles, circles, and squares show the experimental results for the corresponding samples in Fig. 1. The longitudinal acoustic branch is indicated by (1) and the flat band by (2).Reuse & Permissions

Figure 3

Phononic band structure of ${\mathrm{SiO}}_2/\mathrm{SR}256$ fcc crystals with $\varphi =0$, $\varphi =0.54$, and $\varphi =0.74$ along their [111] ($\Gamma \mathrm{\text{−}}L$) direction. The flat band of interest is indicated by an arrow. For $\varphi =0$, the solid and dashed lines denote nondegenerate and threefold degenerate bands, respectively, corresponding to reciprocal-lattice vectors (in units $2\pi /a$): (1): $(0,0,0)$; ($1^{\prime }$): $(-1,-1,-1)$; ($1^{\prime \prime }$): $(1,1,1)$; (2): $(1,-1,-1)$, $(-1,1,-1)$, $(-1,-1,1)$; (3): $(0,0,-2)$, $(0,-2,0)$, $(-2,0,0)$; (4): $(-1,1,1)$, $(1,-1,1)$, $(1,1,-1)$. For $\varphi =0.54$ and $\varphi =0.74$, the black and gray solid lines denote the actual nondegenerate and doubly degenerate bands, respectively. Dotted lines show schematically the nondegenerate bands that would be in the absence of anticrossing interaction, with the corresponding number denoting their origin in the empty-lattice ($\varphi =0$) diagram.Reuse & Permissions