We compare the atomic dynamics of the glass to that of the relevant crystal. In the spectra of inelastic scattering, the boson peak of the glass appears higher than the transverse acoustic (TA) singularity of the crystal. However, the density of states shows that they have the same number of states. Increasing pressure causes the transformation of the boson peak of the glass towards the TA singularity of the crystal. Once corrected for the difference in the elastic medium, the boson peak matches the TA singularity in energy and height. This suggests the identical nature of the two features.

Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 2 2 2 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data.

Systems containing the ideal kagome lattice can exhibit several distinct and novel exotic states of matter. One example of such systems is a recently discovered $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) family of compounds. Here the coexistence of the charge density wave (CDW) and superconductivity is observed. In this paper, we study the dynamic properties of the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ systems in context of origin of the CDW phase. We show and discuss the structural phase transition from $P6/mmm$ to $C2/m$ symmetry that is induced by the presence of phonon soft modes. We conclude that the CDW observed in this family of compounds is a consequence of the atom displacement, from the high-symmetry position of the kagome net, in the low-temperature phase. Additionally, using the numerical ab initio methods, we discuss the charge distribution on the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ surface. We show that the observed experimental stripelike modulation of the surface can be related to surface reconstruction and manifestation of the three-dimensional $2\times 2\times 2$ bulk CDW. Finally, the consequence of realization of the $C2/m$ structure on the electronic properties is discussed. We show that the electronic band structure reconstruction and the accompanying modification of density of states correspond well to the experimental data.

The recently discovered heavy fermion ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ compound crystallizes in nonsymmorphic $P4/nmm$ symmetry, which enables the occurrence of topological protection. Experimental results show that this material exhibits unusual behavior, which is manifested by the appearance of two superconducting phases. In this Letter, we uncover and discuss the role of ${\mathrm{Rh}}_2{\mathrm{As}}_2$ layers and their impact on the electronic and dynamical properties of the system. The location of Ce atoms between two nonequivalent layers allows for the realization of orbital order. We point out that the electronic band structure around the Fermi level is associated mostly with Ce $4f$ and Rh $4d$ orbitals and suggest the occurrence of the Lifshitz transition induced by an external magnetic field. We discuss also the role played by the $f-d$ orbital hybridization in the electronic band structure.

Ab initio calculations and a direct method have been applied to derive the phonon dispersion curves and phonon density of states for the TiC crystal. The results are compared and found to be in a good agreement with the experimental neutron scattering data. The force constants have been determined from the Hellmann-Feynman forces induced by atomic displacements in a 2x2x2supercell. The calculated phonon density of states suggests that vibrations of Ti atoms form acoustic branches, whereas the motion of C atoms is confined to optic branches. The elastic constants have been found using the deformation method and compared with the results obtained from acoustic phonon slopes.