Second-order Raman scattering in the group-Vbsemimetals: Bi, Sb, and As

Second-order Raman scattering has been observed in the group-${\mathrm{V}}_b$ semimetals Bi, Sb, and As. Comparison of the spectra in Bi and Sb, which are primarily of even $A_{1g}$ symmetry, with neutron-scattering measurements indicate a predominance of overtone scattering. Variations in the form of the second-order spectra are attributed to differences in the phonon density of states within the group-${\mathrm{V}}_b$ system. In contrast to Bi and Sb, the optical modes at $\Gamma$ in As are shifted to relatively higher frequency so that the $E_g\left(\Gamma \right)$ mode no longer occurs at the minimum of the optic branch. Differences in the vibrational spectra near $\Gamma$ between As and Bi or Sb are attributed to a decrease in second- or further-neighbor interactions. From the ratio of the second- to first-order scattered intensities the corresponding ratios of average electron—one-phonon to electron—two-phonon deformation potentials are determined.