Contrasting the Surface Phonon Dispersion of ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Se}$ in Its Topologically Trivial and Nontrivial Phases

We report inelastic He atom scattering measurements of the (001) surface phonon dispersion of the topological crystalline insulator ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Se}$. This material exhibits a temperature-dependent topological transition, so we measure the surface dispersion curves in both the trivial and nontrivial phases. We identify that, peculiarly, most surface modes are resonances, rather than pure surface states. We find that a shear vertical surface resonance branch around 9.0 meV dramatically changes on going from the trivial to the topological phase. We associate this remarkable change with the emergence of surface Dirac fermions. We use the measured dispersion of this resonance branch to determine the corresponding mode-dependent electron-phonon coupling ${\lambda }_{\nu }(\mathbf{q})$.

Figure 1

Surface Brillouin zone with double-Dirac-cone structure.

Figure 2

Surface diffraction patterns along the (a) [10] and (b) [11] directions of the (001) rocksalt surface.

Figure 3

Two typical inelastic spectra along $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction. The elastic peak is depicted as a dashed green line with incident beam energy width. Inelastic peaks are shown as solid blue lines with their corresponding $\mathrm{\Delta }K$ as indicated.

Figure 4

Calculated PbSe bulk dispersion curves (red) fitted to available neutron data (blue) from Ref. [36].

Figure 5

(a) Bulk dispersion curves projected onto the $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction of the surface Brillouin zone. Longitudinal polarization is shown in dark gray (blue). Shear horizontal polarization is shown in gray (red) and vertical shear polarization is shown in light gray (light green). (b) Surface dispersion curves in trivial phase regime. Calculated surface modes of longitudinal polarization are shown in black (dark blue) and those of shear vertical polarization are shown in dark gray (dark green). Measured phonon events are depicted as points with error bars (orange). (c) Surface dispersion curves in topological phase regime.

Figure 6

Left: Double-Dirac-cone structure around $\overline{X}$ point. Right: Simplified elliptic cone used for electron-phonon calculation. The Fermi level is shown as green surface.

Figure 7

(a) Renormalized surface phonon mode with measurements. (b) Mode-specific $\mathbf{q}$-dependent electron-phonon coupling ${\lambda }_{\nu }(\mathbf{q})$.