Band Structure of SnTe Studied by Photoemission Spectroscopy

We present an angle-resolved photoemission spectroscopy study of the electronic structure of SnTe and compare the experimental results to ab initio band structure calculations as well as a simplified tight-binding model of the $p$ bands. Our study reveals the conjectured complex Fermi surface structure near the $L$ points showing topological changes in the bands from disconnected pockets, to open tubes, and then to cuboids as the binding energy increases, resolving lingering issues about the electronic structure. The chemical potential at the crystal surface is found to be 0.5 eV below the gap, corresponding to a carrier density of $p=1.14\times {10}^{21}{\mathrm{cm}}^{-3}$ or $7.2\times {10}^{-2}$ holes per unit cell. At a temperature below the cubic-rhombohedral structural transition a small shift in spectral energy of the valance band is found, in agreement with model predictions.

Figure 1

Photoemission spectra at $T=300\mathrm{K}$ and $T=20\mathrm{K}$ at a sequence of energies. The right-hand panels show the calculated isoenergy surfaces projected onto the (100) direction, whereas the 3D isoenergy surfaces for the three relevant bands are shown in the center to clarify the topology. Here, the indexing of the calculated isoenergy surfaces corresponds to the electronic band index in the density-functional theory (DFT) calculation. Band no. 22 reaches closest to the Fermi surface. The inset illustrates the fcc Brillouin zone. We note that the dark line at $k_y=1$ is due to shadowing during data collection.

Figure 2

Band structure of cubic SnTe calculated without (left-hand panel) and with (right-hand panel) the inclusion of spin-orbit coupling, with the densities of states (DOS) below. Notice that the pocket near $L$ contributes a small amount to the density of states, and the dominant gap in the spectrum is the roughly 2 eV feature corresponding to the saddle point seen at $W$ and intersected along $\Gamma \mathrm{\text{−}}X$.

Figure 3

Constant-energy surfaces from the band structure of Fig. 2 for a set of different energies. The projected Brillouin zone onto the (001) plane is shown for reference in the lower panels, whereas the upper panels provide a 3D rendering at an oblique angle which makes the topological structure evident.

Figure 4

Dispersion projected onto the (100) direction at two temperatures. Away from the tube position one sees a weakly dispersive and sharply defined edge at all temperatures, which shifts downward by $\sim 0.1\mathrm{eV}$ in the low-temperature state. A similar shift is seen in the lower band maximum between $\Gamma$ and $X$ which can be identified from Fig. 2.