Bulk and Surface Electronic Structure of the Dual-Topology Semimetal ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$

We report high-resolution angle-resolved photoemission measurements on single crystals of ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$ grown by high-pressure synthesis. Our data reveal a gapped Dirac nodal line whose (001) projection separates the surface Brillouin zone in topological and trivial areas. In the nontrivial $k$-space range, we find surface states with multiple saddle points in the dispersion, resulting in two van Hove singularities in the surface density of states. Based on density-functional theory calculations, we identify these surface states as signatures of a topological crystalline state, which coexists with a weak topological phase.

Figure 1

Bulk jacutingaite single crystals. (a) Sketch of the high-pressure cell: 1, pyrophyllite cell; 2, graphite heater; 3, BN crucible; 4, sample; 5, thermocouples. (b) Broken as-grown boule: shiny crystal surfaces are visible inside the polycrystalline pellet. (c) Scanning electron micrograph of a ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$ crystal extracted from the pellet. (d),(e) Top and side views of the crystal structure. In (d) the blue lines indicate the three mirror planes relevant for the topology of the band structure. (f) Sketch of the 3D Brillouin zone. The blue shaded plane is one of the three mirror planes in momentum space. The nodal lines inside the BZ are marked in red. (g) DFT band structure calculation including SOC. (Inset) Enlarged view of the Dirac-like dispersion at $K$, gapped by SOC interactions.

Figure 2

Bulk and surface electronic structure. (a) ARPES Fermi surface measured with $h\nu =19\mathrm{eV}$ excitation energy and $p$ polarization. (b) Projected Fermi surface contours of hole (orange) and electron (green) pockets extracted from measurements at 19 and 62 eV photon energies [20]. (c),(e) ARPES dispersion plots. (d),(f) Projected bulk band structure obtained by combining data at 19, 28, 36, and 62 eV photon energies (left half). The dispersion of the surface state is indicated with green dots. DFT calculations of the surface spectral density (right half). (g) Cut along the white dashed line marked on the Fermi surface in (a). (h) Radial cuts across the electronlike lens pocket measured at the positions marked by solid white lines in (a). The dispersion of the nodal line is traced by a red line. (i) DFT bands calculated at $k_{z1}=-0.2962{\AA }^{-1}$ (left) and $k_{z2}=-0.2735{\AA }^{-1}$ (right) showing the nodal line crossings along ${\mathrm{\Gamma }}_1{M}_1$ and ${\mathrm{\Gamma }}_2{K}_2$.

Figure 3

Dispersion of the topological surface state (TSS). (a) Stack of constant energy maps around the $M$ point. (b),(c) Dispersion along $KMK$ ($k_y$) and $\mathrm{\Gamma }M\mathrm{\Gamma }$ ($k_x$), respectively. On the right-hand side, the extracted surface and bulk band dispersions are superimposed on the data. (d) 3D plot of the energy and momentum dispersion of the TSS extracted over the momentum range indicated by vertical dashed lines in (b) and (c). (e) Associated isoenergy contours of the lower (blue) and upper (red) surface state branches. (f) Histograms of the corresponding $\epsilon (k)$ values, showing sharp peaks at the energy positions of the van Hove singularities.