Metacinnabar ($\beta$-HgS): A Strong 3D Topological Insulator with Highly Anisotropic Surface States

We establish the presence of topologically protected edge states on the (001) surface of HgS in the zinc-blende structure using density-functional electronic structure calculations. The Dirac point of the edge state cone is very close to the bulk valence band maximum. The Dirac cone is extremely anisotropic with a very large electron velocity along one diagonal of the surface elementary cell $x^{\prime }$ and a nearly flat dispersion in the perpendicular direction $y^{\prime }$. The strong anisotropy originates from a broken fourfold rotoinversion symmetry at the surface.

Figure 1

Band structure of HgS in the bulk. It is an inverted semiconductor which is visible at the $\Gamma$ point: small gap and electronlike dispersion at the top of the valence band.

Figure 2

Schematic representation of the (001) surface of HgS. Shown are the mercury top layer (full circles: Hg atoms, dashed circles: surplus Hg atom that has been removed) and the subsurface sulfur layer (squares: $S$). At the surface the rotoinversion symmetry of the bulk crystal structure is broken.

Figure 3

Band structure of the 8-layer slab (lines) superimposed with the bulk band structure projected onto the surface (shaded area). The relevant surface bands are indicated in red ([medium gray] top surface) and blue ([dark gray] bottom surface).

Figure 4

(a) Width of the gap as a function of the number of elementary cells (EC) and (b) sum of $3p$ weights over the four surface states at $\Gamma$, resolved for each sulfur layer in the slab of 8 EC.

Figure 5

Schematic representation of the anisotropic Dirac cone (top) emerging from the surface bands of an 8-layer slab of HgS (below). The band structure data near the Fermi level are shown as points and the fit with the effective long-wavelength model as lines. The points in the surface Brillouin zone are denoted as $\overline{X}=(\pi /a_0,0)$, $\overline{M}=(\pi /a_0,\pi /a_0)$, and ${\overline{M}}^{\prime }=(\pi /a_0,-\pi /a_0)$ in the ($k_x$, $k_y$) coordinate system.