Tilted elliptical Dirac cones at a half-metal surface

The surface electronic structure of the half-metallic alloy NiMnSb is investigated in detail, revealing the presence of Dirac cones in the minority-spin states. Surface-localized carriers of suitable energy will consequently behave as massless Dirac fermions, a remarkable situation for a half-metallic material and potentially of great significance in future spintronic device applications. Unlike related features observed previously in graphene and at the surfaces of topological insulators, the Dirac cones described here are of elliptical cross section and are tilted with respect to the energy axis. Such unique properties are permitted due to the lower symmetry in the present case.

Figure 1

(Color online) Minority-spin surface-state dispersion for clean NiMnSb{001}. The flat horizontal plane represents the Fermi level, and extends to fill the two-dimensional surface Brillouin zone; energy is represented on the vertical axis.

Figure 2

(Color online) Minority-spin surface states in the vicinity of the Dirac point. The square modulus of the fermion eigenfunction (i.e., the solution found on the upper sheet of the cone) is depicted by a silver (light) isosurface while that corresponding to the antifermion eigenfunction (i.e., the solution found on the lower sheet of the cone) is depicted by a bronze (dark) isosurface. Note that for any given fermion solution the corresponding antifermion solution is to be found at the wavevector inverted across the Dirac point. Isosurfaces are drawn at a threshold density of $1.2\times {10}^{-2}{\text{Å}}^{-3}$. Also depicted are the Brillouin zone and a plan view of the surface labeled with numerals indicating the layer to which each visible atom belongs.