Topologicalα-Sn surface states versus film thickness and strain

Abstract

The theoretical prediction that gray tin represents a strong topological insulator under strain [L. Fu and C.L. Kane, Phys. Rev. B 76, 045302 (2007)] is proven for biaxially strained α-Sn layers with varying thickness by means of a generalized density functional theory with a nonlocal exchange-correlation potential that widely simulates quasiparticle bands and a tight-binding method including intra-and interatomic spin-orbit interaction. Hydrogen-passivated surfaces are modeled by symmetric slabs. In contrast to the conventional picture of a topological insulator, we find topological gapless surface states below the strain-induced bulk gap, in agreement with photoemission studies. The topological surfaces states do not emerge out of the lower + 8 states but are strongly influenced by the inverted bulk − 7 band, i.e., lie within the negative bulk sp gap. We show that the position of the Dirac point and the dispersion of the surrounding bands depend on the thickness of the α-Sn layer but are less influenced by strain. The resulting Fermi velocities agree well with available photoemission data.

Structural and electronic properties of the pure and stable elemental 3D topological Dirac semimetal α-Sn

“…From the fit of the slopes of the Dirac cone branches we extracted Fermi velocity values (v F ) of 0.48(1) × 10 6 m/s (left) and 0.52(1) × 10 6 m/s (right). These v F values are close to the theoretically predicted value for thick films of elemental α-Sn (0.58 × 10 6 m/s) 53 , but clearly reduced compared to the previously reported values for Bi/Te doped α-Sn (∼ 0.7 × 10 6 m/s) 7,10 . This suggests that the effect of shifting E F upwards in the case of Bi/Te doped α-Sn is actually accompanied by a contraction of the Γ − 7 energy band (which hosts the Dirac cone), spanning, in that case, a smaller k-space in the surface Brillouin zone.…”

Conversion between spin and charge currents with topological insulators

“…2 in Ref. [14]). In contact with Ag and from ARPES measurements, the Dirac cone is still observed and the Fermi level is at 0.65 meV above the Dirac point, whereas the contact with Fe destroys the Dirac cone [10].…”

Gapped electronic structure of epitaxial stanene on InSb(111)

“…Sb s-orbitals were set to -3.5, 4, and -9, respectively, in order to yield the correct band ordering as reported in previous experimental [33,34] and theoretical studies [35].…”