Structural model of orthorhombic tin sulfide (SnS). Gray and yellow balls represent Sn and S, respectively. (a) Unit cell, repeated twice in the bc-plane, and (b) corresponding Brillouin zone.
Band structure for model (a) single-layer, (b) double-layer and (c) bulk SnS, and [(d)–(f)] corresponding Brillouin zone and constant energy surfaces close to the edge of the conduction (purple) and valence (yellow) band. In [(a)–(c)] the band structure is shown along the path that traces the edge of the Brillouin zone in a clock-wise fashion. At each k-point the energy eigenvalues are color-coded with respect to the relative contribution of the s- (red), p- (blue), and d- (green) levels of Sn (top panel), and s- and p-levels of S (bottom panel), and the symbol size is proportional to the relative total contribution of the element. The shaded horizontal strip delimits the band gap. The lowest-energy level of each band structure is shifted to −17 eV (level is not shown).
Maximally-localized Wannier functions constructed from the occupied valence states in bulk SnS, describing (a) Sn lone-pair states of which there are 4, one for each Sn atoms, (b) bonding states of which are 12, three for each Sn-S pair, and (c) states localized around the S atoms, of which there are 4. (d) Projection of the Wannier functions onto the Bloch band structure. At each k-point, the energy eigenvalues are color-coded with respect to the relative contribution of the Sn lone-pair states (red), and the bonding and S-states states (blue).
Minimum band gap Eg for (a) direct and (b) indirect transitions and associated band extrema in bulk (filled circles) and double-layer (empty circles) SnS with respect to strain, , applied along the layer stacking direction. Negative and positive values of correspond to compressive and tensile strain, respectively, ( = 0 for the unstrained SnS). The horizontal dashed line marks the band gap of single-layer SnS.
Absorption coefficient, , as a function of photon energy, , for the model single-layer, double-layer, and bulk structures of SnS. Solid, dashed, and dotted lines correspond to unstrained structures, and structures under 5% compressive and 5% tensile strain along the layer stacking direction (a-axis in Fig. 1 ).
Imaginary part of the dielectric function, , as a function of photon energy for the model bulk (top) and double-layer (bottom) structure of SnS with light polarized in the direction of each structural axis. Solid, dashed, and dotted lines correspond to unstrained structures, and structures under 5% compressive and 5% tensile strain along the layer stacking direction (a-axis in Fig. 1 ).
Kohn-Sham band gap (EKS), derivative discontinuity ( ), indirect ( ), and direct ( ) band gaps, all in eV, and the electron ( ) and hole ( ) effective masses in units of bare electron mass at k-points involved in indirect transitions along the b- and c-direction (see also Fig. 2 ).
Static dielectric constants for the model single-layer, double-layer, and bulk structures of SnS, obtained within the random phase approximation and the bootstrap approximation.
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