Structural and electronic properties of two-dimensional stanene and graphene heterostructure

Table 1 Heterostructure configurations for the stanene/graphene bilayers (abbreviated as Sn/G)

Sn/G	a (Å)	α (°)	θ (°)	Δ (Å)	L _Sn	L _G	L _Sn/G	Mismatch (%)	Strain (%)	E _b (meV)
\( 3/\sqrt{31} \)	4.53	9	111.2	0.84	13.68	13.61	13.62	0.07	−0.4	−76
\( 2\sqrt{7}/\sqrt{97} \)	4.55	3.8	111.3	0.82	24.12	24.07	24.07	0.29	−0.2	−77
\( \sqrt{21}/\sqrt{73} \)	4.56	5.1	111.3	0.82	20.89	20.88	20.87	0.48	−0.1	−78
\( \sqrt{7}/5 \)	4.61	19.1	112.2	0.80	12.06	12.22	12.20	1.8	1.1	−72
\( \sqrt{13}/4\sqrt{3} \)	4.68	16.1	112.2	0.80	16.43	16.93	16.89	3.6	2.8	−57

Each configuration is built by combining different supercells in individual layers with a relative rotational angle α between them. L _Sn/G is the lattice constant of the relaxed bilayer heterostructure and the corresponding a is the effective lattice constant of stanene in the relaxed heterostructure, while L _Sn and L _G are the lattice constants for the particular unrelaxed supercells of stanene and graphene, respectively. θ and Δ are the bond angle and buckling height in stanene, respectively. The mismatch, strain, and E _b are defined in the text