First Principle Study Of Z₂ Topological Phase In Sb/graphene/Sb Heterostructure

The two dimensional(2D) topological insulators(TIs) have been the focus of the research recently. It has been found that the 2D materials with strong spin-orbit coupling(SOC), such as Bi, Sb bilayers, Bi2Se3 and Bi2Te3 quintuple layers, are TIs. In comparison with these strong SOC 2D materials, 2D materials with very weak SOC, including graphene and silicene, have much higher charge mobility and heat conductivity. However, they have tiny SOC gap and are not TIs. Therefore, combining exceptional properties of graphene-like materials with the unique properties of TIs, we study how to obtain the nontrivial Z2 topological phase in graphene-like materialsIn this work, we take graphene as an example and try to induce nontrivial Z2 topological phase in graphene by sandwiching it between strong SOC materials, Bi and Sb bilayers, respectively. By performing density functional calculations, it is revealed that robust nontrivial topological phase can be realized in graphene and that the material sandwiching the graphene makes great difference. Bi/graphene/Bi is gapless and not a TI, whereas Sb/graphene/Sb is gapped and a TI. Analyses of the differential charge density show that a dipole field is formed between the graphene and pnictogen layer, pulling down the bands of graphene. Depending on the kinds of pnictogen bilayers, the position of Dirac point of graphene is below the valence band maximum in Bi/graphene/Bi, while it is within the energy gap in Sb/graphene/Sb. We calculated the parity of the valence bands at the time reversal invariant momenta and obtained the Z2 index, which shows that a band inversion occurs at the Dirac point of graphene and the nontrivial topological phase appears in Sb/graphene/Sb. We further found that strains can tune the topological phase effectively and revealed that the topological phase transition is mainly ascribed to the changing of the thickness of Sb bilayers.Our findings show that the proximity effect can induce robust nontrivial Z2 topological phase in graphene, but the feasibility depends on the size of the energy gap of the pnictogen bilayers and the initial relative position of the Dirac point of graphene with respect to this gap. The guideline is that choosing a strong SOC material with sufficiently large gap so that the Dirac point of graphene is initially positioned in the middle of this gap before interaction and remains within this gap after interaction. We think that our results can help the researchers in TI community to search new TIs and realize nontrivial topological phase in weak SOC materials.