Strain-modulated intercalated phases of Pb monolayer with dual periodicity in SiC(0001)-graphene interface

Intercalation of metal atoms at the SiC(0001)-graphene (Gr) interface can provide confined 2D metal layers with interesting properties. The intercalated Pb monolayer (ML) has shown the coexistence of the Gr(10x10)-moire and a stripe phase, which still lacks understanding. Using density functional theory calculation and thermal annealing with ab initio molecular dynamics, we have studied the formation energy of SiC(0001)/Pb/Gr for different coverages of intercalated Pb. Near the coverage of a Pb(111)-like ML mimicking the (10x10)-moire, we find a slightly more stable stripe structure, where one half of the structure has compressive strain with Pb occupying the Si-top sites and the other half has tensile strain with Pb off the Si-top sites. This stripe structure along the Gr zigzag direction has a periodicity of 2.3 nm across the [1-210] direction agreeing with the previous observations using scanning tunneling microscopy. Analysis with electron density difference and density of states show the tensile region has a more metallic character than the compressive region, while both are dominated by the charge transfer from the Pb ML to SiC(0001). The small energy difference between the stripe and Pb(111)-like structures means the two phases are almost degenerate and can coexist, which explains the experimental observations.