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 electronic properties. The intercalated Pb monolayer (ML) has shown the coexistence of the Gr(10 x 10)-moiré and a stripe phase, which still lacks understanding. Using density functional theory calculation and thermal annealing with ab initio molecular dynamics as motivated by experiment, we have studied the formation energy of Gr/Pb/SiC(0001) for different Pb coverages. Near the coverage of a Pb(111)-like ML mimicking the (10 x 10)-moiré, 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$\overline{2}$10] 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 charge transfer from Pb ML to SiC(0001). As a result, 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.