A novel ground state of the (2$\surd $3x2$\surd $3)R30$^{\circ}$ Sn double layer on Si(111) induced by modulation hole-doping

Charge doping provides a tuning knob of the delicate interactions between spin, orbital, charge and lattice degrees of freedom in low-dimensional systems, which dictate many intriguing quantum phenomena. Using scanning tunneling microscopy/spectroscopy, we characterize the (2$\surd $3x2$\surd $3)R30$^{\circ}$ Sn double layer grown on a ($\surd $3x$\surd $3)-B reconstructed Si(111) surface, where 1/3 monolayer B dopants resides in the subsurface layer without forming direct chemical bonds with the Sn layer. The B atoms donate holes to the Sn double layer and shift the Fermi level toward the valence band edge. Surprisingly, it further induces a fraction of the 2$\surd $3x2$\surd $3 phase to gradually transform to a new 4$\surd $3x2$\surd $3 phase below 80 K. The two phases coexist down to 2.5 K, indicating a phase-separated ground state for the hole doped Sn double layer, in contrast to a homogenous 2$\surd $3x2$\surd $3 phase for the undoped one. The new 4$\surd $3x2$\surd $3 phase has a larger band gap than the 2$\surd $3x2$\surd $3 phase and the valence band edge shifts a few tens meV away from the Fermi level to higher binding energy, suggesting that the transition to the 4$\surd $3x2$\surd $3 structure is accompanied by an electronic structure rearrangement.