The cumulant Green's functions method for a triangular lattice: Mott transition and superconductivity

We study the single-band Hubbard model for a triangular two-dimensional (2D) lattice using the cumulant Green's functions method (CGFM) [1,2]. The starting point of the method is to diagonalize a 2D cluster containing N correlated sites ("seed") and employ the cumulants calculated from the cluster solution to obtain the full Green's functions for the lattice. All calculations are done directly, and no self-consistent process is needed.

We apply the method to study the triangular lattice formed by the Sn adatoms on a Si(111) substrate with the 1/3 monolayer coverage. The system exhibits geometric frustration and strong electronic correlations. We use as a "seed" of the atomic cumulants closed clusters of three atoms (triangular), seven atoms (a hexagon with a central site), and nine atoms (a cluster formed by eight triangles), including high order hopping realistic process up to fifth order. The Sn triangular develops non-conventional superconductivity in the presence of heavily doped p-type Si(111) substrates [4]. We study the interplay of geometric frustration and correlation in the Mott transition and in the development of unconventional superconductivity.

[1] R N Lira et al. J. Phys.: Condens. Matter 35 (2023) 245601

[2] R N Lira Physics Letters A 474 (2023) 128818

[3] Gang Li et al. NATURE COMMUNICATIONS | 4:1620 | DOI: 10.1038/ncomms2617

[4] F Ming et al. Nature Physics | Volume 19 | April 2023 | 500–506