Tunable square lattice Hubbard model in twisted bilayer C₅₆₈

We propose twisted homobilayer C₅₆₈ as a candidate for realizing tunable single-band square lattice Hubbard model even without displacement field. C₅₆₈ is a recently predicted 2D carbon allotrope which has square lattice periodicities and features the rotoinversion symmetry S₄ instead of C_4z. The monolayer hosts a valence top at the M-point, the square Brillouin zone corner, which is the focus of our study

We derive a continuum model where necessary parameters are calibrated with the ab-initio results, and then construct a single-band extended Hubbard model for the top moiré valence band. Inspections on the derived Hubbard model reveal that (i) the twist angle enables wide-ranging tuning of the ratio between the nearest and the next nearest neighbor hoppings in the Hubbard model, and (ii) a finite displacement field induces anisotropy in the nearest neighborhoppings. These results highlight the potential of C₅₆₈ as a versatile material for studying artificial stackings and can potentially lead to high-temperature superconductivity which resembles curate physics.