Paring From Strong Repulsion in Triangular Lattice Hubbard Model

A. Sherman

L. B. Ioffe, A. I. Larkin

Jordan Venderley, Eun-Ah Kim

With the discovery of strong-coupling physics and superconductivity in moir\'e superlattices, it is essential to have an understanding of strong-coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here, we use density matrix renormalization group to investigate the dominant superconducting channels in the hole-doped triangular lattice Hubbard model over a range of repulsive interaction strengths. We find a clear transition from $p$-wave superconductivity at a moderate on-site repulsion strength ($U/t=2$) at filling above 1/4 ($n\ensuremath{\sim}0.65$) to $d$-wave superconductivity at a strong on-site repulsion strength ($U/t=10$) at filling below 1/4 ($n\ensuremath{\sim}0.4$). The unusual tunability that moir\'e superlattices offer in controlling $U/t$ would open up the opportunity to realize this transition between $d$-wave and $p$-wave superconductivity.

Kun Woo Kim, T. Pereg-Barnea

Inspired by recent advances in the fabrication of surface superlattices, and in particular the triangular lattice made of tin (Sn) atoms on silicon, we study an extended Hubbard model on a triangular lattice. The observations of magnetism in these systems justify the inclusion of a strong on-site repulsion, and the observation of superconductivity suggests including an effective, nearest-neighbor attractive interaction. The attractive interaction mimics the effect of strong on-site repulsion near half filling, which can be seen in strong-coupling vertex calculations such as the Eliashberg method. With this extended Hubbard model on a triangular lattice with its geometrical frustration, we find a rich phase diagram of various magnetic orders and pairing functions, within the framework of self-consistent mean field theory. We uncover the competition between magnetism and unconventional superconductivity, and their coexistence for triplet pairings. We follow the Fermi surface of the system as the system is doped away from half filling and find nesting vectors and a Lifshitz transition, which provide an intuitive understanding of the phase transitions between the many orders we consider.

Oracio Navarro, Luis Antonio Pérez, C. Wang

R. O. Zaǐtsev, Yu. V. Mikhaǐlova

The spin magnetic susceptibility is determined in the self-consistent field approximation. It is shown that in the case of a square lattice as well as a triangular lattice with a negative hopping integral, the system retains its paramagnetic properties for all electron concentrations n<l. In the case of a triangular lattice with a positive hopping integral, the system goes over to the ferromagnetic state for a concentration close to 0.4.