We propose the $\ensuremath{\pi}$ flux triangular lattice Hubbard model ($\ensuremath{\pi}$ THM) as a prototypical setup to stabilize magnetically disordered quantum states of matter in the presence of charge fluctuations. The quantum paramagnetic domain of the $\ensuremath{\pi}$ THM that we identify for intermediate Hubbard
U is framed by a Dirac semimetal for weak coupling and by 120\ifmmode^\circ\else\textdegree\fi{} N\'eel order for strong coupling. Generalizing the Klein duality from spin Hamiltonians to tight-binding models, the $\ensuremath{\pi}$ THM maps to a Hubbard model which corresponds to the $({J}_{\mathrm{H}},{J}_{\mathrm{K}})=(\ensuremath{-}1,2)$ Heisenberg-Kitaev model in its strong coupling limit. The $\ensuremath{\pi}$ THM provides a promising microscopic testing ground for exotic finite-
U spin liquid ground states amenable to numerical investigation.
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.