Finite temperature transport and magnetism of a generalized Wigner pinball crystal

Correlated insulating generalized Wigner crystal (GWC) states of matter in hetero-bilayer transition metal dichalcogenides have been recently reported and modelled theoretically [Nature 587, 214 - 218 (2020), Nature 597, 650 - 654 (2021), npj Quantum Materials, 10, 95 (2025)]. The theoretical calculations have also reported the intriguing possibility of a partially melted GWC crystal – the so-called pinball crystal, at n=⅓ and n=½, in a realistic parameter regime of the extended Hubbard model on the triangular lattice. In this phase, with no classical analog, a majority of the electrons remain frozen or pinned (the "pins") while the others delocalize ("the balls"), providing a rare example of a situation where insulating and conducting properties coexist. Using finite temperature exact diagonalization and large-scale ground state density matrix renormalization group calculations, we predict the signatures associated with this phase that should be observable in finite temperature transport measurements. We also identify prominent temperature scales associated with Kondo singlet formation, and the melting of charge order, along with probing their response to an applied external magnetic field. Our work leads us to explore the phase diagram of the extended Hubbard model on the triangular lattice where we identify the nature of the metallic and insulating phases in the vicinity of the pinball phase.