Superconductor-Insulator Transition in the TMD moir\'{e} systems and the Deconfined Quantum Critical Point

We propose that the recently observed superconductor-insulator transition (SIT) in the twisted bilayer transition metal dichalcogenides moir\'{e} system at hole filling $\nu = 1$ may be described by the deconfined quantum critical point (DQCP), which was originally proposed for the transition between the N\'{e}el order and the valence bond solid (VBS) order on the square lattice. The key symmetries involved in the original DQCP include a $\mathrm{SO}(3)_s$ spin symmetry, as well as a $C_4$ lattice rotation symmetry for the VBS order that is enlarged into a $\mathrm{U}(1)_v$ symmetry near the DQCP. In the current SIT under consideration, the counterpart of the $\mathrm{SO}(3)_s$ spin symmetry is an approximate $\mathrm{SO}(3)_v$ symmetry that transforms between different crystalline orders on the triangular lattice; and the role of the $\mathrm{U}(1)_v$ symmetry is replaced by the ordinary charge-$\mathrm{U}(1)_e$ symmetry. And at the DQCP the $\mathrm{SO}(3)_v \times \mathrm{U}(1)_e$ may enlarge into an emergent $\mathrm{SO}(5)$ symmetry. Under strain, the SIT is driven into either a prominent first order transition, or an "easy-plane" DQCP, which is expected to have an emergent $\mathrm{O}(4)$ symmetry.