Relativistic Mott transition and high-order van Hove singularity in moiré semiconductors

Synopsis

Recent experiments on twisted double bilayer tungsten diselenide have demonstrated that moiré semiconductors can realize a relativistic Mott transition, i.e., a quantum phase transition from a Dirac semimetal to a correlated insulating state, by twist-angle tuning. In addition, signatures of van Hove singularities were observed in the material's moiré valence bands, suggesting further potential for the emergence of strongly correlated states. In my talk, I will provide a detailed analysis of the twist-angle dependence of the system's band structure, focusing on the evolution of the Dirac excitations and the Fermi-surface structure with its Lifshitz transitions across the van Hove fillings. I will show that the twist angle can be used to band engineer a high-order van Hove singularity, which can be accessed by gate tuning. The, I will discuss the magnetic phase diagram of an effective Hubbard model for twisted double bilayer tungsten diselenide on the effective honeycomb superlattice with tight-binding parameters fitted to the two topmost bands of the continuum model. To that end, we employed a self-consistent Hartree-Fock mean-field approach in real space and explored a broad parameter range of twist angle, filling, and temperature. We found a rich variety of magnetic states that we expect to be accessible in future experiments, including, e.g., a noncoplanar spin-density wave with nonzero spin chirality and a half-metallic uniaxial spin-density wave. We also employed a functional renormalization group approach to also study the competition between density-wave and superconducting instabilities. Finally, I will discuss some aspects of the quantum critical behavior that has, however, not been quantitatively been studied experimentally.