Electronic Transport in Twisted Bilayer Tungsten Diselenides - Zaher, Walid (AUC Knowledge Fountain, 2026)
This thesis investigates density waves (DWs) in twisted bilayer tungsten diselenide (tWSe₂) using a mean field approximation, with a focus on electron-electron interactions, and the system’s free energy at zero temperature. For the mean field approximation, the study initially employed same-spin nesting vectors, which were found insufficient to induce DWs formation. In contrast, when opposite-spin nesting vectors were used, DWs emerged, indicating that these vectors can support DWs formation. The plots were produced under perfect nesting conditions, where van Hove singularities (VHS) occur. At zero temperature, perfect nesting provides a complete picture of the upper limit of DWs formation, as DWs’ strength peaks under these conditions. The plots were in terms of the applied displacement field and electronic filling, showing both the order parameter (OP) and the modulation of the electronic charge density. The plots revealed that DWs’ strength increases as the system moves away from half-filling and weakens near half-filling. The modulation patterns showed that the DWs state comprises coupled charge density waves (CDWs) and spin density waves (SDWs), with no evidence of competition between them. These findings from the mean field approximation offer valuable insights for future experimental and theoretical investigations of DWs in tWSe₂. To complement this, McMillan’s free energy framework was applied to model DWs, including a formulation for incommensurate order. This free energy analysis was then used to assess the viability of commensurate orders predicted by earlier theoretical studies. Corresponding formulations were developed for these potential commensurate states. Finally, the competition between superconductivity (SC) and DWs was explored using a Ginzburg-Landau free energy approach for SC. Together, the free energy formulations for DWs and SC provide a theoretical foundation to map out a complete phase diagram of their interactions in tWSe₂ using experimental results.