Study of Twistronics Induced Superconductivity in Twisted Bilayer Graphene

This work investigates the electronic properties of twisted bilayer graphene (TBG) through computational calculations, with the aim of understanding the emergence of flat bands and conditions favorable for superconductivity close to the magic angle. This study utilizes a k\cdot p continuum model, and the low-energy Hamiltonians are derived from angle-dependent datasets provided by Carr et al. Using this model, the band structure, density of states (DoS), and Fermi velocity are systematically calculated across a range of twist angles. The calculations are performed by discretizing high-symmetry paths in the moire Brillouin zone for band structure calculations, uniformly sampling a square grid for DoS analysis, and employing finite-difference methods to evaluate the Fermi velocity near the Dirac points. The results identify a narrow magic-angle window around $\theta \approx 0.98^\circ-1.00^\circ$, where the bands become nearly dispersionless, the DoS exhibits a sharp peak, and the Fermi velocity is strongly suppressed. This computational framework does not directly predict superconductivity, but rather establishes the electronic foundation for exploring flat-band physics and correlation-driven phenomena such as unconventional superconductivity in twisted bilayer graphene.