Research Topics

Below is a list of the research papers I authored during my PhD.

• The Composite Operator Method: An article revisiting this analytical technique—originally developed by Roth, Beenen, Stanescu, and others in the 1970s using modern numerical methods. The study reviews the self-consistent schemes and extends the formalism to higher-order tight-binding parameters as well as to superconducting phases. arXiv link


• Extension to the Two-Orbital Hubbard Model: A numerical implementation of the method applied to the two-orbital Hubbard model, revealing a spontaneous orbital-selective Mott phase. arXiv link


• Proximity-Induced Charge Density Wave: A numerical study demonstrating the existence of a non-zero proximity-induced charge density wave in a tight-binding model. The order persists over a finite length scale in a weakly interacting metal adjacent to an ordered material. arXiv link


• Twisted Bilayer Graphene (Series of Three Papers): A set of three articles employing the T-matrix formalism to analyze pairing symmetries, associated topological states, and impurity-induced subgap states in ABA and ABC stacked graphene.
  
  arXiv link [I]
  
  arXiv link [II]
  
  arXiv link [III]

In the space below, I will outline future research directions. This section is intentionally left empty for now, as I prefer to consolidate my notes and revisit foundational material before engaging in new projects. Nevertheless, I am particularly interested in statistical physics applied to biophysics, strongly correlated materials, and numerical simulation more broadly.