Моделювання електронної зонної структури моношарового та вертикально вирощеного графену на основі моделі сильного зв`язку

Abstract

The electronic band structure of graphene was modeled using a tight-binding (TB) approach, leveraging Google Tensor Processing Units (TPUs) to accelerate computations. Graphene, as a two-dimensional material with unique electronic properties–notably the presence of Dirac cones–requires efficient computational frameworks for detailed investigation. The tightbinding model provides an optimal balance between physical accuracy and computational efficiency, making it ideal for largescale simulations of systems that are too resource-intensive for ab initio methods. This study details the theoretical foundations of the tight-binding model for graphene, including the Hamiltonian derivation and the critical importance of incorporating higherorder interactions. The application of the TB method within the Google TPU architecture was first validated on a standard graphene monolayer and subsequently applied to the specific case of vertically oriented graphene (VG) grown on a thin copper layer. It is demonstrated that in vertically oriented graphene, an energy gap emerges due to the confinement of charge carriers within a quasi-one-dimensional (1D) periodic system. The utilization of TPUs significantly expands the capabilities for researching graphene and other quantum materials, enabling the modeling of larger and more complex systems, which opens new frontiers in materials science.