Graphene: Study in Electronic Structure, Superconductivity and Potential in Quantum Information Sciences

Graphene, a two-dimensional lattice of carbon atoms, exhibits remarkable electronic properties due to its Dirac-like electronic excitations. This paper reviews the elementary electronic properties of graphene, including the tight-binding model for single-layer graphene and the band structure formation. The tight-binding Hamiltonian provides a fundamental understanding of graphene’s linear energy dispersion near the Dirac points, leading to unique phenomena such as massless Dirac fermions and chiral tunneling. We explore the potential of superconductivity in graphene using BCS theory. We find that BCS theory cannot explain superconductivity in graphene and its forms. This is in contradiction with the discovery of unconventional superconductivity in twisted bilayer graphene (TBG). The study further explores the potential application of bilayer graphene quantum in quantum information sciences, highlighting the development of states with relaxation times exceeding 500 ms. These valley states, arising from the hexagonal lattice structure, can be used to encode information as robust valley qubits for fault-tolerant quantum computing