Thermodynamic Behavior of Doped Graphene: Impact of Heavy Dopant Atoms.

This study investigates the effect of incorporating heavy dopant atoms on the topological transitions in the energy spectrum of graphene, as well as on its thermodynamic properties. A tight-binding model is employed that incorporates a lattice composition parameter associated with the dopant's effect to obtain the electronic spectrum of graphene. Thus, the substitutional atoms in the lattice impact the electronic structure of graphene by altering the connectivity of the Dirac cones and the symmetry of the energy surface in their spectrum. The Gibbs entropy is numerically calculated from the energy surface of the electronic spectrum, and other thermodynamic properties, such as temperature, specific heat, and Helmholtz free energy, are derived from theoretical principles. The results show that topological changes induced by the heavy dopant atoms in the graphene lattice significantly affect its electronic structure and thermodynamic properties, leading to observable changes in the distances between Dirac cones, the range of the energy spectrum, entropy, positive and negative temperatures, divergences in specific heat, and instabilities within the system.