Entropy and Negative Specific Heat of Doped Graphene: Topological Phase Transitions and Nernst’s Theorem Revisited

This study explores the thermodynamic properties of doped graphene using an adapted electronic spectrum. We employed the one-electron tight-binding model to describe the hexagonal lattice structure. The dispersion relation for graphene is expressed in terms of the hopping energies using a compositional parameter that characterizes the different dopant atoms in the lattice. The focus of the investigation is on the impact of the compositions, specifically the presence of dopant atoms, on the energy spectrum, entropy, temperature, and specific heat of graphene. The numerical and analytical results reveal distinct thermodynamic behaviors influenced by the dopant composition, including topological transitions, inflection points in entropy, and specific heat divergences. In addition, the use of Boltzmann entropy and the revision of Nernst's theorem for doped graphene are introduced as novel aspects.