Abstract
In this work, we use two different statistical mechanics formalisms like, Shannon and Tsallis formalisms (extensive and non-extensive), to study the thermodynamic properties of quantum rings (QRs) in monolayer and bilayer graphene under a uniform external magnetic field. To this goal, we first employ a simplified model to obtain energy eigenvalues of monolayer and bilayer graphene quantum rings. Then, by applying the Shannon and Tsallis formalisms, we have calculated the entropy, specific heat, magnetization, and magnetic susceptibility of monolayer and bilayer graphene. Our results show that thermodynamic quantities in the Shannon formalism have oscillation behaviors with increasing external magnetic fields. Unlike the Shannon formalism, the obtained properties by the Tsallis formalism show a peak structure. Also, the peak location depends on the number of graphene layers.
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