Susceptibility, entropy and specific heat of quantum rings in monolayer graphene: comparison between different entropy formalisms

In this paper, the eigenstates and energy levels of carriers confined in quantum rings (QRs) in single-layer graphene under an applied magnetic field are calculated analytically. Extensive (Shannon) and non-extensive (Tsallis) formalisms are then used to determine the entropy, specific heat, and susceptibility of the system. Specifically, by using the Tsallis entropy formalism, the entropy, specific heat, and magnetic susceptibility of this system are investigated. We also compare these quantities for QR monolayer graphene in two statistical mechanics regimes: extensive (Shannon entropy) and non-extensive (Tsallis entropy). Our findings show that the thermodynamic quantities in the Shannon entropy have periodic behavior with increasing external magnetic field, and the properties obtained by the Tsallis formalism show a peak structure. In particular, the specific heat calculated by the Tsallis formalism shows a Schottky anomaly effect. The results obtained in this work can serve as a good starting point for future experimental works.