Algebraic solution and thermodynamic properties of graphene in the presence of minimal length

Abstract

Graphene is a zero-gap semiconductor, where the electrons propagating inside are described by the ultra-relativistic Dirac equation normally reserved for very high energy massless particles. In this work, we show that graphene under a magnetic field in the presence of a minimal length has a hidden $su(1,1)$ symmetry. This symmetry allows us to construct the spectrum algebraically. In fact, a generalized uncertainty relation, leading to a non-zero minimum uncertainty on the position, would be closer to physical reality and allow us to control or create bound states in graphene. Using the partition function based on the Epstein zeta function, the thermodynamic properties are well determined. We find that the Dulong-Petit law is verified and the heat capacity is independent of the deformation parameter.