Title: Algebraic solution and thermodynamic properties of graphene in the presence of minimal length
Author(s):

	J. Gbètoho (Laboratory of Physics and Applications (LPA), Université Nationale des Sciences, Technologies, Ingénierie et Mathématiques (UNSTIM) Abomey, BP: 2282 Goho Abomey, Rep du Bénin ),
	F. A. Dossa (Laboratory of Physics and Applications (LPA), Université Nationale des Sciences, Technologies, Ingénierie et Mathématiques (UNSTIM) Abomey, BP: 2282 Goho Abomey, Rep du Bénin ),
	G. Y. H. Avossevou (Institut de Mathématiques et de Sciences Physiques (IMSP), Université d'Abomey-Calavi (UAC), 01 BP 613 Porto-Novo, Rep du Bénin)

Graphene is a zero-gap semiconductor, 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 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.

Key words: graphene, minimal length su(1,1), symmetry, thermodynamic properties

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