Fractional statistical potential in graphene

In this work the fractional statistics is applied to an anyon gas in graphene to obtain the special features that the arbitrary phase interchange of the particle coordinates introduce in the thermodynamic properties. The electron gas is constituted by N anyons in the long wavelength approximation obeying fractional exclusion statistics and the partition function is analyzed in terms of a perturbation expansion up to first order in the dimensionless constant λ/L being L the length of the graphene sheet and λ=βℏvF the thermal wavelength. By considering the correct permutation expansion of the many-anyons wavefunction, taking into account that the phase changes with the number of inversions in each permutation, the statistical fermionic/bosonic potential is obtained and the intermediate statistical behavior is found. It is shown that “extra” fermonic and bosonic particles states appears and this “statistical particle” distribution depends on N. Entropy and specific heat is obtained up to first order in λ/L showing that the results obtained differs from those obtained in different approximation to the fractional exclusion statistics.