Some metallic properties in the framework of Tsallis generalized statistics

Abstract:

Some metallic quantities are calculated on the grounds of Tsallis generalized statistics: the specific heat at constant volume, c _V (T); the chemical potential, $\mu (T)$; the Pauli paramagnetic susceptibility,_X(T) and the Korringa constant, C_K. First it is found that for a general value of q, the Sommerfeld expansion series will exhibit both, odd and even terms, contrary to what is obtained if we use the Fermi-Dirac (FD) statistics, where only even terms appear. It follows that: (i) the specific heat coefficient,μ, is q-dependent, but the temperature dependence of c_V remains linear, as in the FD case; (ii) the Fermi energy, E_F, differs from the chemical potential by a linear term in T, and not quadratic, as in FD, the same happening for _x(T) (iii) the Korringa constant is q-dependent, but not T-dependent. In the limit $q \to 1$ the results of FD statistics are recovered. Metallic thin films and multilayers exhibiting fractal surface structures are possible systems where the present results could be tested.