Semiclassical spatially dispersive intraband conductivity tensor and quantum capacitance of graphene

摘要: Analytical expressions are presented for the intraband conductivity tensor of graphene that includes spatial dispersion arbitrarily wave-vector values and presence a nonzero Fermi energy. The elements derived from semiclassical Boltzmann transport equation under both relaxation-time approximation Bhatnagar-Gross-Krook model (which allows an extra degree freedom to enforce number conservation). based on linear electron near Dirac points, extend previous results assumed small values; these shown be inadequate very slow waves expected nanoribbons. new also compared obtained by numericalintegrationoverthefirstBrillouinzoneusingtheexact(tight-binding)electrondispersionrelation.Very good agreement is found between analytical exact numerical results. Furthermore, comparison with longitudinal random-phase made. It analytically lead correct value quantum capacitance sheet ignoring leads serious errors in propagation properties fundamental modes