Theory of Seebeck Coefficient in Multi-Walled Carbon Nanotubes

Based on the idea that different temperatures generate different conduction electron densities and the resulting carrier diffusion generates the thermal electromotive force (emf), a new formula for the Seebeck coefficient (thermopower) S is obtained: S=(2/3)ln2(qn)^-1ε_Fk_BD₀, where k_B is the Boltzmann constant, and q, n, ε_F, D₀ are charge, carrier density, Fermi energy, density of states at ε_F, respectively. Ohmic and Seebeck currents are fundamentally different in nature, and hence, cause significantly different behaviors. For example, the Seebeck coefficient S in copper (Cu) is positive, while the Hall coefficient is negative. In general, the Einstein relation between the conductivity and the diffusion coefficient does not hold for a multicarrier metal. Multi-walled carbon nanotubes are superconductors. The Seebeck coefficient S is shown to be proportional to the temperature T above the superconducting temperature T_c based on the model of Cooper pairs as carriers. The S follows a temperature behavior, , where T_g ^’= constant, at the lowest temperatures.