Abstract
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)-1εFkBD0, where kB is the Boltzmann constant, and q, n, εF, D0 are charge, carrier density, Fermi energy, density of states at εF, 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 Tc based on the model of Cooper pairs as carriers. The S follows a temperature behavior, , where Tg ’= constant, at the lowest temperatures.
Highlights
In 2003 Lu et al and Kang et al [1,2] observed a logarithmic temperature T -dependence of the seebeck coefficient S in multiwalled carbon nanotubes (MWNTs) at low temperatures
The Seebeck coefficient S is shown to be proportional to the temperature T above the superconducting temperature Tc based on the model of Cooper pairs as carriers
Where TF F is the Fermi energy, in Equation (7), we obtain. This formula for S is often quoted in materials handbook [4]
Summary
In 2003 Lu et al and Kang et al [1,2] observed a logarithmic temperature T -dependence of the seebeck coefficient S in multiwalled carbon nanotubes (MWNTs) at low temperatures. The Seebeck coefficient S of highly oriented pyrolytic graphite (HOPG), single crystal, is shown. This S is negative (“electron”-like) at low temperatures and become positive (“hole”-like) and constant above 150 K: Sgraphite. Conduction electrons are denoted by quotation marked “electrons” (“holes”) whereas generic electrons are denoted without quotation marks
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