%0 Journal Article
%T Theory of Seebeck Coefficient in Multi-Walled Carbon Nanotubes
%A Shigeji Fujita
%A James McNabb III
%A Akira Suzuki
%J Journal of Modern Physics
%P 628-637
%@ 2153-120X
%D 2013
%I Scientific Research Publishing
%R 10.4236/jmp.2013.45091
%X <p align=\"justify\">
	<span><span><span style=\"font-family:Verdana;\">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) </span><i><span style=\"font-family:Verdana;\">S</span></i><span style=\"font-family:Verdana;\"> is obtained: <i>S</i>=(2/3)ln2(<i>qn</i>)<sup>-1<i></i></sup></span></span><i><span style=\"font-family:verdana;\">¦Å</span><span style=\"font-family:verdana;\"><sub>F</sub>k<sub>B</sub></span></i>D<sub>0</sub>, where <i>k<sub>B</sub></i> is the Boltzmann constant, and <i>q, n, <i></i></i></span><i><span><span style=\"font-family:verdana;\">¦Å</span><span style=\"font-family:verdana;\"><sub>F</sub></span></span></i><span style=\"font-family:verdana;\">, D<sub>0</sub> are charge, carrier density, Fermi energy, density of states at <i></i></span><i><span style=\"font-family:verdana;\">¦Å</span><span><span style=\"font-family:Verdana;\"><sub>F</sub></span></span></i>, respectively. Ohmic and Seebeck currents are fundamentally different in nature, and hence, cause significantly different behaviors. For example, the Seebeck coefficient <i><span style=\"font-family:Verdana;\">S</span></i><span style=\"font-family:Verdana;\"> 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 </span><i><span style=\"font-family:Verdana;\">S</span></i><span style=\"font-family:Verdana;\"> is shown to be proportional to the temperature </span><i><span style=\"font-family:Verdana;\">T</span></i><span style=\"font-family:Verdana;\"> above the superconducting temperature </span><i><span style=\"font-family:Verdana;\">T</span><sub><span style=\"font-family:Verdana;\">c</span></sub></i><span style=\"font-family:Verdana;\"> based on the model of Cooper pairs as carriers. The </span><i><span style=\"font-family:Verdana;\">S</span></i><span style=\"font-family:Verdana;\"> follows a temperature behavior, <img style=\"width:93px;height:18px;\" alt=\"\" src=\"Edit_1cfa0380-5f74-40cf-a937-e984bde4fe7c.bmp\" width=\"189\" height=\"39\" /></span><span></span><span style=\"font-family:verdana;\">, where <i>T<sub>g</sub></i> <sup style=\"margin-left:-7px;\">¡¯</sup>= constant, at the lowest temperatures.</span> 
</p>
%K Thermoelectric Power (Seebeck Coefficient)
%K Multi-Walled Carbon Nanotubes
%K The Model of Cooper Pairs
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=31903