T-Square Term of Electrical Resistivity

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Abstract
The electrical resistivity, R , in metals at low temperature T is given by R0 + AT2 , where R0 and A are the residual resistivity due to impurities and the coefficient of T2 -term due to electron interactions, respectively. In this paper, we discuss the magnitude of A for the systems composed of two kinds of electrons possessing different effective masses, such as transition and rare earth metals. Starting with the Kubo fomula, we obtain coupled equations for the current vertex functions of light and heavy electrons. By using these equations, we can show that the resistance of light electrons originates from the collision between the two kinds of electrons ( s-d scattering or s-f scattering) as believed. In this mechanism, a mutual interaction between heavy electrons is indispensable for the momentum, transferred from the light electron to the heavy electron, to decay. If the system has the mixing term between light and heavy electrons like heavy fermion system, the quasi-particles are composed of the both kinds of electrons. For this case, the contributions of the two kinds of electrons to the conductivity are separated to determine the main contributions for some limiting cases.

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