Linear temperature dependence of electrical resistivity in a single-impurity model.

Abstract

Using the Majorana fermion representation, we consider a compactified Anderson impurity model, which has a non-Fermi-liquid weak-coupling fixed point. The impurity free energy, self-energies, and vertex function are perturbatively formulated in terms of Pfaffian determinants. A linear temperature dependence of the electrical resistivity is obtained from the second-order perturbation. In the third order of $U$, the vertex function is found to be logarithmic divergent. A summation of the leading logarithmic terms gives a new weak-coupling low-temperature energy scale ${T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}\mathrm{exp}[\ensuremath{-}\frac{1}{9}(\frac{\ensuremath{\pi}\ensuremath{\Delta}}{U}{)}^{2}]$.