Kondo Effects in Quantum Dots at Large Bias

Abstract

Recently, the issue of whether the Kondo problem in quantum dots at large bias is a weak-coupling problem or not has been raised. In this paper, we revisit this problem by carefully analyzing a corresponding model in the solvable limit -- the Emery-Kivelson line, where various crossover energy scales can be easily identified. We then try to extract the scaling behavior of this problem from various physical correlation functions within the spirit of ``poor man's scaling.'' Our conclusions support some recent suggestions made by Coleman {\em et al.} [Phys. Rev. Lett. {\bf 86}, 4088 (2001)], which are obtained by perturbative analysis: The voltage acts as a cutoff of the renormalization group flow for {\em only} half of the impurity so that the low-temperature physics is controlled by a strong-coupling fixed point. But the low-temperature response functions in general show one-channel Kondo behaviors with two-channel Kondo behaviors occurring only through proximity to a quantum critical point.