Conductance of a spin-1 quantum dot: The two-stage Kondo effect

We discuss the physics of a spin-1 quantum dot, coupled to two metallic leads, and develop a simple model for the temperature dependence of its conductance. Such quantum dots are described by a two-channel Kondo model with asymmetric coupling constants, and the spin screening of the dot by the leads is expected to proceed via a two-stage process. When the Kondo temperatures ${T}_{K1}$ and ${T}_{K2}$ of each channel are widely separated on cooling, the dot passes through a broad crossover regime ${T}_{K2}⪡T⪡{T}_{K1}$ dominated by underscreened Kondo physics. A singular or non-Fermi-liquid correction to the conductance develops in this regime. At the lowest temperatures, destructive interference between resonant scattering in both channels leads to the eventual suppression of the conductance of the dot. We develop a model to describe the growth, and ultimate suppression, of the conductance in the two channel Kondo model as it is screened successively by its two channels. Our model is based upon large-$N$ approximation in which the localized spin degrees of freedom are described using the Schwinger boson formalism.