Slave boson theory for transport through magnetic molecules with vibronic states

We study the electron transport through a magnetic molecular transistor in the Kondo limit using the slave boson technique. We include the electron-phonon coupling and analyze the cases where the spin of the molecule is either S=1/2 or S=1. We use the Schrieffer-Wolff transformation to write down a low energy Hamiltonian for the system. In the presence of electron-phonon coupling, and for $S\smeq1$, the resulting Kondo Hamiltonian has two active channels. At low temperature, these two channels interfere destructively, leading to a zero conductance.