Two-channel orbital Kondo effect in a quantum dot with SO(n) symmetry

A scenario for the formation of non-Fermi-liquid (NFL) Kondo effect (KE) with spin variable enumerating Kondo channels is suggested and worked out. In a doubly occupied symmetric triple quantum dot within parallel geometry, the NFL low-energy regime arises provided the device possesses both source-drain and left-right parity. Kondo screening follows a multistage renormalization group mechanism: reduction of the energy scale is accompanied by the change of the relevant symmetry group from SO(8) to SO(5). At low energy, three phases compete: (1) an underscreening spin-triplet (conventional) KE, (2) a spin-singlet potential scattering, and (3) a NFL phase where the roles of spin and orbital degrees of freedom are swapped.