Dynamical Symmetries in Kondo Tunneling through Complex Quantum Dots

Kondo tunneling reveals hidden $\mathrm{S}\mathrm{O}(n)$ dynamical symmetries of evenly occupied quantum dots. As is exemplified for an experimentally realizable triple quantum dot in parallel geometry, the possible values $n=3,4,5,7$ can be easily tuned by gate voltages. Following construction of the corresponding $o_n$ algebras, scaling equations are derived and Kondo temperatures are calculated. The symmetry group for a magnetic field induced anisotropic Kondo tunneling is $\mathrm{S}\mathrm{U}(2)$ or $\mathrm{S}\mathrm{O}(4)$.

Figure 1

Triple quantum dot in parallel geometry.

Figure 2

Scaling trajectories resulting in an $\mathrm{S}\mathrm{O}(5)$ symmetry in the SW regime.

Figure 3

Phase diagram of TQD.

Figure 4

Kondo temperature.