Spin-valley Kondo effect in multielectron Si quantum dots

We study the spin-valley Kondo effect of a silicon quantum dot occupied by N electrons, with N up to 4. We show that the Kondo resonance appears in the N=1,2,3 Coulomb blockade regimes, but not in the N=4 one, in contrast to the spin-1∕2 Kondo effect, which only occurs at N=odd. Assuming large orbital level spacings, the energy states of the dot can be simply characterized by fourfold spin-valley degrees of freedom. The density of states (DOS) is obtained as a function of temperature and applied magnetic field using a finite-U equation-of-motion approach. The structure in the DOS can be detected in transport experiments. The Kondo resonance is split by the Zeeman splitting and valley splitting for double- and triple-electron Si dots, in a similar fashion to single-electron ones. The peak structure and splitting patterns are much richer for the spin-valley Kondo effect than for the pure spin Kondo effect.