Spin-valley Kondo effect in multielectron Si quantum dots

Abstract

We study the spin-valley Kondo effect of a silicon quantum dot occupied by $%\n\\mathcal{N}$ electrons, with $\\mathcal{N}$ up to four. We show that the Kondo\nresonance appears in the $\\mathcal{N}=1,2,3$ Coulomb blockade regimes, but not\nin the $\\mathcal{N}=4$ one, in contrast to the spin-1/2 Kondo effect, which\nonly occurs at $\\mathcal{N}=$ odd. Assuming large orbital level spacings, the\nenergy states of the dot can be simply characterized by fourfold spin-valley\ndegrees of freedom. The density of states (DOS) is obtained as a function of\ntemperature and applied magnetic field using a finite-U equation-of-motion\napproach. The structure in the DOS can be detected in transport experiments.\nThe Kondo resonance is split by the Zeeman splitting and valley splitting for\ndouble- and triple-electron Si dots, in a similar fashion to single-electron\nones. The peak structure and splitting patterns are much richer for the\nspin-valley Kondo effect than for the pure spin Kondo effect.\n