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We study the spin-valley Kondo effect of a silicon quantum dot occupied by $% mathcal{N}$ electrons, with $mathcal{N}$ up to four. We show that the Kondo resonance appears in the $mathcal{N}=1,2,3$ Coulomb blockade regimes, but not in the $mathcal{N}=4$ one, in contrast to the spin-1/2 Kondo effect, which only occurs at $mathcal{N}=$ 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.
Numerical analysis of the simplest odd-numbered system of coupled quantum dots reveals an interplay between magnetic ordering, charge fluctuations and the tendency of itinerant electrons in the leads to screen magnetic moments. The transition from lo
A dilute concentration of magnetic impurities can dramatically affect the transport properties of an otherwise pure metal. This phenomenon, known as the Kondo effect, originates from the interactions of individual magnetic impurities with the conduct
The presence of valley states is a significant obstacle to realizing quantum information technologies in Silicon quantum dots, as leakage into alternate valley states can introduce errors into the computation. We use a perturbative analytical approac
The Kondo effect is a key many-body phenomenon in condensed matter physics. It concerns the interaction between a localised spin and free electrons. Discovered in metals containing small amounts of magnetic impurities, it is now a fundamental mechani
Collective motions of electrons in solids are often conveniently described as the movements of quasiparticles. Here we show that these quasiparticles can be hierarchical. Examples are valley electrons, which move in hyperorbits within a honeycomb lat