  Recent progress in the fabrication of quantum dots using silicon opens the
prospect of observing the Kondo effect associated with the valley degree of
freedom. We compute the dot density of states using an Anderson model with
infinite Coulomb interaction $U$, whose structure mimics the nonlinear
conductance through a dot. The density of states is obtained as a function of
temperature and applied magnetic field in the Kondo regime using an
equation-of-motion approach. We show that there is a very complex peak
structure near the Fermi energy, with several signatures that distinguish this
spin-valley Kondo effect from the usual spin Kondo effect seen in GaAs dots. We
also show that the valley index is generally not conserved when electrons
tunnel into a silicon dot, though the extent of this non-conservation is
expected to be sample-dependent. We identify features of the conductance that
should enable experimenters to understand the interplay of Zeeman splitting and
valley splitting, as well as the dependence of tunneling on the valley degree
of freedom.
