  We have theoretically studied the effect of disorder on ultracold
alkaline-earth atoms governed by the Kondo lattice model in an optical lattice
via simplified double-well model and hybridization mean-field theory.
Disorder-induced narrowing and even complete closure of hybridization gap have
been predicted and the compressibility of the system has also been investigated
for metallic and Kondo insulator phases in the presence of the disordered
potential. To make connection to the experimental situation, we have
numerically solved the disordered Kondo lattice model with an external harmonic
trap and shown both the melting of Kondo insulator plateau and an
compressibility anomaly at low-density.
