Interacting heavy fermions in a disordered optical lattice

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 a compressibility anomaly at low-density.