Anomalous Hall effect and quantum criticality in geometrically frustrated heavy fermion metals

Studies on the heavy-fermion pyrochlore iridate (Pr$_2$Ir$_2$O$_7$) point to the role of time-reversal-symmetry breaking in geometrically frustrated Kondo lattices. With this motivation, here we study the effect of Kondo coupling and chiral spin liquids in a frustrated $J_1-J_2$ model on a square lattice. We treat the Kondo effect within a slave-fermion approach, and discuss our results in the context of a proposed global phase diagram for heavy fermion metals. We calculate the anomalous Hall response for the chiral states of both the Kondo destroyed and Kondo screened phases. Across the quantum critical point, a reconstruction of the Fermi surface leads to a sudden change of the Berry curvature distribution and, consequently, a jump of the anomalous Hall conductance. We discuss the implications of our results for the heavy-fermion pyrochlore iridate and propose an interface structure based on Kondo insulators to further explore such effects.