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

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