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The frustrated pyrochlore iridate Pr$_2$Ir$_2$O$_7$ was proposed as ametallic quantum spin liquid located at a zero-field quantum critical point.Here we present the ultralow-temperature thermal conductivity measurements onthe Pr$_2$Ir$_2$O$_7$ single crystals to detect possible exotic excitations. Inzero field, the thermal conductivity shows a dramatic suppression above acharacteristic temperature $T_s \approx$ 0.12 K. With increasing field, $T_s$increases and the thermal conductivity tends to saturate above $H$ = 5 T. TheWiedemann-Franz law is verified at high fields and inferred at zero field. Itsuggests the normal behavior of electrons at the quantum critical point, andthe absence of mobile fermionic magnetic excitations. The strong suppression ofthermal conductivity is attributed to the scattering of phonons by the spinsystem, likely the fluctuating spins. These results shed new light on themicroscopic description on this novel compound.

Ultralow-temperature thermal conductivity of Pr2Ir2O7: a metallic spin-liquid candidate with quantum criticality