  Magnetic fluctuations induced by geometric frustration of local Ir-spins
disturb the formation of long range magnetic order in the family of pyrochlore
iridates, R$_{2}$Ir$_{2}$O$_{7}$ (R = lanthanide)$^{1}$. As a consequence,
Pr$_{2}$Ir$_{2}$O$_{7}$ lies at a tuning-free antiferromagnetic-to-paramagnetic
quantum critical point and exhibits a diverse array of complex phenomena
including Kondo effect, biquadratic band structure, metallic spin-liquid (MSL),
and anomalous Hall effect$^{2-5}$. Using spectroscopic imaging with the
scanning tunneling microscope, complemented with machine learning K-means
clustering analysis, density functional theory, and theoretical modeling, we
probe the local electronic states in single crystal of Pr$_{2}$Ir$_{2}$O$_{7}$
and discover an electronic phase separation. Nanoscale regions with a
well-defined Kondo resonance are interweaved with a non-magnetic metallic phase
with Kondo-destruction. Remarkably, the spatial nanoscale patterns display a
correlation-driven fractal geometry with power-law behavior extended over two
and a half decades, consistent with being in proximity to a critical point. Our
discovery reveals a new nanoscale tuning route, viz. using a spatial variation
of the electronic potential as a means of adjusting the balance between Kondo
entanglement and geometric frustration.
