Inhomogeneous Kondo-lattice in geometrically frustrated Pr$_{2}$Ir$_{2}$O$_{7}$

TL;DR

This study uncovers nanoscale electronic phase separation in Pr$_{2}$Ir$_{2}$O$_{7}$, revealing a fractal pattern near a critical point, using advanced microscopy, machine learning, and theoretical modeling to explore complex quantum phenomena.

Contribution

It demonstrates the existence of electronic phase separation with fractal geometry in Pr$_{2}$Ir$_{2}$O$_{7}$, linking spatial electronic variations to quantum criticality and Kondo physics.

Findings

Nanoscale regions with Kondo resonance interweave with non-magnetic metallic phases.

Spatial patterns exhibit power-law fractal behavior over two and a half decades.

Electronic potential variation can tune the balance between Kondo entanglement and frustration.

Abstract

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.