Many-body electronic structure in the pyrochlore superconductor CsBi₂ and spin-liquid candidate Pr₂Ir₂O₇

The pyrochlore lattice materials can exhibit geometrical frustration, while the related many-body electronic states remain elusive. In this work, we performed scanning tunneling microscopy measurements on the pyrochlore superconductor CsBi₂ and spin liquid Pr₂Ir₂O₇ at 0.3 K. For the first time, we obtained atomically resolved images of their (111) surfaces, revealing a hexagonal lattice or a kagome lattice. Tunneling spectroscopy in CsBi₂ reveals a nearly fully opened superconductivity gap. The ratio of 2Δ/k_BT_C = 4.7 suggests relatively strong coupling superconductivity, as compared with that in kagome superconductors AV₃Sb₅ (A = K, Rb, Cs). In contrast to the previous study categorizing CsBi₂ as a type-I superconductor, the appliedmagnetic field induces a hexagonal vortex lattice in which each vortex core exhibits an intriguing threefold symmetry state. In Pr₂Ir₂O₇, we observed a spatially homogeneous Kondo-lattice resonance, which is compared with that in the kagome Kondo-lattice material CsCr₆Sb₆. We further discover that the Kondo resonance exhibits a spatial modulation with threefold symmetry, and the applied magnetic field induces a Zeeman splitting of the Kondo resonance with intriguing atomic site dependence. We discuss the relations of these many-body electronic phenomena with the pyrochlore lattice geometry and its charge or spin frustration. Our systematic observations offer atomic-scale insights into the many-body electronic structures of the geometrically frustrated pyrochlore superconductors and spin liquids.