1：Experimental Design and Method Selection:

The experiment utilized resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge to probe electronic excitations in Ba3CeIr2O9 single crystals. The design was based on the theoretical prediction of double-slit-type interference in RIXS for diatomic molecules, adapted to crystalline solids with quasi-molecular electronic structures.

2：Sample Selection and Data Sources:

Single crystals of Ba3CeIr2O9 and Ba3Ti

3：7Ir3O9 were grown using the melt-solution technique with spontaneous nucleation. Samples were characterized by x-ray diffraction, energy-dispersive x-ray analysis, and magnetization measurements. List of Experimental Equipment and Materials:

Equipment included a high-resolution RIXS spectrometer at the ID20 beamline at ESRF, using a Si(844) backscattering monochromator and R = 2 m Si(844) spherical diced crystal analyzers for energy resolution of 27 meV, and a Si(311) channel-cut monochromator for lower resolution (

4：36 eV). A continuous-flow He cryostat was used for cooling samples. Materials involved BaCO3, CeO2, IrO2, TiO2, and BaCl2·2H2O for crystal growth. Experimental Procedures and Operational Workflow:

RIXS measurements were performed on polished (0 0 1) surfaces with the c axis in the horizontal scattering plane. Incident photons were p polarized. Spectra were measured by scanning energy at constant momentum transfer q or scanning q at constant energy, depending on the data set. Measurements were conducted at temperatures down to 10 K.

5：Data Analysis Methods:

Data analysis involved integrating RIXS intensities over specific energy loss ranges and fitting interference patterns using sinusoidal functions. Theoretical modeling included exact diagonalization of a Hamiltonian for two t2g holes on Ir sites, considering spin-orbit coupling, crystal field, hopping, and Coulomb interactions, with RIXS matrix elements calculated in the dipole approximation.