1：Experimental Design and Method Selection:

The study integrates monolayer graphene Josephson junctions into microwave frequency superconducting circuits to create graphene based transmons. Dispersive microwave spectroscopy is used to resolve graphene’s characteristic band dispersion and observe coherent electronic interference effects.

2：Sample Selection and Data Sources:

Two graphene JJ transmon devices with slightly different fabrication techniques are used. Device A uses a Ti/Au gate stack deposited directly on the hBN, before the junction is shaped via dry etching. Device B is shaped before a Ti/Au gate stack with a SiNx interlayer is deposited.

3：List of Experimental Equipment and Materials:

The devices are fabricated using 20 nm NbTiN sputtered onto intrinsic Si wafers, with resonators, feedline, and transmon reactive ion etched in an SF6/O2 atmosphere. Monolayer graphene is encapsulated between two hBN flakes and deposited between pre-fabricated capacitors using a PMMA based van der Waals pickup method.

4：Experimental Procedures and Operational Workflow:

Measurements are performed in a dilution refrigerator with a base temperature of 15 mK. The samples are enclosed in a light tight copper box and thermally anchored to the mixing chamber. An external magnetic field is applied using a 3-axis vector magnet.

5：Data Analysis Methods:

The magnitude of the shift χ = g2/Δ depends on the transmon-resonator coupling g, and the difference Δ = fr ? ft between fr and the ground state to first excited state transition frequency ft, allowing inference of EJ from χ.