Coupling of Klein-Andreev resonant states in Bi₂Sr₂CaCu₂O₈+_x-graphene-Bi₂Sr₂CaCu₂O₈+_x devices

Quantum devices require coherent coupling over macroscopic distances. Recently, resonances due to Klein tunneling and Andreev reflection states (KARS) have been observed in a naturally occurring p-n junction at the interface between Bi₂Sr₂CaCu₂O₈+_x (BSCCO), a high-T_c superconductor (HTS), and graphene. The resonances appear as conductance oscillations with gating. Here, we show coupling between the KARS in BSCCO-graphene-BSCCO devices of varying separation (L). The coupling is evidenced by a power-law decay of resonance period as L increases from tens of nanometers to microns. These results demonstrate the long-distance coupling of KARS cavities in graphene-HTS junctions. The length dependence seen in experiments is supported by single-particle spectral functions which show KARS are coupled by transport modes in graphene. The strong coupling between KARS in BSCCO-graphene-BSCCO devices showcases the possibility of HTS-graphene junctions for quantum circuits and unconventional Josephson junctions.