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We calculate the tunnelling resistance at the quantum critical point of amesoscopic SQUIDs array in the presence of magnetic flux. We find theanalytical relation between the magnetic flux induced dissipation strength andthe Luttinger liquid parameter of the system. While the experimental findingfor the system is around 40-50 mK, we find the behavior of the system even atlower temperatures through the analysis of renormalization group. Apart fromthe length scale dependent superconductor-insulator transition, we also predictthe evidence of length scale independent metallic state. This study alsoemphasizes the importance of Co-tunelling effect.

Non-universal tunneling resistance at the quantum critical point of mesoscopic SQUIDs array