Planckian superconductor*

The Planckian relaxation rate h/t_P=2πk_BT sets a characteristic time scale for both equilibration of quantum critical systems and maximal quantum chaos. We show that at the critical coupling between a superconducting dot and the complex Sachdev-Ye-Kitaev model, known to be maximally chaotic, the pairing gap Δ behaves as η h/t_P at low temperatures, where η is an order one constant. The lower critical temperature emerges with a further increase of the coupling strength so that the finite Δ domain is settled between the two critical temperatures