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Planckian superconductor

The Planckian relaxation rate $\hbar/t_\mathrm{P} = 2πk_\mathrm{B} T$ sets a characteristic time scale for both equilibration of quantum critical systems and maximal quantum chaos. In this note, 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 $η\,\, \hbar/t_\mathrm{P}$ 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.