Planckian superconductor

The Planckian relaxation rate $\mathrm{\hslash }\mathrm{/}{t}_{\mathrm{P}}=2\pi k_{\mathrm{B}}T$ 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 $\mathrm{\Delta }$ behaves as $\eta ,, \hbar/t_$\mathrm{P}$$atlowtemperatures,where$\eta$ is an order one constant. The lower critical temperature emerges with a further increase of the coupling strength so that the finite $\mathrm{\Delta }$ domain is settled between the two critical temperatures.