Planckian superconductor

Abstract

The Planckian relaxation rate $\hslash /t_{\mathrm{P}}=2\ddot{I}€k_{\mathrm{B}}T$ 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 $\hat{I}”$ behaves as $\hat{I}\cdot \hslash /t_{\mathrm{P}}$ at low temperatures, where $\hat{I}\cdot$ is an order one constant. The lower critical temperature emerges with a further increase of the coupling strength so that the finite $\hat{I}”$ domain is settled between the two critical temperatures.

9 pages, 5 figures, 1 table; Published version