Planckian superconductor

Abstract

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

9 pages, 5 figures, 1 table; Published version

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Cited by in corpus (7)

• Quantum Phase Transition in the Yukawa-SYK Model
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Phase diagram of the spin-1/2 Yukawa-SYK model: Non-Fermi liquid, insulator, and superconductor
• SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
• Quantum tunneling dynamics in a complex-valued Sachdev-Ye-Kitaev model quench-coupled to a cool bath
• Solvable model for a charge-$4e$ superconductor
• Josephson current through the SYK model