# Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model

**Authors:** Ilya Esterlis, Jörg Schmalian  
**arXiv:** [1906.04747](https://arxiv.org/abs/1906.04747)  
**Date:** 2019-06-11  
**Summary page:** https://www.summarizepaper.com/en/paper/1906.04747v1/

## Key points

- Authors Ilya Esterlis and Jörg Schmalian present a model of interacting electrons and phonons leading to superconductivity at low temperatures
- Emergence of two Non-Fermi liquid fixed points with distinct universal exponents in the normal state
- Prevention of low-temperature quantum criticality by superconductivity at weak coupling
- Identification of pairing of highly incoherent fermions deep within the Non-Fermi liquid regime at strong coupling
- Protection of pairing between incoherent time-reversal partners attributed to a mechanism akin to Anderson's theorem for disordered superconductors

## Summary

, , , , 


Authors Ilya Esterlis and Jörg Schmalian present a model of interacting electrons and phonons that serves as a natural extension of the Sachdev-Ye-Kitaev model, leading to superconductivity at low temperatures. In their study, they observe the emergence of two Non-Fermi liquid fixed points with distinct universal exponents in the normal state. At weak coupling, the onset of low-temperature quantum criticality is prevented by superconductivity, a behavior reminiscent of heavy-electron and iron-based materials. Furthermore, at strong coupling, the authors identify the pairing of highly incoherent fermions deep within the Non-Fermi liquid regime. This behavior bears similarity to the characteristics observed in underdoped cuprate superconductors. The protection of pairing between incoherent time-reversal partners is attributed to a mechanism akin to Anderson's theorem for disordered superconductors. The resulting superconducting ground state is characterized by coherent quasiparticle excitations and higher-order bound states, indicating a departure from an ideal gas of Cooper pairs towards a strongly coupled pair fluid. The authors note that normal-state incoherency primarily acts to suppress the weight of the superconducting coherence peak and reduce condensation energy. Based on their findings, strong superconducting fluctuations are expected, particularly at strong coupling regimes. This comprehensive study sheds light on the intricate interplay between electron-phonon interactions and superconductivity, offering valuable insights into complex quantum systems.