Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals

Abstract

Superconductivity is abundant near quantum-critical points, where fluctuations suppress the formation of Fermi liquid quasiparticles and the BCS theory no longer applies. Two very distinct approaches have been developed to address this issue: quantum-critical Eliashberg theory and holographic superconductivity. The former includes a strongly retarded pairing interaction of ill-defined fermions, the latter is rooted in the duality of quantum field theory and gravity theory. We demonstrate that both are different perspectives of the same theory. We derive holographic superconductivity in form of a gravity theory with emergent space-time from a quantum many-body Hamiltonian -the Yukawa SYK model -where the Eliashberg formalism is exact. Exploiting the power of holography, we then determine the dynamic pairing susceptibility of the model. Our holographic map comes with the potential to use quantum gravity corrections to go beyond the Eliashberg regime.

Quantum Chaos, Superconductivity, and Information Scrambling in Disordered Magic-Angle Twisted Bilayer Graphene

“…In the present letter, we study the behavior of OT OCs in Coulomb disordered magic-angle twisted TBG to pin- point the region where superconductivity is stabilized [31][32][33][34][35] and understand the nature of the phase outside the superconducting region. Our analysis suggests the emergence of SYK physics in TBG and establishes a connection with superconductivity.…”