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Holographic superconductivity of a critical Fermi surface

Veronika C. Stangier1 and Jörg Schmalian1,2

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Phys. Rev. B 114, 094510 – Published 14 August, 2026

DOI: https://doi.org/10.1103/wkfp-fsd2

Abstract

We construct an emergent geometric description of triplet pairing fluctuations in a two-dimensional metal at a ferromagnetic quantum critical point. The analysis also applies to the behavior of the half-filled lowest Landau level, as well as to other two-dimensional systems featuring emergent gauge fields. Starting from a large-N Yukawa-Sachdev-Ye-Kitaev model of compressible fermions coupled to quantum-critical Ising ferromagnetic fluctuations, we reformulate the pairing problem in terms of bilocal collective fields and analyze Gaussian fluctuations around the quantum-critical normal state. After projecting onto the dominant low-energy triplet pairing sector, the resulting Gaussian pairing action can be mapped onto a scalar field theory in an emergent curved spacetime with AdS2⊗R2 geometry. The additional holographic dimension is shown to encode the internal dynamics of Cooper pairs and is related nonlocally to the frequency dependence of the anomalous Gor'kov function via a Radon transform. Within this framework, the onset of superconductivity corresponds to a Breitenlohner-Freedman instability of the scalar field, which is shown to be equivalent to the pairing instability obtained from the linearized Eliashberg equations. The factorized AdS2⊗R2 geometry reflects the local-in-space but critical-in-time character of fermionic excitations near a metallic quantum critical point and corresponds to what one expects in the vicinity of a Reissner-Nordström black hole. Accordingly, our construction establishes a holographic map for the pairing sector of a compressible quantum critical metal and reveals the geometric structure underlying quantum-critical pairing.

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Phys. Rev. B 114, 094510– Published 14 August, 2026
  • Received 3 September 2022
  • Revised 11 June 2026
  • Accepted 6 July 2026
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