2022/09/01 by Stangier, Veronika C., Schmalian, Jörg, Jörg Schmalian · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Cosmology and Gravitation Theories
paper · pdf · doi:10.48550/arxiv.2209.00474
We derive a holographic formulation of triplet superconductivity in a two-dimensional metal at a ferromagnetic quantum critical point. 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. We demonstrate that the resulting 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. Our results provide a microscopic derivation of holographic superconductivity in a compressible quantum critical metal and clarify the geometric structure underlying quantum-critical pairing.