Holographic superconductivity of a critical Fermi surface
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914411833196544 |
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| author | Stangier, Veronika C. Schmalian, Jörg |
| author_facet | Stangier, Veronika C. Schmalian, Jörg |
| contents | 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 AdS$_2 \otimes \mathbb{R}_2$ 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 AdS$_2 \otimes \mathbb{R}_2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00474 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Holographic superconductivity of a critical Fermi surface Stangier, Veronika C. Schmalian, Jörg Strongly Correlated Electrons High Energy Physics - Theory 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 AdS$_2 \otimes \mathbb{R}_2$ 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 AdS$_2 \otimes \mathbb{R}_2$ 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. |
| title | Holographic superconductivity of a critical Fermi surface |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2209.00474 |