Beyond Homes scaling: disorder, the Planckian bound and a new universality
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2025
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| author | Broun, D. M. Mishra, Vivek Dodge, J. S. Hirschfeld, P. J. |
| author_facet | Broun, D. M. Mishra, Vivek Dodge, J. S. Hirschfeld, P. J. |
| contents | Beginning with high-$T_c$ cuprate materials, it has been observed that many superconductors exhibit so-called "Homes scaling", in which the zero-temperature superfluid density, $ρ_{s0}$, is proportional to the product of the normal-state dc conductivity and the superconducting transition temperature, $σ_\mathrm{dc} T_c$. For conventional, s-wave superconductors, such scaling has been shown to be a natural consequence of elastic-scattering disorder, not only in the extreme dirty limit but across a broad range of scattering parameters. Here we show that when an analogous calculation is carried out for elastic scattering in d-wave superconductors, a stark contrast emerges, with $ρ_{s0} \propto \left(σ_\mathrm{dc} T_c \right)^2$ in the dirty limit, in apparent violation of Homes scaling. Within a simple approximate Migdal--Eliashberg treatment of inelastic scattering, we show how Homes scaling is recovered. The normal-state behavior of near optimally doped cuprates is dominated by inelastic scattering, but significant deviations from Homes scaling occur for disorder-dominated cuprate systems, such as underdoped YBCO and overdoped LSCO, and in very clean materials with little inelastic scattering, such as Sr$_2$RuO$_4$. We present a revised analysis where both axes of the original Homes scaling plot are normalized by the Drude plasma weight, $ω_{p,D}^2$, and show that new universal scaling emerges, in which the superfluid fractions of dirty s-wave and dirty d-wave superconductors coalesce to a single point at which normal-state scattering is occurring at the Planckian bound. The combined result is a new tool for classifying superconductors in terms of order parameter symmetry, as well as scattering strength and character. Although our model starts from a Fermi-liquid assumption it describes underdoped cuprates surprisingly well. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_13351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond Homes scaling: disorder, the Planckian bound and a new universality Broun, D. M. Mishra, Vivek Dodge, J. S. Hirschfeld, P. J. Superconductivity Strongly Correlated Electrons Beginning with high-$T_c$ cuprate materials, it has been observed that many superconductors exhibit so-called "Homes scaling", in which the zero-temperature superfluid density, $ρ_{s0}$, is proportional to the product of the normal-state dc conductivity and the superconducting transition temperature, $σ_\mathrm{dc} T_c$. For conventional, s-wave superconductors, such scaling has been shown to be a natural consequence of elastic-scattering disorder, not only in the extreme dirty limit but across a broad range of scattering parameters. Here we show that when an analogous calculation is carried out for elastic scattering in d-wave superconductors, a stark contrast emerges, with $ρ_{s0} \propto \left(σ_\mathrm{dc} T_c \right)^2$ in the dirty limit, in apparent violation of Homes scaling. Within a simple approximate Migdal--Eliashberg treatment of inelastic scattering, we show how Homes scaling is recovered. The normal-state behavior of near optimally doped cuprates is dominated by inelastic scattering, but significant deviations from Homes scaling occur for disorder-dominated cuprate systems, such as underdoped YBCO and overdoped LSCO, and in very clean materials with little inelastic scattering, such as Sr$_2$RuO$_4$. We present a revised analysis where both axes of the original Homes scaling plot are normalized by the Drude plasma weight, $ω_{p,D}^2$, and show that new universal scaling emerges, in which the superfluid fractions of dirty s-wave and dirty d-wave superconductors coalesce to a single point at which normal-state scattering is occurring at the Planckian bound. The combined result is a new tool for classifying superconductors in terms of order parameter symmetry, as well as scattering strength and character. Although our model starts from a Fermi-liquid assumption it describes underdoped cuprates surprisingly well. |
| title | Beyond Homes scaling: disorder, the Planckian bound and a new universality |
| topic | Superconductivity Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2502.13351 |