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This content will become publicly available on October 1, 2026

Title: Beyond Homes Scaling: Disorder, the Planckian Bound, and a New Universality
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 s 0 is proportional to the product of the normal-state dc conductivity and the superconducting transition temperature σ 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 s 0 ( σ dc T c ) 2 in the dirty limit, in apparent violation of Homes scaling. Within a simple approximate Migdal-Eliashberg treatment of inelastic scattering, we show how the observed 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 YBa 2 Cu 3 O 6.333 and overdoped La 2 x Sr x CuO 4 , 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 a 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.  more » « less
Award ID(s):
2231821
PAR ID:
10644677
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
APS Physical Review Journals
Date Published:
Journal Name:
Physical Review X
Volume:
15
Issue:
4
ISSN:
2160-3308
Page Range / eLocation ID:
041005
Subject(s) / Keyword(s):
Homes scaling, superfluid density, overdoped cuprates, disordered superconductivity
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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