Superconductivity in overdoped cuprates can be understood from a BCS perspective!

TL;DR

The paper argues that the low-energy physics of overdoped cuprates can be captured by a conventional Fermi-liquid description of the normal state and a BCS mean-field framework for the $d$-wave superconducting state, provided disorder from alloying is accounted for and a crossover from the strongly correlated underdoped regime is acknowledged. It supports this view with evidence of a Fermi-liquid ground state in overdoped cuprates (quantum oscillations, ARPES, and modest mass renormalization) and shows that many anomalies (e.g., $T$-linear resistivity, phase fluctuations) can be attributed to mesoscopic disorder, not intrinsic strong-coupling physics; the gap structure and magnitude in the overdoped regime align with a short-range, magnetically driven pairing interaction, inferred from inversion of ARPES data in Bi2212. The work provides falsifiable predictions for ideal, disorder-free overdoped cuprates and emphasizes that reducing intrinsic disorder should yield behavior increasingly consistent with $Fermi$-$liquid$ + $BCS$ theory, potentially extending the overdoped regime and clarifying the pairing mechanism. Overall, the authors offer a coherent, testable path to understanding high-temperature superconductivity from the overdoped side, with implications for identifying new superconductors by focusing on band structure motifs and short-range magnetic correlations.

Abstract

We summarize key experimental studies of the low energy properties of overdoped cuprate high temperature superconductors and conclude that a theoretical understanding of the ``essential physics'' is achievable in terms of a conventional Fermi-liquid treatment of the normal state, and a BCS mean-field treatment of the ($d$-wave) superconducting state. For this perspective to be consistent, it is necessary to posit that there is a crossover from a strongly correlated underdoped regime (where a different theoretical perspective is necessary) to the more weakly correlated overdoped regime. It is also necessary to argue that the various observed features of the overdoped materials that are inconsistent with this perspective can be attributed to the expected effects of the intrinsic disorder associated with most of the materials being solid state solutions (alloys). As a test of this idea, we make a series of falsifiable predictions concerning the expected behavior of an ``ideal'' (disorder free) overdoped cuprate.

Figures (2)

• Figure 2: Doping dependence of $T_\theta$ (defined in Eq. \ref{['Ttheta']} with $L=c$) in YBa$_2$Cu$_3$O$_{6+x}$ (teal points) and Ca doped YBa$_2$Cu$_3$O$_{6+x}$ (orange points). While $T_c$ (shown in purple for YBa$_2$Cu$_3$O$_{6+x}$) at fixed doping is only weakly affected by Ca substitution, the Ca-doped materials exhibit a clear suppression of the superfluid stiffness with hole doping compared to the Ca-free material. As indicated, different ways of measuring the penetration depth, $\lambda$, give somewhat different values. Moreover, since YBa$_2$Cu$_3$O$_{}$ is orthorhombic, the penetration depth is different in the $a$ and $b$ directions - i.e. perpendicular and parallel to the Cu-O "chains" respectively - so different ways of averaging over $\lambda_a$ and $\lambda_b$ produce different results. The dashed lines show the values of $T_\theta$ one would expect in a clean system of electrons with effective mass $m^*=5$ (a representative value extracted from quantum oscillations in overdoped Tl2201) under the assumption that the density of electrons is $n= 1+p$ (light blue) or $p$ (pink) per planar Cu. Low energy $\mu$SR data from baglo_detailed_2014 and kieflDirectMeasurementLondon2010; ESR data from pereg-barnea_absolute_2004; microwave data from brounSuperfluidDensityHighly2007; $\mu$SR data on Ca-YBCO from bernhardAnomalousPeakSuperconducting2001.
• Figure 3: Effective pairing interaction inferred from ARPES data for Bi2212 (from he_rapid_2018): The yellow points are the measured values of $\Delta_0$ and the blue dots are the expected BCS magnitude of $\Delta_0=2.14k_BT_c$ for the measured $T_c$. The red points are the values of the pairing interaction, $\tilde{V}$, obtained by inverting Eq. \ref{['linearizedgap']} using the measured values of $\Delta_0$ and of the normal-state dispersion. The grey and red lines are simple fits to the existing data that allow it to be smoothly extrapolated to higher values of doping, for which no data exists. The purple dots are the values of $\Delta_0$ that would result from values of $\tilde{V}$ on the red line. The inset is a blow-up of the range of doping near the critical point at which the extrapolated $\tilde{V}$ would change sign.