[Paper Review] Universal Correlation between Critical Temperature of Superconductivity and band structure features

Yang Liu, Ning Chen+1 more|arXiv (Cornell University)|Nov 29, 2018

Iron-based superconductors researchMaterials Science3 citations

TL;DR

This paper proposes a universal correlation between the critical temperature ($T_c$) of superconductors and the energy level difference ($\Delta E_{\text{orb}}$) of secondary-outer orbitals, suggesting that orbital hybridization fluctuations—mediated by van der Waals interactions—may act as a pairing glue. The correlation, derived from holistic band structure analysis across diverse superconductors, reveals that $T_c$ maxima are governed by these deep orbital energy levels rather than Fermi-level band features.

ABSTRACT

The critical temperature (${T}_ ext{c}$) of superconductors varies a lot. The factors governing the ${T}_ ext{c}$ may hold key clues to understand the nature of the superconductivity. Thereby, ${T}_ ext{c}$-involved correlations, such as Matthias laws, Uemura law, and cuprates doping phase diagrams, have been of great concern. However, the electronic interaction being responsible for the carriers pairing in high-${T}_ ext{c}$ superconductors is still not clear, which calls for more comprehensive analyses of the experimental data in history. In this work, we propose a novel perspective for searching material gene parameters and ${T}_ ext{c}$-involved correlations. By exploring holistic band structure features of diverse superconductors, we found a universal correlation between the ${T}_ ext{c}$ maxima and the electron energy levels for all kinds of superconducting materials. It suggests that the ${T}_ ext{c}$ maxima are determined by the energy level of secondary-outer orbitals, rather than the band structure nearby the Fermi level. The energy level of secondary-outer orbitals is a parameter corresponding to the ratio of atomic orbital hybridization, implying that the fluctuation of the orbital hybridization is another candidate of pairing glue.

Motivation & Objective

• To identify universal physical parameters governing the maximum critical temperature ($T_c$) across diverse superconducting materials.
• To resolve the ambiguity in existing $T_c$-correlations by focusing on intrinsic band structure features rather than doping or Fermi surface parameters.
• To explore whether orbital hybridization fluctuations and van der Waals interactions could serve as a universal pairing glue in high-temperature superconductors.
• To establish a predictive framework for $T_c$ limits based on elemental and structural properties, independent of strong correlation effects or measurement methods.

Proposed method

• Systematic analysis of band structure features across a broad range of superconductors, including cuprates, iron-based, and conventional superconductors.
• Definition of $\Delta E_{\text{orb}}$ as the energy level difference between secondary-outer orbitals, derived from atomic orbital hybridization and electronic structure calculations.
• Use of density functional theory (DFT) approximations to estimate $\Delta E_{\text{orb}}$ without requiring high-accuracy treatments of strong correlations.
• Statistical correlation of $T_c$ maxima with $\Delta E_{\text{orb}}$ across diverse materials, treating $\Delta E_{\text{orb}}$ as an element-dependent, compositionally intrinsic parameter.
• Exclusion of doping, Fermi surface, and symmetry effects by focusing on intrinsic orbital energy levels.
• Use of a universal upper ceiling line in $T_c$ vs. $\Delta E_{\text{orb}}$ plots to represent the theoretical $T_c$ limit, independent of material-specific tuning parameters.

Experimental results

Research questions

• RQ1 What intrinsic band structure parameter universally correlates with the maximum critical temperature ($T_c$) across diverse superconducting materials?
• RQ2 Can the energy level of secondary-outer orbitals serve as a predictive parameter for $T_c$ limits, independent of Fermi-level band structure or doping?
• RQ3 Is the fluctuation of orbital hybridization—quantified by $\Delta E_{\text{orb}}$—a viable candidate for the pairing glue in high-temperature superconductors?
• RQ4 To what extent does the van der Waals interaction, as reflected in $\Delta E_{\text{orb}}$, influence the $T_c$ maximum in different superconducting families?
• RQ5 Can a universal $T_c$-correlation be established that remains robust despite variations in measurement methods, calculation approximations, and material types?

Key findings

• A universal correlation is established between the maximum $T_c$ and the energy level difference ($\Delta E_{\text{orb}}$) of secondary-outer orbitals across all superconducting materials.
• $T_c$ maxima are found to be governed not by band structure near the Fermi level, but by deep orbital energy levels, indicating a new physical origin for high-$T_c$ superconductivity.
• The parameter $\Delta E_{\text{orb}}$ is intrinsic to the chemical composition, ionic valence, and atomic coordination, making it a robust, element-dependent predictor of $T_c$ limits.
• The correlation is robust across diverse superconductors, including cuprates, iron-based, and conventional superconductors, despite differences in pairing symmetry and electronic correlations.
• The observed $T_c$-$\Delta E_{\text{orb}}$ relationship suggests that fluctuations in orbital hybridization may act as a universal pairing glue, with van der Waals interactions playing a key role.
• The upper envelope of the $T_c$-$\Delta E_{\text{orb}}$ plot serves as a predictive ceiling for $T_c$ in new materials, even when $T_c$ is not yet experimentally measured.