[Paper Review] Oxygen hole content, charge-transfer gap, covalency, and cuprate superconductivity

N. Kowalski, Sidhartha Dash+2 more|arXiv (Cornell University)|Apr 14, 2021

Physics of Superconductivity and MagnetismPhysics and Astronomy89 references61 citations

TL;DR

This paper uses cellular dynamical mean-field theory (CDMFT) to solve the three-band Hubbard model and demonstrates that higher oxygen hole content and a larger charge-transfer gap—both observed in high-Tc cuprates—emerge naturally from the model's covalency and electronic structure. The key finding is that cuprates with stronger Cu-O covalency exhibit enhanced superconducting transition temperatures due to optimal hole delocalization on oxygen and a stabilized charge-transfer gap.

ABSTRACT

Experiments have shown that the families of cuprate superconductors that have the largest transition temperature at optimal doping also have the largest oxygen hole content at that doping. They have also shown that a large charge-transfer gap, a quantity accessible in the normal state, is detrimental to superconductivity. We solve the three-band Hubbard model with cellular dynamical mean-field theory and show that both of these observations follow from the model. Cuprates play a special role amongst doped charge-transfer insulators of transition metal oxides because copper has the largest covalent bonding with oxygen.

Motivation & Objective

• To explain the experimental correlation between high oxygen hole content and elevated Tc in optimally doped cuprates.
• To investigate how the charge-transfer gap influences superconducting transition temperature in doped cuprates.
• To clarify the role of Cu-O covalency in determining electronic structure and superconducting properties.
• To reconcile experimental observations of oxygen hole content and charge-transfer gap with a microscopic many-body theory.

Proposed method

• Solves the three-band Emery-VSA Hubbard model using cellular dynamical mean-field theory (CDMFT) on a 2×2 Cu-cluster with exact diagonalization.
• Uses a bath of non-interacting electrons to self-consistently hybridize with the cluster, capturing local correlations crucial for d-wave superconductivity.
• Treats the Cu 3d and O 2p orbitals on equal footing with site energies εd and εp, and includes Cu-O hopping (tpd), O-O hopping (tpp), and on-site Coulomb repulsion (U) on Cu only.
• Performs calculations at zero temperature and finite temperature using continuous-time quantum Monte Carlo for the cluster embedded in an infinite bath.
• Distinguishes between ionic (large εp) and covalent (small εp) parameter regimes to study the effect of hybridization on electronic structure.
• Computes spectral functions, density of states, and hole content on oxygen and copper to analyze the charge-transfer gap and Zhang-Rice singlet band.

Experimental results

Research questions

• RQ1 Why do cuprates with the highest Tc at optimal doping also exhibit the largest oxygen hole content?
• RQ2 How does the charge-transfer gap influence the superconducting transition temperature in cuprates?
• RQ3 What is the role of Cu-O covalency in determining the electronic structure and superconducting properties of cuprates?
• RQ4 Why does the oxygen hole content correlate with Tc, and how is this linked to the charge-transfer gap?

Key findings

• The model reproduces the experimental correlation between high oxygen hole content and elevated Tc, showing that increased covalency enhances hole delocalization on oxygen.
• A large charge-transfer gap is found to be detrimental to superconductivity, consistent with experimental STM and NMR data.
• In the covalent regime (small εp), the lower Hubbard band is suppressed, and the Zhang-Rice singlet band becomes the dominant feature near the Fermi level.
• The oxygen hole content (2np) increases with covalency, explaining the observed trend in Tc across different cuprate families.
• The charge-transfer gap is stabilized by strong Cu-O hybridization, and its size is inversely related to Tc, indicating a trade-off between gap size and superconducting pairing strength.
• The model shows that cuprates are unique among doped charge-transfer insulators due to the strong covalency of Cu-O bonding, which enables optimal hole distribution and high Tc.