Minimal-size Real Space d-wave Pairing Operator in CuO2 Planes

Abstract

A novel minimal-size pairing operator ${\Delta }_{D0}^{†}$ with $d$-wave symmetry in CuO${}_2$ planes is introduced. This pairing operator creates on-site Cooper pairs at the four oxygens that surround a copper atom. Via the time evolution of ${\Delta }_{D0}^{†}$, an additional inter-orbital pairing operator ${\Delta }_{Dpd}^{†}$ with $d$-wave symmetry is generated that pairs fermions located in a Cu and its four surrounding O's. The subsequent time evolution of ${\Delta }_{Dpd}^{†}$ generates an intra-orbital $d$-wave pairing operator ${\Delta }_{Dpp}^{†}$ involving the four O atoms that surround a Cu, as well as the $d$-wave operator ${\Delta }_D^{†}$ traditionally used in single-band models for cuprates. Because we recover the larger size operators extensively used in the three-orbital Hubbard model, we suggest that long-range order using the canonical extended operators occurs together with long-range order in the new minimal operators. However, our minimal $d$-wave operators could be more practical to study $d$-wave superconductivity because in the finite-size relatively small systems accessible to computational techniques it is easier to observe long-range order using local operators. Moreover, an effective model with the usual tight-binding hopping of the CuO${}_2$ planes supplemented by an attractive potential $V$ in the $d$-wave channel is introduced. Using mean-field techniques we show that a paired ground state is stabilized for any finite value of $V$.

10 pages, 6 figures

References in corpus (6)

• Magnetism and its microscopic origin in iron-based high-temperature superconductors
• Pseudogap, Superconducting Gap, and Fermi Arc in High-Tc Cuprates Revealed by Angle-Resolved Photoemission Spectroscopy
• Phase diagram and single-particle spectrum of CuO${}_2$ layers within a variational cluster approach to the 3-band Hubbard model
• Pairing symmetry and properties of iron-based high temperature superconductors
• Phenomenological Three-Orbital Spin-Fermion Model for Cuprates
• Four-legged starfish-shaped Cooper pairs with ultrashort antinodal length scales in cuprate superconductors

Cited by in corpus (5)

• Orbital structure of the effective pairing interaction in the high-temperature superconducting cuprates
• Pairing correlations in the cuprates: a numerical study of the three-band Hubbard model
• Unified description of cuprate superconductors using four-band $d$-$p$ model
• Superconducting properties of the hole-doped three-band \emph{d-p} model studied with minimal-size real-space \emph{d}-wave pairing operators
• Monte Carlo study of cuprate superconductors in a four-band $d$-$p$ model: Role of orbital degrees of freedom