Minimal-size real-space $d$-wave pairing operator in ${\mathrm{CuO}}_2$ planes

Journal Article · 05 December 2019 · Physical Review B

DOI: https://doi.org/10.1103/PhysRevB.100.214502 · OSTI ID:1606757

Moreo, Adriana ^[1]; Dagotto, Elbio R. ^[1]

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1. Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division

Herein a novel minimal-size pairing operator ${\mathrm{\Delta }}_{D0}^{†}$ with $d$-wave symmetry in ${\mathrm{CuO}}_2$ 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 ${\mathrm{\Delta }}_{D0}^{†}$, an additional interorbital pairing operator ${\mathrm{\Delta }}_{Dpd}^{†}$ with $d$-wave symmetry is generated that pairs fermions located in a Cu and its four surrounding O atoms. The subsequent time evolution of ${\mathrm{\Delta }}_{Dpd}^{†}$ generates an intraorbital $d$-wave pairing operator ${\mathrm{\Delta }}_{Dpp}^{†}$ involving the four O atoms that surround a Cu atom, as well as the $d$-wave operator ${\mathrm{\Delta }}_D^{†}$ 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 ${\mathrm{CuO}}_2$ 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 $V$. We observed that the values of $V$ that lead to gap sizes similar to those in the cuprates are smaller for $d$-wave pairing operators that include Cu $d$ orbitals than those that include only $p$ orbitals. In all cases the gap that opens in the spectrum has standard $d$-wave symmetry. Finally, a simpler effective model is introduced to study the phenomenology of multiorbital $d$-wave superconductors, similar to how the negative- $U$ Hubbard model is used for properties of $s$-wave superconductors.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1606757
• Report Number(s): arXiv:1909.04084v1
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 21 Vol. 100; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English