Recently, Prof. ZOU Liangjian’s group from the Hefei Institutes of Physical Science (HFIPS), Chinese Academy of Sciences (CAS), investigated the magnetic phase diagram of the high-TC superconducting compound Ba₂CuO_4-δ and its superconducting pairing symmetry based on the spin-fluctuation mechanism.

These results were published in Physical Review B.

It is well-known that two electrons in vacuum repulse each other. However, in superconductors, two electrons near the Fermi surface form a Cooper pair by exchanging bosonic quasi-particles. These Cooper pairs with the same phase condensate the superfluid which has zero resistivity. The pairing symmetry of Cooper pairs is an important feature for uncovering the effective pairing interaction in a superconductor.

A newly-discovered cuprate superconductor Ba₂CuO_4-δ featured on high-Tc of 73 K, about 2 to 3 times higher than isostructural conventional cuprate La₂CuO_4-δ. Also, it displayed compressed CuO₆ octahedra, which were inverted to the CuO₆ octahedra or CuO₅ pyramids in the parent phases of conventional cuprates. This led to more than one orbital contributing to superconducting properties in Ba₂CuO_4-δ. The phase diagrams of the previous cuprates superconductors showed antiferromagnetism in close proximity, or in some cases coexisting, with superconductivity. Hence, it is proposed that the effective pairing interaction is mediated by spin fluctuation in the cuprates superconductors. To understand which mechanism contributes the effective pairing interaction in Ba₂CuO_4-δ, it is crucial to investigate the magnetic phase diagram of it.

In this work, by using the rotationally invariant slave boson (RISB) method, researchers investigated the magnetic phase diagram of the high-TC superconducting compound Ba₂CuO_4-δ. They also studied the superconducting pairing symmetry in its based on the spin-fluctuation mechanism within random phase approximation (RPA).

The results obtained by the RISB method showed that in the intermediate correlation regime (U ~ 2 eV), the system behaved as single-band paramagnetic metal when n > 2.4, and had only one antiferromagnetic insulating parent phase.

In the strongly correlated regime (U > 4 eV) the system displayed two different antiferromagnetic insulating parent phases at n = 2 and 3, corresponding to two-band and single-band nature, respectively. Comparing the experimental spin coupling value of about 150 meV with the total-energy difference between the Néel antiferromagnetic and paramagnetic phases, researchers estimated that U ≈ 2~3 eV in Ba₂CuO_3.2.

Researchers further studied the superconducting pairing symmetry in its based on the spin-fluctuation mechanism and found that the pairing strengths of s-wave and d-wave are nearly degenerate.

This suggests that Cooper pairs in Ba₂CuO_3.2 are s+d –wave symmetric.

It’s the first time that scientists theoretically illustrated the magnetic phase diagram of Ba₂CuO_4-δ, which suggested that Cooper pairs in Ba₂CuO_3.2 were s+d –wave symmetric provided that the effective pairing interaction is mediated by spin fluctuations.

This work is supported by the National Natural Science Foundation of China. The calculations were performed in the Center for Computational Science of HFIPS, and partly using a Tianhe-2JK computing time award at the Beijing Computational Science Research Center (CSRC)

Figure 1. An effective interaction mediated by exchanging an antiferromagnetic paramagnon. (Image by BAI Xiaocheng)

Figure 2. The magnetic phase diagrams of Ba₂CuO_4-δ at U = 2 eV (a) and U = 4 eV (b). (Image by BAI Xiaocheng)