Predicting Unconventional High-Temperature Superconductors in Trigonal Bipyramidal Coordinations

Cuprates and iron-based superconductors are two classes of unconventional high-$T_c$ superconductors based on $3d$ transition elements. Recently, two principles, the correspondence principle and the magnetic selective pairing rule, have emerged to unify their high-$T_c$ superconducting mechanisms. These principles strongly regulate electronic structures that can host high-$T_c$ superconductivity. Guided by these principles, here, we propose high-$T_c$ superconducting candidates that are formed by cation-anion trigonal bipyramidal complexes with a $d^7$ filling configuration on the cation ions. Their superconducting states are expected to be dominated by the $d_{xy}\pm i{d}_{x^2-y^2}$ pairing symmetry.

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Two well-known high-critical-temperature ($T_c$) superconductors—cuprates and iron-based superconductors—were both discovered accidentally in the lab. Their superconductivity mechanism remains one of the most challenging problems in physics. Here, we highlight the fact that both of these materials host special electronic environments that maximize the antiferromagnetic superexchange coupling strength, which results in high-$T_c$ superconductivity. These environments are uniquely created under the $d^9$ filling configuration of ${\mathrm{Cu}}^{2+}$ in the octahedral complex of cuprates and the $d^6$ filling configuration of ${\mathrm{Fe}}^{2+}$ in the tetrahedral complex of iron-based superconductors. By revealing this uniqueness, we explain why high-$T_c$ superconductivity is such a rare phenomenon, and we propose new directions to search for possible new high-$T_c$ superconductor candidates.

We find a new candidate with such an electronic environment in a two-dimensional hexagonal lattice structure that is constructed by corner-shared trigonal-bipyramidal complexes with a $d^7$ filling configuration at the cation sites. This lattice structure has been observed in Mn- and Fe-based compounds. However, realizing a $d^7$ filling configuration requires ${\text{Co}}^{2+}$ and ${\text{Ni}}^{3+}$ $3d$ transition-metal cation ions. We predict that the new materials, if synthesized, will have superconducting states with a $d\pm id$ pairing symmetry, and the maximum $T_c$ is expected to exceed those of iron-based superconductors.

We believe that our work will pave the way for discovering new classes of high-$T_c$ superconductors and help to settle the debate about unconventional high-$T_c$ superconducting mechanisms.

Figure 1

Structural units, crystal field splitting in one unit complex and energy splitting in a two-dimensional lattice structure created by the corresponding complexes. (a) Octahedral complex (cuprates, ${\text{CuO}}_6$, the Cu-O plane). (b) Tetrahedral complex (iron-based superconductors, ${\text{FeAs}}_4/{\mathrm{Se}}_4$, the $\mathrm{FeAs}/\mathrm{Se}$ layer). (c) Trigonal bipyramidal complex ($\mathrm{Ni}/{\mathrm{CoO}}_3$, the $\mathrm{Ni}/\mathrm{Co}\text{−}\mathrm{O}$ triangular layer). The $d$ orbitals with the blue color are active for superconductivity.

Figure 2

The two-dimensional hexagonal lattice formed by the corner-shared trigonal bipyramidal complexes. The gray cation atoms further form a triangle lattice. The superconducting pairing configuration in a $d\pm id$ pairing state is sketched.

Figure 3

(a) The band structures of ${\text{YNiO}}_3$ obtained from the first-principles calculations and (b) the extracted three bands for the tight-binding model. The orbital characters of the bands in (a) are indicated by the different colors specified in the right top corner of the figure.

Figure 4

The overlap between Fermi surfaces of the $\alpha$ band and gap functions. (a) The extended $s$ wave $\cos k_y+2\cos (\sqrt{3}/2)k_x\cos \frac{1}{2}{k}_y$. (b) $d\pm id$ wave $\cos k_y-\cos (\sqrt{3}/2)k_x\cos \frac{1}{2}{k}_y\pm i\sqrt{3}\sin (\sqrt{3}/2)k_x\sin \frac{1}{2}{k}_y$. The dashed black lines represent the Fermi surfaces. The solid black lines represent the first Brillouin zone.

Figure 5

The crystal structure of $AMO{X}_2$ ($A=\mathrm{Y}$, K, Ba, Yb; $M=\text{Ni}$, Co, Pd; and $X=\text{Cl}$, O).

Figure 6

The in-out AFM state and the $\mathrm{GGA}+U$ band structure of this state for ${\mathrm{YNiO}}_3$.

Figure 7

The crystal structure and band structure of ${\mathrm{YbNi}}_2{\mathrm{O}}_4$.

Figure 8

The band structures of (a) ${\mathrm{KNiOCl}}_2$, (b) ${\mathrm{KNiOF}}_2$, (c) ${\mathrm{BaCoOF}}_2$, (d) ${\mathrm{KCoF}}_3$, (e) ${\mathrm{KPdOCl}}_2$, and (f) ${\mathrm{KPdOF}}_2$.