⇦Chinese Physics Letters, 2021, Vol. 38, No. 1, Article code 017501Express Letter BaCuS$_{2}$: A Superconductor with Moderate Electron-Electron Correlation Yuhao Gu (顾雨豪)1, Xianxin Wu (吴贤新)1, Kun Jiang (蒋坤)1, and Jiangping Hu (胡江平)1,2* Affiliations 1Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2CAS Center of Excellence in Topological Quantum Computation and Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China Received 16 September 2020; accepted 12 November 2020; published online 18 November 2020 Supported by the National Key R&D Program of China (Grant No. 2017YFA0303100), the National Natural Science Foundation of China (Grant No. 11888101), and the Strategic Priority Research Program of CAS (Grant No. XDB28000000).

*Corresponding author. Email: jphu@iphy.ac.cn Citation Text: Gu Y H, Wu X X, Jiang K and Hu J P 2021 Chin. Phys. Lett. 38 017501    Abstract We show that the layered-structure BaCuS$_{2}$ is a moderately correlated electron system in which the electronic structure of the CuS layer bears a resemblance to those in both cuprates and iron-based superconductors. Theoretical calculations reveal that the in-plane $d$–$p$ $\sigma^*$-bonding bands are isolated near the Fermi level. As the energy separation between the $d$ and $p$ orbitals are much smaller than those in cuprates and iron-based superconductors, BaCuS$_{2}$ is expected to be moderately correlated. We suggest that this material is an ideal system to study the competitive/collaborative nature between two distinct superconducting pairing mechanisms, namely the conventional BCS electron-phonon interaction and the electron-electron correlation, which may be helpful to establish the elusive mechanism of unconventional high-temperature superconductivity. DOI:10.1088/0256-307X/38/1/017501 © 2021 Chinese Physics Society Article Text From conventional BCS superconductors to unconventional high $T_{\rm c}$ superconductors, e.g., cuprates,[1] it has been widely suggested that the superconducting mechanism changes from phonon-mediated attraction to electron-electron correlation driving pairing. However, the existence of such a difference is still under intensive debate. For example, in the search of conventional BCS superconductors with relatively high transition temperatures, a possible guiding principle is to find systems with metallized $\sigma$-bonding electrons from light atoms so that the electron-phonon interaction can be maximized.[2–4] Such a textbook example is MgB$_2$,[2,5,6] in which the in-plane $\sigma$ bands are formed by the $p_x$ and $p_y$ orbitals of B atoms. The Mg$^{2+}$ ions further lower the B $\pi$ ($p_z$) bands, which causes a charge transfer from $\sigma$ to $\pi$ bands and drives the self-doping of the $\sigma$ band. The 2D nature of $\sigma$ bonds then leads to an extremely large deformation potential for the in-plane $E_{2g}$ phonon mode, which greatly enhances the electron-phonon coupling.[2,6] This principle was also argued to be valid even for cuprates, in which the $d$–$p$ $\sigma$-bonding band is responsible for superconductivity.[4,7] The argument has left a room to discuss the likelihood of the electron-phonon mechanism in cuprates.[8] However, the $d$–$p$ bonding displays fundamental differences from the $p$–$p$ bonding because of the multiplicity and strong localization of the $d$-orbitals. Such a simple extension is highly questionable. For example, the absence of clear isotope effect,[9] unconventional electronic properties in normal states and strongly antiferromagnetic fluctuations in cuprates suggest that the electron-electron correlation can be responsible for high $T_{\rm c}$ superconductivity.[10,11] Furthermore, the discovery of high $T_{\rm c}$ iron-based superconductors (SCs) finishes another large part of the superconducting jigsaw puzzle. Much evidence has suggested that the superconductivity of iron-based superconductors originates from the Fe–As/Te plane with strong electron-electron correlation and is very similar to cuprates.[12–14] On the other hand, electron-phonon coupling also plays a non-negligible role in iron-based superconductors.[15–17] Recently, focusing on the $d$-orbitals and emphasizing electron-electron interaction, we have suggested a new guiding principle for search of unconventional high $T_{\rm c}$ superconductors: those $d$-orbitals with $d$–$p$ $\sigma$-bondings must be isolated near Fermi energy. Under this principle, local cation complexes, the connection between the complexes, the electron filling factor at transition metal atoms and lattice symmetries must collaborate to fulfill the criteria.[18–22] This simple principle can explain why cuprates and iron-based superconductors are so special as high $T_{\rm c}$ superconductors. It is noticeable that the above-mentioned two principles are linked. While they emphasize different interactions, both of them are featured by $\sigma$-bonding. Thus, why are the two types of $\sigma$-bonding fundamentally different? In order to answer these two questions, we want to find a system with a moderate electron-electron correlation from the $d$–$p$ $\sigma$-bonding so that an explicit comparison between the electron-electron correlation and electron-phonon interaction can be examined. In this Letter, we propose that a new material BaCuS$_2$ can fulfill the above task. BaCuS$_{2}$ is a moderately correlated electron system in which the $d$–$p$ $\sigma^*$-bonding bands solely control the electronic physics near Fermi energy. Similar to cuprates, iron pnictides and MgB$_2$, BaCuS$_2$ also has a layered structure, where the electronic structure is dominated by the CuS$_2$ square layer. We demonstrate that the electron-electron correlation may drive superconductivity in BaCuS$_{2}$ with a $d$-wave pairing symmetry, very similar to the superconductivity in cuprates. However, if the superconductivity is caused by electron-phonon couplings, a conventional BCS s-wave state will be expected, similar to La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$. According to first-principles calculations, we find that the BaCuS$_2$ phase is thermodynamically stable and has lower formation energy under pressure compared with other known phases, suggesting that it can be synthesized in future experiments under external pressure.
cpl-38-1-017501-fig1.png
Fig. 1. (a) Crystal structure of BaCuS$_{2}$. Here S$_{\rm a}$ represents the apical S atoms while S$_{\rm h}$ represents the horizontal S atoms. (b)–(d) Crystal structures of other layered superconductors: (b) CaCuO$_{2}$, (c) FeSe, and (d) La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$. (e) The comparison of parameters in $dp$-models of BaCuS$_{2}$, CaCuO$_{2}$, FeSe and La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$. Here $|t_{dp}|$ is the amplitude of the major hopping parameter in each compound ($|t_{{\rm Cu},d_{x^2-y^2}-{\rm S}_{\rm h},p_{x/y}}|$ in BaCuS$_{2}$, $|t_{{{\rm Cu},d_{x^2-y^2}}-{{\rm O},p_{x/y}}}|$ in CaCuO$_{2}$, $|t_{{{\rm Fe},d_{xz/yz}}-{{\rm Se},p_{x/y}}}|$ in FeSe and $|t_{{{\rm Ni},d_{xz/yz}}-{{\rm B},p_{x/y}}}|$ in La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$) and $\varDelta_{dp}$ is the corresponding on-site energy difference.
BaCuS$_2$ Electronic Structure and Comparison with Other SC Materials. We start from the crystal structure and electronic structure. The layered ternary transition metal sulfide BaCuS$_{2}$ has a structure: the BaS layers alternate with Cu$_{2}$S$_{2}$ layers and the transitional metal atom is in square pyramidal coordination, as shown in Fig. 1(a). The upward-pointing square pyramidals connect the downward-pointing ones by sharing edges, forming the glide symmetric Cu$_{2}$S$_{2}$ plane. Similar to other layered SCs, the main electronic structure of BaCuS$_{2}$ stems from its Cu$_{2}$S$_{2}$ layer. To demonstrate it, we carried out density functional theory calculations for BaCuS$_{2}$. The electronic structure and density of states (DOS) of BaCuS$_{2}$ are plotted in Fig. 2. The crystal structure is fully relaxed and the structural parameters are summarized in Table 1. The bands around the Fermi level are formed by the $d$–$p$ valence manifold. Partially filled $d$–$p$ $\sigma^*$-bonding bands cross the Fermi level, where Cu $d_{x^2-y^2}$ orbitals strongly hybridize with in-plane S $p_{x/y}$ orbitals and Cu $d_{z^2}$ orbitals strongly couple with apical S $p_z$ orbitals. Owing to the planar nature of Cu $d_{x^2-y^2}$ orbitals and S $p_{x/y}$ orbitals, these bands have a weak dispersion along the $k_z$ direction. In contrast, the bands from Cu $d_{z^2}$ orbitals and apical S $p_z$ orbitals exhibit a large dispersion. We expect that the SC of BaCuS$_{2}$ is mainly contributed from the 2D cylindrical Fermi surface, which is similar to the other layered SCs.
cpl-38-1-017501-fig2.png
Fig. 2. The band structure and density of states for BaCuS$_{2}$ from density functional theory (DFT) calculation. The sizes of dots represent the weights of the projection. Here S$_{\rm a}$ represents the apical S atoms while S$_{\rm h}$ represents the horizontal S atoms.
It is interesting to compare the electronic structure of BaCuS$_{2}$ with those of high-$T_{\rm c}$ superconductors (CaCuO$_{2}$,[23] FeSe[24]) and known BCS superconductor (La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$[25]). These three materials are layered transition metal compounds, as shown in Figs. 1(b)–1(d). Their electronic structures are mainly attributed to the square layers. In CaCuO$_{2}$ and FeSe, the electron correlation plays an important role in the unconventional superconductivity.[19] From an electronic-structure perspective, this is consistent with the fact that the $d$-orbitals dominate around the Fermi surfaces in these materials, giving rise to strong correlations. However, in La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$, the extended $s$–$p$ bands of anions dominate Fermi surfaces and are featured by strong electron-phonon couplings via B's high frequency $A_{1g}$ phonons, while Ni's $d$-orbitals play a less pronounced role.[26,27] As shown in Fig. 2, in the $d$–$p$ $\sigma^*$-bonding bands of BaCuS$_{2}$ near Fermi energy, the weight of $p$-orbitals of the in-plane S atoms is much larger than those in cuprates and iron-based superconductors. In contrast to La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$, the weight of $d_{x^2-y^2}$ orbitals of Cu atoms is still sizable. To quantitatively confirm this point, we construct tight-binding models including the $d$-orbitals of transition-metal atoms and the $p$-orbitals of coordinated anions to analyze their electronic structures by calculating the maximally localized Wannier functions (MLWFs).[28] Our Wannierization results successfully reproduce the DFT-calculated band structures, as shown in our the Supplementary Information (Fig. S3 in the Supplementary Information). Then, we extract hopping parameters and on-site energies from our Wannierization results and display the representative parameters in the Supplementary Information (Table S1). In cuprate CaCuO$_{2}$ and iron-based superconductor FeSe, the electronic physics is dominated by $d$-orbitals near the Fermi level, whose on-site energies are much higher (about 2 eV) than those of coupled $p$-orbitals. Nevertheless, in BCS-type superconductor La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$, where the NiB layer is isostructural to the FeSe layer, the electronic physics is quite distinct: the on-site energy of B-$p_{x/y}$ orbital is even higher than that of Ni-$d_{xz/yz}$ orbital. This is consistent with previous studies:[26,27] multiple components cross the Fermi level, showing that La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$ is a good metal. The scenario of BaCuS$_{2}$ is different from the above examples: the on-site energies of $d$-orbitals are still higher than the $p$-orbitals, whereas the energy difference is only about 1 eV, much less than those in high-$T_{\rm c}$ superconductors. It is suggested that the antiferromagnetic (AFM) order may not be stabilized in BaCuS$_{2}$ due to the weak superexchange coupling.[29] Moreover, the difference in hopping parameters between partially filled $d$-orbitals and coupled $p$-orbital is not so significant, as shown in Fig. 1(b). The above analysis for BaCuS$_{2}$ is consistent with the absence of any magnetically ordered states in our calculation. Therefore, BaCuS$_{2}$ tends to be a material with a moderate electron-electron correlation.
Table 1. The optimized structural parameters for BaCuS$_{2}$ (space group $P4/nmm$). Here S$_{\rm a}$ represents the apical S atoms while S$_{\rm h}$ represents the horizontal S atoms.
System $a$ (Å) $c$ (Å) Cu–S$_{\rm h}$ (Å) Cu–S$_{\rm a}$ (Å) Cu–S$_{\rm h}$–Cu angle
BaCuS$_{2}$ 4.49 9.14 2.41 2.32 97.6$^\circ$
As mentioned above, the guiding principle for searching high transition temperature BCS superconductors are light atoms and metallized $\sigma$-bonding electrons.[2,3] In principle, in BaCuS$_{2}$, the $d$–$p$ $\sigma^*$-bonding bands cross the Fermi level, where those metallic $\sigma$-bonding electrons can support the BCS-type superconductivity. Thus, we calculate the electron-phonon coupling (EPC) properties of BaCuS$_{2}$.[28] The EPC strength $\lambda$ is about 0.59 in BaCuS$_{2}$, which is lower than that in La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$ ($\lambda \sim 0.86$, $T_{\rm c} \sim 13$ K[30]) but slightly higher than that in LaNiBN ($\lambda \sim 0.52$, $T_{\rm c} \sim 4.1$ K[31]). However, due to the heavy mass of Cu and S atoms, we find that the electron-phonon coupling in BaCuS$_{2}$ can only induce superconductivity of $T_{\rm c}$ less than 4 K.[28] The Effective Two-Band Model and RPA Results. To study the correlation effect, we first construct an effective minimal model by Wannierization based on the $d_{x^2-y^2}$-like and $d_{z^2}$-like MLWFs on Cu sites in BaCuS$_{2}$.[28,32,33] The $d$–$p$ $\sigma^*$-bonding bands are obviously more delocalized in BaCuS$_{2}$ than that in CaCuO$_{2}$ [More details can be found in Figs. S4(c)–S4(e) in the Supplementary Information]. As a consequence, the correlation strength in BaCuS$_{2}$ should be weaker. Then by fitting the Wannierization results,[28] we arrive at an effective tight-binding model in the basis of $d_{x^2-y^2}$ orbital and $d_{z^2}$ orbital.
cpl-38-1-017501-fig3.png
Fig. 3. (a) Lattice structure of Cu layer in the tight-binding model. In each unit cell, there are two Cu atoms sitting above and below the $xy$ plane. We label these two sublattices by A and B, respectively. The conventional crystal structure direction is defined for Cu$_{\rm A}$$\to$Cu$_{\rm A}$ direction, labeled as $x$–$y$. To simplify our model using glide symmetry, we rotate the global axis to Cu$_{\rm A}$$\to$Cu$_{\rm B}$ direction, labeled as $X$–$Y$. (b) The two-Cu tight-binding model for BaCuS$_2$ in Eq. (1) (black lines). The blue dashed lines are the folded energy bands with a folding vector $Q=(\pi,\pi)$. The coordinate is $X$–$Y$ here.
There are two Cu atoms in each unit cell, as shown in Fig. 3(a), which indicates that the minimal model for BaCuS$_{2}$ contains four bands. Similar to FeSe, the space group of BaCuS$_{2}$ is $P4/nmm$. There is a glide symmetry which consists of a translation Cu$_{\rm A}$$\to$Cu$_{\rm B}$ and a mirror reflection perpendicular to the S plane. Then, using the glide symmetry, one can unfold the band structure into the Brillouin zone of one-Cu unit cell and write down a two-band model for BaCuS$_{2}$. Note that the conventional crystal structure direction of BaCuS$_{2}$ is defined for the Cu$_{\rm A}$$\to$Cu$_{\rm A}$ direction, labeled as $x$–$y$. Similar to iron based superconductors,[34,35] we can define a new coordinate system with the $X$ and $Y$ axes aligned to the Cu$_{\rm A}$$\to$Cu$_{\rm B}$ direction, labeled as $X$–$Y$. The two-band model for the one-Cu unit cell in the basis $\psi_k=[d_{z^2}(k),d_{XY}(k)]$ (the spin index is omitted here) can be written as $$\begin{align} H=\sum_{k}\psi_k^† \hat{H}_k \psi_k ,~~ \tag {1} \end{align} $$ where the 2$\times$2 matrix $H_k$ and more details are provided in the Supplementary Information. It is worth noting that the basis can also be written as $\psi_k=[d_{z^2}(k),d_{x^2-y^2}(k)]$ in $x$–$y$ coordinates but we use $X$–$Y$ coordinates in this session. The band structure in the original unit cell can be obtained by folding the band structures of the Hamiltonian $H_k$, as plotted in Fig. 3(b), where the blue dashed lines are folded bands with a folding vector $Q=(\pi,\pi)$. The corresponding FSs are displayed in Fig. 4(d) and the large oval FSs around ($\pi$,0) or (0,$\pi$) are mainly attributed to $d_{XY}$ orbital while the smaller circular FS around the ($\pi$,$\pi$) point is mainly attributed to $d_{z^2}$ orbitals.
cpl-38-1-017501-fig4.png
Fig. 4. (a) Distribution of the largest eigenvalues for bare susceptibility matrices $\chi_0(\boldsymbol{k})$ at $n=2.0$. (b) Largest eigenvalues of RPA susceptibility with $U=0.9$ eV and $J/U=0.2$. (c) Pairing strength eigenvalues for the leading states as a function of interaction $U$ with $J/U=0.2$. (d) Gap function of the dominant $B_{2g}$ state ($d_{XY}$-wave pairing).
Using the above two-band model, we can apply the standard approach to investigate the intrinsic spin fluctuations by carrying out random phase approximation (RPA) calculation.[36–40] We adopt the general multi-orbital Coulomb interactions, including on-site Hubbard intra- and inter-orbital repulsion $U/U^{\prime}$, Hund's coupling $J$ and pair-hopping interactions $J^{\prime}$, $$\begin{align} H_{\rm i n t}={}& U \sum_{i \alpha} n_{i \alpha \uparrow} n_{i \alpha \downarrow}+U^{\prime} \sum_{i, \alpha < \beta} n_{i \alpha} n_{i \beta} \\ &+J \sum_{i, \alpha < \beta, \sigma \sigma^{\prime}} c_{i \alpha \sigma}^† c_{i \beta \sigma^{\prime}}^† c_{i \alpha \sigma^{\prime}} c_{i \beta \sigma} \\ &+J^{\prime} \sum_{i, \alpha \neq \beta} c_{i \alpha \uparrow}^† c_{i \alpha \downarrow}^† c_{i \beta \downarrow} c_{i \beta \uparrow},~~ \tag {2} \end{align} $$ where $n_{i \alpha}=n_{i \alpha \uparrow}+n_{i \alpha \downarrow}$. The distribution of the largest eigenvalues of bare susceptibility matrices is displayed in Fig. 4(a). There is a prominent peak at $q_1$, close to ($\frac{\pi}{2}$,$0$). In addition, the bare susceptibility shows a broad peak at $q_2$. The former is attributed to the inter-pocket nesting between $\alpha$ and $\beta$, and the latter is contributed by intra pocket nesting in $\alpha$ Fermi surface. From the RPA spin susceptibility along high-symmetry lines shown in Fig. 4(b), we find that these peaks get significantly enhanced when interactions are included. All peaks in the susceptibility are far away from the $\varGamma$ point, indicating intrinsic antiferromagnetic fluctuations in the system. To investigate the pairing symmetry, we calculate the pairing strengths as a function of Coulomb interaction $U$ with $J/U=0.2$. The dominant pairing has a $B_{2g}$ symmetry, whose gap function is shown in Fig. 4(d). Each pocket has a $d_{XY}$-wave gap but the intrapocket nesting in $\alpha$ pockets induces additional sign changes in the corresponding gap functions. Moreover, there is a sign change between the gap functions on $\alpha$ and $\beta$ pockets, which is determined by inter pocket nesting. The gap functions on these Fermi surfaces can be qualitatively described by a form factor $\sin k_X \sin k_Y (\cos k_X+\cos k_Y)$, which is classified as the $d_{XY}$ ($B_{2g}$) pairing symmetry. In this superconducting state, there are gapless nodes on high symmetry lines as well as nodes on the original BZ boundary. The $d_{XY}$ pairing symmetry is quite robust here. In fact, if we consider the system in a strong electron-electron correlation limit in which a short AFM interaction can be produced through the superexchange mechanism, we can easily argue that the pairing symmetry in this limit is still $d_{XY}$ based on the Hu–Ding principle,[41] which states that the pairing symmetry is selected by the momentum space form factor of AFM exchange couplings that produce the largest weight on Fermi surfaces. In this case, we would expect that the gap function is proportional to $\sin k_X \sin k_Y$, in which the nodal points at the BZ boundary in the above RPA calculations will not appear.
cpl-38-1-017501-fig5.png
Fig. 5. (a) Formation energies of BaCuS$_{2}$ and Ba$_{3}$Cu$_{2}$S$_{5}$ under different pressures. (b) The band structure of BaCuS$_{2}$ with an external pressure $P= 20$ GPa from the DFT calculation. The sizes of dots represent the weights of the projection.
In summary, we have proposed a new superconducting material BaCuS$_{2}$. By comparing the electronic structures with CaCuO$_{2}$, FeSe and La$_{3}$N$_{3}$Ni$_{2}$B$_{2}$, we find that BaCuS$_{2}$ should be a moderately correlated electron system with strong $p$–$d$ hybridization. The calculations based conventional BCS electron-phonon coupling suggests that it is a standard s-wave superconductor with $T_{\rm c} < 4$ K, while the electron-electron correlation results in an unconventional $B_{2g}$-wave superconductor and possibly much higher $T_{\rm c}$.
Table 2. The optimized volumes of BaCuS$_2$, Ba$_{3}$Cu$_{2}$S$_{5}$ and their decomposition phases under different pressures. All the data are normalized according to the formula. The volume is in units of Å$^3$.
0 GPa 5 GPa 10 GPa 15 GPa 20 GPa
BaCuS$_{2}$ 92.07 85.29 80.50 76.73 73.78
BaS+CuS 101.41 93.42 87.99 83.89 80.55
Ba$_{3}$Cu$_{2}$S$_{5}$ 253.46 234.47 220.87 210.59 202.20
3BaS+2CuS 270.09 247.89 232.96 221.74 212.65
The structure of the material is in a highly stable phase according to our theoretical calculations. In particular, we find that the structure has much lower formation energy than other known structures under external pressure. We calculate the formation energy of BaCuS$_{2}$ and its sister compound Ba$_{3}$Cu$_{2}$S$_{5}$[42] under different pressures, as shown in Fig. 5(a). The volume of BaCuS$_{2}$/Ba$_{3}$Cu$_{2}$S$_{5}$ is remarkably less than that of BaS+CuS/3BaS+2CuS, as listed in Table 2. The main electronic physics does not vary much under pressure as shown in Fig. 5(b), in which the band structure of BaCuS$_{2}$ under 20 GPa is plotted. Therefore, it is promising that BaCuS$_{2}$ can be synthesized in future experiments and studying its superconductivity can help us reveal the relationship between conventional and unconventional superconducting mechanisms. We thank Jianfeng Zhang and Yuechao Wang for the useful discussions. References Doping a Mott insulator: Physics of high-temperature superconductivitySuperconductivity of MgB 2 : Covalent Bonds Driven MetallicPrediction of phonon-mediated high-temperature superconductivity in Li 3 B 4 C 2 Finding high-temperature superconductors by metallizing the σ-bonding electronsSuperconductivity of Metallic Boron in MgB 2 Two-band superconductor magnesium diborideEffective Hamiltonian for the superconducting Cu oxidesNodeless pairing in superconducting copper-oxide monolayer films on Bi2Sr2CaCu2O8+Phenomenological model of nuclear relaxation in the normal state of YBa 2 Cu 3 O 7 The case for dx2 − y2 pairing in the cuprate superconductorsMagnetism and its microscopic origin in iron-based high-temperature superconductorsPairing Symmetry in a Two-Orbital Exchange Coupling Model of OxypnictidesStrong Correlations and Magnetic Frustration in the High T c Iron PnictidesA large iron isotope effect in SmFeAsO1 - xF x and Ba1 - xK x Fe2As2Coexistence of Replica Bands and Superconductivity in FeSe Monolayer FilmsUltrafast Quasiparticle Dynamics and Electron-Phonon Coupling in (Li 0.84 Fe 0.16 )OHFe 0.98 SePredicting Unconventional High-Temperature Superconductors in Trigonal Bipyramidal CoordinationsIdentifying the genes of unconventional high temperature superconductorsA possible family of Ni-based high temperature superconductorsPredicting diamond-like Co-based chalcogenides as unconventional high temperature superconductorsNi-based transition metal trichalcogenide monolayer: A strongly correlated quadruple-layer grapheneSuperconductivity at 110 K in the infinite-layer compound (Sr1-xCax)1-yCuO2Superconductivity in the PbO-type structure -FeSeSuperconductivity in lanthanum nickel boro-nitrideBand structure and superconducting properties of La3Ni2B2N3Electronic and structural properties of La 3 Ni 2 B 2 N 3 Electronic structures and phonon spectra in boronitride superconductors La M BN ( M = Ni , Pt)wannier90: A tool for obtaining maximally-localised Wannier functionsMaximally localized Wannier functions: Theory and applications S 4 Symmetric Microscopic Model for Iron-Based SuperconductorsTopological Phases in the Single-Layer FeSeNear-degeneracy of several pairing channels in multiorbital models for the Fe pnictidesSensitivity of the superconducting state and magnetic susceptibility to key aspects of electronic structure in ferropnictidesg-wave pairing in BiS 2 superconductorsTriplet p z -wave pairing in quasi-one-dimensional A 2 Cr 3 As 3 superconductors ( A = K , Rb , Cs ) Triplet superconductivity in the Dirac semimetal germanene on a substrateLocal antiferromagnetic exchange and collaborative Fermi surface as key ingredients of high temperature superconductors
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[42]Ba$_{3}$Cu$_{2}$S$_{5}$ shares similar electronic physics with BaCuS$_{2}$, and Cu is also in square pyramidal coordination. Please find more details in our Supplementary Information.