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Chuck-Hou Yee Editting section 3.2 over 7 years ago

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Using the convex hull, we can assess the stability of the reactants and products reported in experiment. In Fig. 2, Fig.~\ref{fig:ehulls}, we plot the energies relative to the convex hull for all reported compounds. Negative values are stability energies against decomposition. We find that La2CuS2O2 and La2CuSO3 are highly unstable at nearly 500meV/atom above the hull. Additionally, LaCuSO is marginally unstable at 23meV/atom above the hull, but this is indistinguishable from zero given the error bars of the current method. In hindsight, we could have predicted that the proposed compounds would not have formed and instead have decomposed into: \begin{align*} \text{La}_2\text{CuS}_2\text{O}_2 &\rightarrow \text{La}_2\text{SO}_2 + \text{CuS} \\ 4 \text{La}_2\text{CuS}\text{O}_3 &\rightarrow 3 \text{La}_2\text{SO}_2 + 4\text{Cu} + \text{La}_2\text{SO}_6

\subsection{Hg-based Cuprates} With the hindsight of the experience of our first attempt in designing new cuprates, we revisited the problem from a slightly different viewpoint. The cuprates are a functional stack: the composition of each layer is chosen to play a specific role. The central copper oxide (CuO$_2$) plane supports superconductivity and roughly constrains the in-plane lattice constant. The remaining layers must tune the chemical potential of the CuO$_2$ layer without rumpling the plane or introducing disorder, and isolate each CuO$_2$ plane to create a 2D system. In the Hg-cuprates, the HgO$_\delta$ layer harbors dopant atoms which tune the chemical potential. The BaO layers immediately adjacent to the CuO$_2$ plane spatially separate the superconducting electrons from the detrimental effects of the disordered dopant layer. Additionally, the highly ionic nature of the BaO layer means they do not capture dopant electrons intended for the CuO$_2$ plane. The preference of Hg to be dumbbell coordinated bonds the entire structure together without introducing structural distortions. Finally, the highly ionic O-Hg-O dumbbells minimize $c$-axis hopping to maintain 2-dimensionality. Due to their spatial proximity, the adjacent BaO layers tune the hoppings and interaction strengths of the in-plane Hamiltonian. Designing compounds with novel adjacent layers provides a mechanism for controlling superconductivity by, e.g., reducing the charge-transfer energy. We quickly realized the most stringent constraint is structural stability, so we focused first on isolating stable candidates, then subsequently investigating their electronic properties. To maximize the likelihood that a proposed composition is stable, we note that the layers adjacent to the CuO$_2$ plane form a rock salt structure. Using materials databases, we selected all naturally occurring rock salt compounds AX, composed of an cation A and an anion X. The phase space is large and the rate limiting step is structural prediction, so we quickly pre-screen candidates by discarding compositions with (1) large lattice mismatches relative to the in-plane Cu-Cu distance, which we took to be 3.82~\AA, and (2) anions less electronegative than Cu, as these anions would capture dopants intended for the superconducting plane, producing additional Fermi surfaces. With the hindsight of Revisisted with a and b done very well.

Work by Zanaan, Sawatzsky and Allan showed that the relative alignment of the oxygen 2$p$ and copper 3$d$ orbital levels combined with the magnitude of the onsite repulsion $U$ controls the charge transfer energy. Dynamical mean-field calculations corroborated this picture by showing how the spectral charge transfer energy varies with the underline parameters of the hamiltonian. Additionally, density functional theory showed that the distance of the apical oxygen from the CuO$_2$ plane there is a charge transfer energy. Since we wanted to reduce the charge transfer energy to produce higher Tc's, we replaced the apical oxygen with sulfur, reasoning that its more extended 3$p$ orbitals would screen and reduce the strength of the in plane correlations. \emph{Structure prediction} -- We chose the $T$-type layered perovskite La$_2$CuO$_4$ as the starting point. Our intuition led us to propose the site substitution of the apical oxygen with sulfur. Due to the larger ionic radius of sulfur as compared to oxygen, we expect that the LaS charge reservoir layer to be crowded. To compensate, we explored the effect of substituting the large La ion with smaller trivalent ions, ions $R$, selected from the lanthanide-like elements. The compositions we considered were $R_2$CuO$_2$S$_2$ and $R_2$CuO$_3$S. We include the monosulfide in hopes that the configurational entropy of only replacing a quarter of the apical oxygens with sulfur would help stabilize the target phase. While we did not perform global structural prediction, we performed local checks for stability, which we acknowledged were by no means exhaustive. Using a $2\times2\times1$ unit cell, we performed full structural relaxation to check if the structure would be unstable towards distortion to the $T'$-type layered perovskite, knowing that substitution of the large La ion for the smaller Pr and Nd led to a rearrangement of the charge reservoir layer into the fluorite structure. We found that the $T$-type structure was indeed stable and there was no out-of-plane buckling, although the CuO$_6$ octahedra favored axial rotations ($a^0a^0c_p^-$ in Glazer notation). \emph{Global stability} -- We checked the thermodynamic stability of the proposed compounds against competing phases by selecting commonly known reactants and computing the formation enthalpies of the synthesis pathways. to check for pathways as shown in Table~\ref{tbl:pathways}. We computed the dynamic stability,Check some slices using reactions. More work shows total energies of formation $\Delta E = E_\text{products} - E_\text{reactants}$, and find that all differentials are positive, indicating the reactions target phases are unfavorable. However, it is known that slices give a different picture. BirdOutcome : do any many functional materials are metastable, protected from decay by large energetic barriers. The parent cuprate La$_2$CuO$_4$ is an example: as shown on the last line of Table~\ref{tbl:pathways}}, LCO is actually unstable by 28kJ/mol. We also examined the volume differentials $\Delta V = V_\text{products} - V_\text{reactants}$ with the knowledge that often high pressure synthesis allows otherwise unstable compounds to form. We indeed find that $\Delta V$ are overwhelming negative, meaning the application of high pressure may allow the formation of the target phases. \begin{table} \begin{tabular}{r|r|rl} \hline $\Delta E$ & $\Delta V$ & \multicolumn{2}{c}{Synthesis pathway} \\ \hline \hline 141 & -7.3 & La$_2$O$_2$S + CuS & $\rightarrow$ La$_2$CuO$_2$S$_2$\\ 223 & -3.4 & Y$_2$O$_2$S + CuS & $\rightarrow$ Y$_2$CuO$_2$S$_2$\\ 267 & -5.0 & Lu$_2$O$_2$S + CuS & $\rightarrow$ Lu$_2$CuO$_2$S$_2$\\ 356 & -3.0 & Sc$_2$O$_2$S + CuS & $\rightarrow$ Sc$_2$CuO$_2$S$_2$\\ 101 & -4.9 & La$_2$O$_2$S$_2$ + Cu & $\rightarrow$ La$_2$CuO$_2$S$_2$\\ \hline 148 & -3.3 & La$_2$O$_3$ + CuS & $\rightarrow$ La$_2$CuO$_3$S \\ 454 & -0.7 & Sc$_2$O$_3$ + CuS & $\rightarrow$ Sc$_2$CuO$_3$S \\ 97 & -4.9 & La$_2$O$_2$S + CuO & $\rightarrow$ La$_2$CuO$_3$S \\ 269 & 2.8 & Sc$_2$O$_2$S + CuO & $\rightarrow$ Sc$_2$CuO$_3$S \\ \hline 28 & -5.1 & La$_2$O$_3$ + CuO & $\rightarrow$ La$_2$CuO$_4$ \\ \hline \end{tabular} \caption{Synthesis pathways for various cuprate oxysulfides based on substitution of sulfur for both (top block) or only one (middle block) of the apical oxygens in $R_2$CuO$_4$. Energies in kJ/mol and volumes in kJ/mol/GPa. Since the energies of formation ($\Delta E = E_\text{products} - E_\text{reactants}$) are positive, none of these materials exist ? pathways appear favorable at ambient conditions. However, high-pressure synthesis will help stabilize these pathways, since the majority of volume differentials ($\Delta V = V_\text{products} - V_\text{reactants}$) are negative. We benchmark our method against the standard synthesis pathway for La$_2$CuO$_4$, shown on the last line. Surprisingly, $\Delta E$ is +28~kJ/mol, so either DFT systemmatically overestimates enthalpies (which means the actual enthalpies for our hypothetical compounds are \emph{smaller}, in our favor), or we must add a bi-directional uncertainty of $\pm 30$~kJ/mol to the computed enthalpies. Additionally, positional entropy of the apical $S$ in the half-substituted $R_2$CuO$_3$S compounds should also assist in synthesis.} \label{tbl:pathways} \end{table} \emph{Reexamination} -- In the intervening years, the maturation of materials databases allowed us to revisit the question of global stability. Various databases have computed and tabulated the convex hulls of binary, ternary and some quaternary systems, and provided tools for researchers to apply their framework to novel chemical systems. In the following, we describe our new understanding of the global stability of La$_2$CuO$_2$S$_2$ and La$_2$CuO$_3$S$_S$ against all known competing phases in the La-Cu-S-O chemical system. Since the Cu site contains significant correlations, we must address the effect of $U$ on the energies provided by density functional theory.

In earlier work, we had proposed several chemical reaction pathways to synthesize La2CuS2O2 and La2CuSO3 [PRB 89, 094517 (2014)] which were subsequently tested by experiment [ref. Hua He, unpublished] and concluded that the two compounds were unstable (at least at high temperatures). Additionally, LaCuSO seemed to be quite stable at high temperatures, as it was the preferred quaternary composition in almost all the experimentally analyzed reactions. With modern materials databases, we are able to reanalyze the entire La-Cu-S-O system to construct the convex hull (plotted in Fig. 1) and globally investigate stability. Notice that La2CuS2O2 and La2CuSO3 are not among the stable compounds on the hull.