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[Wataru Hayami](https://orcid.org/0000-0003-0497-8690), Xavier Rocquefelte, [Jean-François Halet](https://orcid.org/0000-0002-2315-4200)

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in Inorganic Chemistry, copyright © 2024 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acs.inorgchem.4c02221.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Possible Superconductivity for Layered Metal Boride Carbide Compounds MB<sub>2</sub>C<sub>2</sub> (M = Alkali, Alkaline-Earth, or Rare-Earth Metals)](https://mdr.nims.go.jp/datasets/4d15872d-dada-40fd-98e0-0a01eb565edd)

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1  Possible Superconductivity for Layered Metal Boride Carbide Compounds MB2C2 (M = Alkali, Alkaline-Earth or Rare-Earth Metals) Wataru Hayami,1* Xavier Rocquefelte,2 and Jean-François Halet2,3* 1Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan 2Univ Rennes, CNRS, Ecole Nationale Supérieure de Chimie de Rennes (ENSCR), Institut des Sciences Chimiques de Rennes (ISCR), UMR 6226, F-35000 Rennes, France  3CNRS–Saint-Gobain–NIMS, IRL 3629, Laboratory for Innovative Key Materials and Structures (LINK), National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan  Inorg. Chem. 2024, 63, 20975−20983 https://doi.org/10.1021/acs.inorgchem.4c02221     * Corresponding authors. E-mail: hayami.wataru@nims.go.jp (W.H.), Jean-Francois.Halet@univ-rennes.fr (J.-F. H.) 2  ABSTRACT The possible emergence of superconductivity in layered metal boride carbide compounds MB2C2 (M = Sc, Y, Be, Ca) was investigated using density functional theory calculations upon the topology of a boron–carbon network and the nature of the metal. ScB2C2 and YB2C2 show metallic and superconductive properties with low critical temperatures (Tcs). The semi-conducting BeB2C2 compound may show superconductivity upon carrier doping with a high Tc of 47.8 K by hole doping – comparable to the structurally related MgB2 superconductor – but with a low Tc by electron doping. In contrast, the semi-conducting CaB2C2 compound is predicted to be a superconductor by hole and electron doping but with low Tcs. These differences arise from the spatial distribution of electrons at the Fermi level. For compounds with low Tcs, electrons at the Fermi level are localized primarily on B and C  states perpendicular to the BC layers, experiencing minimal influence from atomic oscillations and resulting in weak electron–phonon interactions. Conversely, for a high Tc, electrons are found in σ-bonding states, leading to strong electron–phonon interactions. Electrons at the Fermi level in boron–carbon σ-bonding states seem to be a prerequisite to expect high Tc superconductivity in this kind of compound.  1. INTRODUCTION With the recent advent of high-pressure superconducting metal hydrides,1–3 exploring new superconductors with a high critical temperature (Tc) continues to be one of the main topics in the fields of materials science and condensed matter physics. It is generally accepted that, in the case of conventional Bardeen−Cooper−Schrieffer phonon-mediated superconductors, Tc strongly depends upon a large density of states (DOS) at the Fermi energy, strong electron−phonon coupling, and high-frequency phonons.4 This has been shown for compounds consisting of nonmagnetic metals and light elements, such as alkali, alkaline-earth, and nonmagnetic and magnetic transition-metal borides and carbides, as well as quaternary rare-earth-metal–transition-metal boride carbides, for instance.5–17 Among these compounds, the well-known magnesium diboride, MgB2, which adopts an AlB2-type structure with boron honeycomb layers alternating with Mg metallic sheets, is the highest-temperature conventional superconductor known at atmospheric pressure with a Tc of 39 K.5 This (relatively) high Tc has, over the years, favored numerous studies aiming to optimize MgB2 superconducting characteristics (chemical doping) and/or to discover novel related boron-containing compounds.18 More recently, superconductivity was also observed in the new ternary layered compound Sc20BC27 at Tc = 7.7 K.8 Using Eliashberg 3  theory,19 the experimentally characterized three-dimensional clathrate SrB3C320 was predicted to be a high-temperature conventional superconductor with Tc up to ∼40 K at ambient pressure,21 and recent experiments indicate superconductivity above 20 K under pressure.9 Higher Tcs were recently predicted for related hypothetical binary-guest C−B clathrates.22,23 Superconductivity was also experimentally demonstrated for some layered MB2C2 (M = rare-earth metal) compounds, such as YB2C2 or LuB2C2 with Tc = 3.6 and 2.4 K, respectively.24,25 Higher Tcs have been predicted for some hypothetical MB2C2 compounds containing alkali and alkaline-earth metals.7,26,27 Using Eliashberg theory and the Allen–Dynes formula,28,29 one of us has speculated that Tcs higher than that reported for MgB2 could also be observed for some structurally related layered alkali-metal M0.5BC2 (M = Li, Na, and K) compounds.30 Comparable Tcs have been proposed for MgB2-like LixBC (x < 1.0),6 Li4B5C3, and Li2B3C.31 An analysis of the electronic structure of M0.5BC2 reveals that the DOS at the Fermi energy is strongly B–C σ-bonding in character. It was demonstrated that the σ character is indeed essential for reaching high Tc values because the B–C σ-bonding states couple strongly with the bending-like phonon modes of the BC2 layers. With these results in mind, though they have not been proved yet experimentally, we thought that it would be worth extending the study carried out on M0.5BC2 to some existing and hypothetical rare-earth metal or alkaline-earth metal MB2C2-layered compounds to explore their possible superconductivity using first-principles electron–phonon calculations. Structures of rare-earth-metal and alkaline-earth-metal MB2C2 (M = Sc, Y, Be, Ca) layered compounds, which are part of ternary solid-state rare-earth metal boride carbides,32–34 consist of the stacking of alternatively two-dimensional (2D) B/C layers and metal sheets (Figure 1). Depending on the metal, different B/C topologies are experimentally encountered. For instance, fused 4- and 8-membered rings (482 network) are observed in YB2C235–38 and CaB2C2,39 fused 5- and 7-membered rings (572 network) appear in ScB2C2,40,41 and fused 6-membered rings (63 network) are found in BeB2C2,42 the latter being somewhat related to MgB2C2.43 High or moderate Tc superconductivity has been achieved or predicted for compounds with 63 honeycomb networks. Therefore, it is of great interest to investigate whether high-Tc superconductivity can also emerge in layered compounds with networks other than 63. As mentioned above, high-Tc superconductivity is essentially related to the B–C σ-bonding of sp2 hybridized orbitals. In the structures of the 482 and 572 networks, B–C bonding angles somewhat deviate from the ideal 120° angle of sp2 bonding. In this situation, deviation from true sp2 hybridization may significantly affect the energy levels and strength of the σ-bonding, and consequently Tc. For this reason, we theoretically investigated existing or hypothetical MB2C2-layered structures to examine the occurrence of superconductivity and the dependence of Tc with respect to their structural, vibrational, and electronic properties. 4   2. CALCULATION METHODS Calculations of the electronic structures were conducted using the Quantum ESPRESSO (QE) code44,45 based on density functional theory (DFT) with plane waves and pseudopotentials. The ultrasoft pseudopotentials46 of boron, carbon, and metal atoms were used from the library of QE.47 The generalized gradient approximation functional of Perdew, Burke, and Ernzerhof was employed.48 An energy cutoff of 50 Ry for plane waves and 350 Ry for electron density was sufficient to provide convergence of the total energy. The total energies were calculated upon optimization of the lattice parameters and the atomic positions of the experimentally confirmed structures taking into account the boron/carbon distribution (B vs C coloring problem) (see Figure 1),33,37,39,41 using a Monkhorst–Pack k-point sampling,49 with an (8  4  8) mesh for ScB2C2 and (8  8  8) meshes for BeB2C2, YB2C2, and CaB2C2. For the substituted phases of BeB2C2 and CaB2C2, the structures were optimized starting from the same initial structures as the nonsubstituted phases with M being replaced, using the same meshes as those used for the nondoped phases. Their optimized structures are provided in Figure S1 and Table S1 in the Supporting Information. The convergence threshold for the forces on atoms was 10-4 a.u. Phonon dispersion curves and Eliashberg spectral functions (2F) were calculated by using the PHonon code available in the QE package. For the calculation of electron–phonon coupling coefficients, fine meshes of (24 × 24 × 24) to (48 × 48 × 48) were used for the Fermi surface calculations. The k-grid and q-grid meshes for ScB2C2 were (8  4  8) and (4  2  4), respectively. For BeB2C2, YB2C2, and CaB2C2, both meshes were (4  4  4). The summation at the Fermi energy was performed using the interpolation method.50 Using the Fermi surface data, the optimal broadening parameters were determined to maximize the integration of the DOS at the Fermi level, ensuring the most accurate summation of electron–phonon interaction calculations. Tc values were estimated using the Allen–Dynes formula,28,29 with a Coulomb repulsion parameter * of 0.1. For a convergence test concerning the k- and q-grid meshes in electron-phonon interaction calculations, we compared (8  8  8) and (4  4  4) k-grid meshes for YB2C2 and observed an error in Tc of 0.1 K. The (4  4  4) and (2  2  2) q-grid meshes for YB2C2 produced a difference in Tc of 0.01 K.  3. RESULTS AND DISCUSSION 3.1. Electronic Structures. The DOS at the Fermi level, phonon dispersion curves, and Eliashberg spectral functions are necessary to elucidate whether superconductivity can be achieved. The electronic DOS was first calculated and analyzed for each of the unsubstituted rare-earth-5  metal and alkaline-earth metal ScB2C2, YB2C2, BeB2C2, and CaB2C2 compounds (Figure 2). It has been proposed previously that the electronic properties of a boron–carbon network – and therefore the electrical properties of the MxByCz compounds – are related to the average valence electron concentration (VEC) per main group atom.51 Assuming a Zintl–Klemm ionic bonding scheme between the metal and the nonmetal atoms in a first approximation, VEC is given by VEC = (nx + 3y + 4z)/(y + z), where n is the number of valence electrons of the metal. This was checked with theoretical studies, which have shown that MB2C2 compounds having a VEC of 4 should display semiconducting properties,33,42 whereas those with more (or less) than 4 should be metallic in character. This is confirmed again here (Figure 2), where MB₂C₂ compounds are metallic with the trivalent Sc and Y metals (VEC = 4.25) and semiconducting with the divalent Be and Ca metals (VEC = 4.0) with narrow band gaps of approximately 0.3 eV (insets in Figure 2c,d).  3.2. Superconductivity. The calculated DOS (Figure 2) suggests that ScB2C2 and YB2C2 could potentially exhibit superconductivity, while BeB2C2 and CaB2C2 may not unless carrier doping is applied. It is generally admitted that the necessary condition for a metallic compound to become a superconductor is the simultaneous occurrence of flat and steep bands reflected in high peaks of DOS at the Fermi level with a fairly large coupling of the flat band states with the lattice phonons.52,53 The electronic band structures of the compounds listed in Table 1 are provided in the Supporting Information (Figure S2). Overall, these band structures appear to feature both flat and steep bands around the Fermi level. Tcs for these materials were calculated and are listed in Table 1, which were then analyzed for each case of metal M.  3.2.1. Case of ScB2C2 and YB2C2. ScB2C2 and YB2C2, which contain trivalent metals, are expected to exhibit superconductivity, regardless of the topology of the boron–carbon layer structure: 572 network for ScB2C2 and 482 network for YB2C2 (see Figure 1). The calculated Tcs are weak, 0.5 and 4.7 K for ScB2C2 and YB2C2, respectively. Interestingly, the computed Tc for YB2C2 is close to the experimental value, as reported by Sakai et al. (3.6 K)24 and Michor et al. (1.0 K).25 The reason for their relatively low Tcs compared with MgB25 and doped MBC6,7,27 was examined from the partial DOS of the constituent atoms. Figures 3 and 4 show the total and atomic orbital-projected DOS of ScB2C2 and YB2C2, respectively. For the former, there are two distinct positions for B and C atoms. "B with B" indicates B atoms adjacent to other B atoms, while "B with C" refers to B atoms with only C neighbors (Figure 1a). The same notation applies to C atoms. It is observed that the electronic states at the Fermi level (0 eV) predominantly consist of pz orbitals (red lines) of the B and C atoms, along with d orbitals of the Sc atoms. The pz orbitals of B and C 6  atoms are geometrically perpendicular to the B2C2 planes and exhibit a small  overlap with each other. This situation is demonstrated in Figure 5a, which shows the spatial distributions of the local DOS at the Fermi level projected onto planes perpendicular to the B2C2 planes. Here, the local DOS at the Fermi level indicates the contributions to the electron density distribution from the crystal orbitals near the Fermi energy. It is clearly observed that pz-like electrons at the Fermi level are localized on B and C atoms, and d-like electrons are similarly localized on Sc atoms. Under these circumstances, the electronic states at the Fermi level are minimally influenced by atomic oscillations, leading to relatively weak electron–phonon interactions (Eliashberg function), as depicted in Figure 6a. The values of the Eliashberg function of ScB2C2 are much smaller than those of hole-doped BeB2C2, for instance, which will be presented in the next section. The preceding discussion also thoroughly applies to YB2C2, with its atomic orbital-projected DOS, spatial distribution of local DOS at the Fermi level, and Eliashberg function as shown in Figures 4, 5b, and 6b, respectively. The slightly higher Tc computed for YB2C2 compared to ScB2C2 may result from the higher Debye frequency of YB2C2 (1328 cm-1) compared to that of ScB2C2 (1205 cm-1). The experimental value of the Tc for YB2C2 (3.624 or 1.0 K25) is slightly lower than the calculated value (4.7 K). This difference might be explained by structural disturbances in experimental samples, as argued in the case of hole-doped LiBC.54–56 However, since the calculation of Tc inevitably includes some error, we do not delve into further detail.  3.2.2. Case of BeB2C2 (63 network). As said earlier, BeB2C2 exhibits semiconductive behavior (Figure 2c) and cannot be superconductive. We therefore attempted (heavy) carrier doping by substituting some Be atoms with Li (hole doping) or Al (electron doping). One Be atom out of four in the unit cell was replaced by a Li or an Al atom to produce Li0.25Be0.75B2C2 (VEC = 3.94) and Al0.25Be0.75B2C2 (VEC = 4.06). These two compositions were computed to be thermodynamically stable and exhibited no imaginary phonon modes. Their kinetic stabilities were also confirmed by Parrinello–Rahman MD simulations (Figure S3 in the Supporting Information). Interestingly, the Tc calculated for Li0.25Be0.75B2C2, 47.8 K (Table 1), is high and is comparable to that reported experimentally for MgB25 and those predicted Tcs for hole-doped LiBC and MgB2C2.6,7 The electronic structure of Li0.25Be0.75B2C2 is shown in Figure 7. The total DOS (Figure 7a) exhibits the features of hole-doping, and the orbital-projected DOS of B and C (Figure 7b,c) indicate that the peak of DOS at the Fermi level mainly consists of bonding -states made of px (green line) and py (dashed blue line) components with almost no pz (red line) participation. The atomic orbital-7  projected DOS of Be and Li are almost null at the Fermi level (they are omitted in the figure). This indicates that electrons at the Fermi level extend parallel to the B2C2 plane. Figure 8 displays the spatial distributions of the local DOS at the Fermi level projected onto planes perpendicular to the BC planes. In Li0.25Be0.75B2C2 (Figure 8a), it is observed that the electrons at the Fermi level are distributed between the B and C atoms. Because of this, the electronic states at the Fermi level are significantly influenced by atomic oscillations, leading to relatively strong electron–phonon interactions, as shown in Figure 9a, contrasting with the cases of the trivalent-metal-containing ScB2C2 and YB2C2 presented in the previous section (Figures 5 and 6). The value of the Eliashberg function is particularly high in the range between 800 and 1000 cm-1 (Figure 9a) corresponding to the bending modes of phonons (Figure 9c), where the bond angles mainly change. Regarding the hole doping of BeB2C2, Moudden27 removed 1/3 of the Be atoms (Be2/3B2C2) and evaluated Tc at 31 K (Table 1). Although the resulting Tc falls within the same range as in our study, the phonon spectrum suggested structural instability.27 In this case, the number of holes (or removed electrons), 0.67 per chemical formula, is much larger than 0.25 in our case (Li0.25Be0.75B2C2). We attempted further substitution of Be with Li by producing Li0.5Be0.5B2C2; however, the structure generated slightly imaginary phonon modes. It is uncertain whether these are intrinsic or due to technical issues. In contrast to the (heavy) hole-doped case (Li0.25Be0.75B2C2), a lower Tc of 5.1 K is computed for electron-doped Al0.25Be0.75B2C2 (Table 1). Its electronic structure is depicted in Figure 7. The atomic orbital-projected DOS of B and C (Figure 7e,f) demonstrate that the DOS at the Fermi level consists almost entirely of pz (red line) orbitals. The spatial distribution of the DOS at the Fermi level is depicted in Figure 8b. This distribution is rather similar to those of the trivalent metal cases ScB2C2 and YB2C2, as shown in Figure 5. Consequently, it is understandable that the electron–phonon interaction in Al0.25Be0.75B2C2 (Figure 9b) is as weak as that in ScB2C2 and YB2C2 (Figure 6), resulting in a low Tc.  3.2.3. Case of CaB2C2 (482 network). As mentioned earlier, CaB2C2 with a 482 network (Figure 1d) exhibits semiconductive behavior similar to BeB2C2 (Figure 2c,d). We attempted both (heavy) hole and electron doping by substituting 1/4 of Ca with K and Sc, respectively. The kinetic stabilities of the doped compounds were confirmed through Parrinello–Rahman MD simulations (Figure S3 in the Supporting Information). As a result, hole-doped K0.25Ca0.75B2C2 shows a low computed Tc of 3.1 K (Table 1), which unexpectedly contrasts with the high Tc (47.8 K) of the hole-doped Li0.25Be0.75B2C2 compound. 8  The reason for this was examined from its electronic structure (Figure 10). The electronic states at the Fermi level mostly consist of -states made of pz orbitals (red lines) of B and C atoms (Figure 10b,c). Therefore, the situation here is rather similar to that in the electron-carrier systems ScB2C2, YB2C2 (Figure 4), and Al0.25Be0.75B2C2 (Figures 7d–f). In K0.25Ca0.75B2C2, the spatial distribution of the states at the Fermi-level is localized in turn on atoms (Figure 11a), which is similar to the above-mentioned electron-carrier systems (Figures 5 and 8b), except that electrons are more localized on C atoms. By the same mechanism as that of the electron-carrier systems, K0.25Ca0.75B2C2 exhibits weak electron–phonon interactions (Figure 12a), leading to the low Tc. Thus, although CaB2C2 and BeB2C2 have a divalent metal atom in common, superconductivity appears in a different manner upon hole doping due to the different layer structures of BC. Electron-doped Sc0.25Ca0.75B2C2 also exhibits a low computed Tc value of 1.9 K (Table 1). Similar to those of the hole-doped K0.25Ca0.75B2C2 compound, the electronic states at the Fermi level mostly consist of pz orbitals of the B and C atoms (Figure 10d–f), which is consistent with other electron-carrier systems mentioned above. In Sc0.25Ca0.75B2C2, the spatial distribution of the states at the Fermi level is strongly localized on B and C atoms (Figure 11b), where pz orbitals of B predominate over those of C. For the same reasons observed in the electron-carrier systems, the electron–phonon interactions are weak (Figure 12b), resulting in a low Tc. In summary, for CaB2C2, both hole and electron doping yield low Tcs, which contrasts with the case of BeB2C2.  4. CONCLUSIONS In this work, the possible superconductivity of the several layered metal boride carbide MB2C2 was theoretically studied. Results show that all of them could be superconductors with Tcs, strongly influenced by both the topology of the boron–carbon layers and the valence of the metal atoms. With trivalent metals, ScB2C2 and YB2C2 exhibit superconductivity with low computed Tcs, regardless of the boron–carbon 2D arrangements: 572 network (ScB2C2) or 482 network (YB2C2). These predicted low Tcs are in agreement with experiments, which showed that YB2C2 is a superconductor at very low temperatures. With divalent metals, BeB2C2 and CaB2C2 become superconductive upon (heavy) carrier doping, but superconductivity emerges differently depending on the topology of the boron–carbon sheets. Interestingly, for BeB2C2 with a 63 network, hole doping (Li0.25Be0.75B2C2) results in a high Tc (47.8 K), while electron doping (Al0.25Be0.75B2C2) leads to a low Tc. In contrast, for CaB2C2, with a 482 network, both hole doping (K0.25Ca0.75B2C2) and electron doping (Sc0.25Ca0.75B2C2) result in low Tcs. The difference in Tc originates from the spatial distribution of the electronic states at the Fermi level. In cases of low Tc (ScB2C2, YB2C2, e- or h-doped CaB2C2, and e-doped BeB2C2), electrons at the Fermi level are 9  localized in  states predominantly made of B and C pz-orbital components perpendicular to the BC layers. Therefore, the electronic states at the Fermi level are less affected by atomic oscillations, leading to weak electron–phonon interactions. On the other hand, in the case of high Tc (h-doped BeB2C2), electrons at the Fermi level reside in σ states in the region between B and C atoms and are significantly affected by atomic oscillations, resulting in strong electron–phonon interactions. Results discussed in this paper seem to indicate that electron-poor (h-doped) metal boride carbide MB2C2 compounds with a 63 boron–carbon network could be promising superconductor candidates with Tcs comparable or superior to those of MgB2, which also contains 63 honeycomb planes. These theoretical findings should strongly encourage further experimental works in this direction.  ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.4c02221.  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Electronic DOS per chemical formula for MB2C2 (M = Sc (a), Y(b), Be (c), and Ca (d)). The Fermi level is defined as zero. Insets in parts (c) and (d) show the DOS enlarged around the Fermi level. 16     Figure 3. Total (a) and atomic orbital-projected (b–f) DOS for ScB2C2. "B with B" in panel (c) refers to boron atoms adjacent to other B atoms, while "B with C" in panel (d) refers to boron atoms with only C neighbors (see Figure 1a). The same notation applies to "C with B" and "C with C". The Fermi level is set at 0. Crystal axes are chosen in such a way that the z axis is perpendicular to the B2C2 layers. 17     Figure 4. Total (a) and atomic orbital-projected (b–d) DOS for YB2C2. The Fermi level is set at 0. 18     Figure 5. Spatial distributions of the local DOS at the Fermi level projected onto planes perpendicular to the B2C2 planes for ScB2C2 (a) and YB2C2 (b). Small spheres represent B (light blue) and C (gray) atoms, while large spheres represent Sc (green) and Y (orange) atoms, respectively. The color scale unit is states/(bohr3 Ry). 19     Figure 6. Phonon dispersion curves (left) with DOS and Eliashberg function 2F (right) for (a) ScB2C2 and (b) YB2C2. The values of  in the right graph are electron–phonon coupling constants. 20     Figure 7. Total and atomic orbital-projected DOS for Li0.25Be0.75B2C2 (a–c) and Al0.25Be0.75B2C2 (d–f). The Fermi level is set at 0. The z axis is perpendicular to the B2C2 layers. 21    Figure 8. Spatial distributions of the local DOS at the Fermi level projected onto planes perpendicular to the B2C2 planes for Li0.25Be0.75B2C2 (a) and Al0.25Be0.75B2C2 (b). Small spheres represent B (light blue) and C (gray) atoms, while large spheres represent Be (blue), Li (yellow), and Al (red) atoms. The color scale unit is states/(bohr3 Ry). 22     Figure 9. Phonon dispersion curves (left) with DOS and the Eliashberg function 2F (right) for (a) Li0.25Be0.75B2C2 and (b) Al0.25Be0.75B2C2. (c) Vibration vector corresponding to the highest peak of 2F at 800 cm⁻¹ in panel (a). The values of  in the right graph are electron–phonon coupling constants. 23     Figure 10. Total and atomic orbital-projected DOS for K0.25Ca0.75B2C2 (a–c) and Sc0.25Ca0.75B2C2 (d–f). The Fermi level is set at 0. 24    Figure 11. Spatial distributions of the local DOS at the Fermi level projected onto planes perpendicular to the B2C2 planes for K0.25Ca0.75B2C2 (a) and Sc0.25Ca0.75B2C2 (b). Small spheres represent B (light blue) and C (gray) atoms, and large spheres represent Ca (pink), K (yellow), and Sc (green) atoms. The unit of the color scale is states/(bohr3 Ry). 25    Figure 12. Phonon dispersion curves (left) with DOS and the Eliashberg function 2F (right) for  (a) K0.25Ca0.75B2C2 and (b) Sc0.25Ca0.75B2C2. The values of  in the right graph are electron–phonon coupling constants. S1  Supporting Information  Possible Superconductivity for Layered Metal Boride Carbide Compounds MB2C2 (M = Alkali, Alkaline-Earth or Rare-Earth Metals) Wataru Hayami,1 Xavier Rocquefelte,2 and Jean-François Halet2,3* 1Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan 2Univ Rennes, CNRS, Ecole Nationale Supérieure de Chimie de Rennes (ENSCR), Institut des Sciences Chimiques de Rennes (ISCR), UMR 6226, F-35000 Rennes, France 3CNRS–Saint-Gobain–NIMS, IRL 3629, Laboratory for Innovative Key Materials and Structures (LINK), National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan Figure S1. Optimized structures of the doped phases Li0.25Be0.75B2C2 (a) and Al0.25Be0.75B2C2 (b) derived from BeB2C2, and K0.25Ca0.75B2C2 (c) and Sc0.25Ca0.75B2C2 (d) derived from CaB2C2. One Be (blue) out of four is replaced by Li (yellow) in (a), and Al (red) in (b). One Ca (pink) out of four is replaced by K (yellow) in (c), and Sc (green) in (d). B and C are represented by light blue and grey spheres, respectively.  * Corresponding authors. E-mail: hayami.wataru@nims.go.jp (W.H.), Jean-Francois.Halet@univ-rennes.fr (J.-F. H.) S2    Figure S2. Electronic band structures of ScB2C2 (a), YB2C2 (b), Li0.25Be0.75B2C2 (c), Al0.25Be0.75B2C2 (d), K0.25Ca0.75B2C2 (e), and Sc0.25Ca0.75B2C2 (f).  S3   Figure S3. Fluctuations of the lattice parameters of the doped phases Li0.25Be0.75B2C2 (a) and Al0.25Be0.75B2C2 (b) derived from BeB2C2, and K0.25Ca0.75B2C2 (c) and Sc0.25Ca0.75B2C2 (d) derived from CaB2C2, during Parrinello-Rahman MD simulations performed at 300 K, 1 atm. (a, b, c) are the lattice lengths, and (, , ) are the lattice angles. The atomic coordinates were nearly identical between the initial and final steps (see Figure S1).   S4  Table S1. Optimized lattice parameters and fractional atomic coordinates.  Optimized lattice paremeters. compounds a (Å) b (Å) c (Å)  (deg)  (deg)  (deg) ScB2C2 5.2811 10.1977 3.4435 90.0 90.0 90.0 YB2C2 5.3505 5.3505 3.5796 90.0 90.0 90.0 BeB2C2 6.1341 5.4328 4.6997 90.0 90.0 90.0 Li0.25Be0.75B2C2 6.4643 5.4141 4.6845 90.0 90.1 90.0 Al0.25Be0.75B2C2 6.2964 5.4579 4.7289 90.0 90.7 90.0 CaB2C2 5.3624 5.3624 7.4160 90.0 90.0 90.0 K0.25Ca0.75B2C2 5.3579 5.3579 7.7971 90.0 90.0 90.0 Sc0.25Ca0.75B2C2 5.3406 5.3406 7.1759 90.0 90.0 90.0  Optimized fractional atomic coordinates.  ScB2C2 Sc            0.1378487640        0.1485379615        0.0000000000 Sc            0.8621512360        0.8514620385        0.0000000000 Sc            0.3621512360        0.6485379615        0.0000000000 Sc            0.6378487640        0.3514620385        0.0000000000 B             0.3560234215        0.4644938330        0.5000000000 B             0.6439765785        0.5355061670        0.5000000000 B             0.1439765785        0.9644938330        0.5000000000 B             0.8560234215        0.0355061670        0.5000000000 B             0.9867208808        0.3110484420        0.5000000000 B             0.0132791192        0.6889515580        0.5000000000 B             0.5132791192        0.8110484420        0.5000000000 B             0.4867208808        0.1889515580        0.5000000000 C             0.3928050638        0.0445390380        0.5000000000 C             0.6071949362        0.9554609620        0.5000000000 C             0.1071949362        0.5445390380        0.5000000000 C             0.8928050638        0.4554609620        0.5000000000 C             0.2968104770        0.3092045552        0.5000000000 C             0.7031895230        0.6907954448        0.5000000000 C             0.2031895230        0.8092045552        0.5000000000 C             0.7968104770        0.1907954448        0.5000000000   YB2C2 Y             0.0000000000        0.0000000000        0.0000000000 Y             0.5000000000        0.5000000000        0.0000000000 B             0.1367863516        0.3632136484        0.5000000000 B             0.8632136484        0.6367863516        0.5000000000 B             0.6367863516        0.1367863516        0.5000000000 S5  B             0.3632136484        0.8632136484        0.5000000000 C             0.1618245098        0.6618245098        0.5000000000 C             0.8381754902        0.3381754902        0.5000000000 C             0.3381754902        0.1618245098        0.5000000000 C             0.6618245098        0.8381754902        0.5000000000   BeB2C2 Be            0.0467917894        0.7500000000        0.3172291807 Be            0.4532082106        0.7500000000        0.3172291807 Be            0.5467917894        0.2500000000        0.6827708193 Be            0.9532082106        0.2500000000        0.6827708193 B             0.2500000000        0.0018011523        0.4918737008 B             0.2500000000        0.2500000000        0.0007886657 B             0.2500000000        0.4981988477        0.4918737008 B             0.2500000000        0.7500000000       -0.0213206621 B             0.7500000000       -0.0018011523        0.5081262992 B             0.7500000000        0.2500000000        0.0213206621 B             0.7500000000        0.5018011523        0.5081262992 B             0.7500000000        0.7500000000       -0.0007886657 C             0.2500000000       -0.0069118397        0.1602987924 C             0.2500000000        0.2500000000        0.6659522374 C             0.2500000000        0.5069118397        0.1602987924 C             0.2500000000        0.7500000000        0.6445049778 C             0.7500000000        0.0069118397        0.8397012076 C             0.7500000000        0.2500000000        0.3554950222 C             0.7500000000        0.4930881603        0.8397012076 C             0.7500000000        0.7500000000        0.3340477626   Li0.25Be0.75B2C2 Be            0.0466972312        0.7500000000        0.3234977152 Be            0.4540856362        0.7500000000        0.3179915708 Be            0.5533358051        0.2500000000        0.6782558781 Li            0.9734371936        0.2500000000        0.6899956019 B             0.2586807430        0.0039176942        0.4934045279 B             0.2659065611        0.2500000000       -0.0038284409 B             0.2586807430        0.4960823058        0.4934045279 B             0.2501865565        0.7500000000       -0.0192475999 B             0.7431142823       -0.0013194231        0.5070953978 B             0.7337430441        0.2500000000        0.0190071616 B             0.7431142823        0.5013194231        0.5070953978 B             0.7344988148        0.7500000000       -0.0033439418 C             0.2538801932       -0.0066684966        0.1608972541 C             0.2786352783        0.2500000000        0.6665334650 C             0.2538801932        0.5066684966        0.1608972541 C             0.2494816825        0.7500000000        0.6450667945 C             0.7325660757        0.0044697191        0.8395152358 C             0.7368163147        0.2500000000        0.3509149785 C             0.7325660757        0.4955302809        0.8395152358 C             0.7466932937        0.7500000000        0.3333319858 S6    Al0.25Be0.75B2C2 Be            0.0452665437        0.7500000000        0.3084351211 Be            0.4552788478        0.7500000000        0.3070150463 Be            0.5465414894        0.2500000000        0.6915745424 Al            0.9693550621        0.2500000000        0.7079075482 B             0.2580866153       -0.0004007542        0.4786659214 B             0.2698508763        0.2500000000       -0.0038328323 B             0.2580866153        0.5004007542        0.4786659214 B             0.2523066995        0.7500000000       -0.0311667290 B             0.7382847116       -0.0047939283        0.5154571369 B             0.7306212546        0.2500000000        0.0348531169 B             0.7382847116        0.5047939283        0.5154571369 B             0.7411356664        0.7500000000        0.0077139399 C             0.2554681384       -0.0061865776        0.1486390830 C             0.2697482643        0.2500000000        0.6515202918 C             0.2554681384        0.5061865776        0.1486390830 C             0.2507260303        0.7500000000        0.6336839798 C             0.7401598220        0.0033763399        0.8498105792 C             0.7391509237        0.2500000000        0.3643027402 C             0.7401598220        0.4966236601        0.8498105792 C             0.7460197672        0.7500000000        0.3428477937   CaB2C2 Ca            0.5000000000        0.5000000000        0.7499997358 Ca            0.0000000000        0.0000000000        0.2500001756 Ca            0.0000000000        0.0000000000        0.7499998244 Ca            0.5000000000        0.5000000000        0.2500002642  B             0.1388374252        0.3611625818        0.5000000000 B             0.8611625748        0.6388374182        0.5000000000 B             0.6388374182        0.1388374252        0.5000000000 B             0.3611625818        0.8611625748        0.5000000000 B             0.8611626428        0.3611626178        0.0000000000 B             0.1388373572        0.6388373822        0.0000000000 B             0.3611626178        0.1388373572        0.0000000000 B             0.6388373822        0.8611626428        0.0000000000 C             0.6594060003        0.8405939834        0.5000000000 C             0.3405939997        0.1594060166        0.5000000000 C             0.1594060166        0.6594060003        0.5000000000 C             0.8405939834        0.3405939997        0.5000000000 C             0.8405939627        0.6594060640        0.0000000000 C             0.6594060640        0.1594060373        0.0000000000 C             0.1594060373        0.3405939360        0.0000000000 C             0.3405939360        0.8405939627        0.0000000000   K0.25Ca0.75B2C2   * (2  2  1) unit cell of CaB2C2 Ca            0.2499699370        0.2499703159        0.7500094619 K             0.0000000000        0.0000000000        0.2499963687 S7  Ca            0.0000000000        0.0000000000        0.7500188534 Ca            0.2499680555        0.2499680614        0.2499911291 B             0.0699839732        0.1806567115        0.5083653007 B             0.4298987569        0.3192827382        0.5083543149 B             0.3192991406        0.0699902099        0.4916335312 B             0.1806673913        0.4299153102        0.4916405014 B             0.4299160117        0.1806672481        0.0083569301 B             0.0699895160        0.3192990849        0.0083646391 B             0.1806574067        0.0699835579       -0.0083611279 B             0.3192826217        0.4298994429       -0.0083544737 C             0.3280054515        0.4200707842        0.5152173688 C             0.1719481898        0.0799622057        0.5152270721 C             0.0799561878        0.3279966049        0.4847876300 C             0.4200590754        0.1719345985        0.4847598386 C             0.4200702648        0.3280056234       -0.0152179615 C             0.3279969138        0.0799561793        0.0152117516 C             0.0799626115        0.1719478980       -0.0152242454 C             0.1719338426        0.4200588143        0.0152377619 Ca            0.7500296841        0.2499699370        0.7500094619 Ca            0.5000000000       -0.0000000000        0.2499903259 K             0.5000000000       -0.0000000000        0.7500038093 Ca            0.7500319386        0.2499680555        0.2499911291 B             0.5700846898        0.1806673913        0.4916405014 B             0.9300097901        0.3192991406        0.4916335312 B             0.8193432885        0.0699839732        0.5083653007 B             0.6807172618        0.4298987569        0.5083543149 B             0.9300164421        0.1806574067       -0.0083611279 B             0.5701005571        0.3192826217       -0.0083544737 B             0.6807009151        0.0699895160        0.0083646391 B             0.8193327519        0.4299160117        0.0083569301 C             0.8280654015        0.4200590754        0.4847598386 C             0.6720033951        0.0799561878        0.4847876300 C             0.5799292158        0.3280054515        0.5152173688 C             0.9200377943        0.1719481898        0.5152270721 C             0.9200438207        0.3279969138        0.0152117516 C             0.8280521020        0.0799626115       -0.0152242454 C             0.5799411857        0.1719338426        0.0152377619 C             0.6719943766        0.4200702648       -0.0152179615 Ca            0.2499703159        0.7500300630        0.7500094619 Ca            0.0000000000        0.5000000000        0.2499903259 K             0.0000000000        0.5000000000        0.7500038093 Ca            0.2499680614        0.7500319445        0.2499911291 B             0.0699902099        0.6807008594        0.4916335312 B             0.4299153102        0.8193326087        0.4916405014 B             0.3192827382        0.5701012431        0.5083543149 B             0.1806567115        0.9300160268        0.5083653007 B             0.4298994429        0.6807173783       -0.0083544737 B             0.0699835579        0.8193425933       -0.0083611279 B             0.1806672481        0.5700839883        0.0083569301 B             0.3192990849        0.9300104840        0.0083646391 C             0.3279966049        0.9200438122        0.4847876300 S8  C             0.1719345985        0.5799409246        0.4847598386 C             0.0799622057        0.8280518102        0.5152270721 C             0.4200707842        0.6719945485        0.5152173688 C             0.4200588143        0.8280661574        0.0152377619 C             0.3280056234        0.5799297352       -0.0152179615 C             0.0799561793        0.6720030862        0.0152117516 C             0.1719478980        0.9200373885       -0.0152242454 Ca            0.7500300630        0.7500296841        0.7500094619 K             0.5000000000        0.5000000000        0.2499939424 Ca            0.5000000000        0.5000000000        0.7500048738 Ca            0.7500319445        0.7500319386        0.2499911291 B             0.5701012431        0.6807172618        0.5083543149 B             0.9300160268        0.8193432885        0.5083653007 B             0.8193326087        0.5700846898        0.4916405014 B             0.6807008594        0.9300097901        0.4916335312 B             0.9300104840        0.6807009151        0.0083646391 B             0.5700839883        0.8193327519        0.0083569301 B             0.6807173783        0.5701005571       -0.0083544737 B             0.8193425933        0.9300164421       -0.0083611279 C             0.8280518102        0.9200377943        0.5152270721 C             0.6719945485        0.5799292158        0.5152173688 C             0.5799409246        0.8280654015        0.4847598386 C             0.9200438122        0.6720033951        0.4847876300 C             0.9200373885        0.8280521020       -0.0152242454 C             0.8280661574        0.5799411857        0.0152377619 C             0.5799297352        0.6719943766       -0.0152179615 C             0.6720030862        0.9200438207        0.0152117516   Sc0.25Ca0.75B2C2  * (2  2  1) unit cell of CaB2C2 Ca            0.2499860229        0.2499859895        0.7499998933 Sc            0.0000000000        0.0000000000        0.2500010303 Ca            0.0000000000        0.0000000000        0.7500006933 Ca            0.2499821331        0.2499822246        0.2499998611 B             0.0685249716        0.1805627236        0.4883943168 B             0.4314016973        0.3193499622        0.4884006677 B             0.3193417502        0.0685148072        0.4883991993 B             0.1805661271        0.4314278729        0.4883960053 B             0.4314278777        0.1805661263        0.0116039535 B             0.0685147767        0.3193417431        0.0116006460 B             0.1805627001        0.0685249673        0.0116057475 B             0.3193499369        0.4314017070        0.0115991938 C             0.3311364988        0.4203846351        0.4876491099 C             0.1687951213        0.0796019657        0.4876400197 C             0.0796172877        0.3311280342        0.4876539348 C             0.4203675975        0.1687809923        0.4876423832 C             0.4203846572        0.3311364720        0.0123507776 C             0.3311279734        0.0796172904        0.0123458485 C             0.0796019364        0.1687951636        0.0123599333 C             0.1687810023        0.4203676228        0.0123574320 Ca            0.7500140105        0.2499860229        0.7499998933 S9  Sc            0.5000000000       -0.0000000000        0.2500006702 Ca            0.5000000000       -0.0000000000        0.7500004975 Ca            0.7500177754        0.2499821331        0.2499998611 B             0.5685721271        0.1805661271        0.4883960053 B             0.9314851928        0.3193417502        0.4883991993 B             0.8194372764        0.0685249716        0.4883943168 B             0.6806500378        0.4314016973        0.4884006677 B             0.9314750327        0.1805627001        0.0116057475 B             0.5685982930        0.3193499369        0.0115991938 B             0.6806582569        0.0685147767        0.0116006460 B             0.8194338737        0.4314278777        0.0116039535 C             0.8312190077        0.4203675975        0.4876423832 C             0.6688719658        0.0796172877        0.4876539348 C             0.5796153649        0.3311364988        0.4876491099 C             0.9203980343        0.1687951213        0.4876400197 C             0.9203827096        0.3311279734        0.0123458485 C             0.8312048364        0.0796019364        0.0123599333 C             0.5796323772        0.1687810023        0.0123574320 C             0.6688635280        0.4203846572        0.0123507776 Ca            0.2499859895        0.7500139771        0.7499998933 Sc            0.0000000000        0.5000000000        0.2500006702 Ca            0.0000000000        0.5000000000        0.7500004975 Ca            0.2499822246        0.7500178669        0.2499998611 B             0.0685148072        0.6806582498        0.4883991993 B             0.4314278729        0.8194338729        0.4883960053 B             0.3193499622        0.5685983027        0.4884006677 B             0.1805627236        0.9314750284        0.4883943168 B             0.4314017070        0.6806500631        0.0115991938 B             0.0685249673        0.8194372999        0.0116057475 B             0.1805661263        0.5685721223        0.0116039535 B             0.3193417431        0.9314852233        0.0116006460 C             0.3311280342        0.9203827123        0.4876539348 C             0.1687809923        0.5796324025        0.4876423832 C             0.0796019657        0.8312048787        0.4876400197 C             0.4203846351        0.6688635012        0.4876491099 C             0.4203676228        0.8312189977        0.0123574320 C             0.3311364720        0.5796153428        0.0123507776 C             0.0796172904        0.6688720266        0.0123458485 C             0.1687951636        0.9203980636        0.0123599333 Ca            0.7500139771        0.7500140105        0.7499998933 Sc            0.5000000000        0.5000000000        0.2500000814 Ca            0.5000000000        0.5000000000        0.7500001660 Ca            0.7500178669        0.7500177754        0.2499998611 B             0.5685983027        0.6806500378        0.4884006677 B             0.9314750284        0.8194372764        0.4883943168 B             0.8194338729        0.5685721271        0.4883960053 B             0.6806582498        0.9314851928        0.4883991993 B             0.9314852233        0.6806582569        0.0116006460 B             0.5685721223        0.8194338737        0.0116039535 B             0.6806500631        0.5685982930        0.0115991938 B             0.8194372999        0.9314750327        0.0116057475 S10  C             0.8312048787        0.9203980343        0.4876400197 C             0.6688635012        0.5796153649        0.4876491099 C             0.5796324025        0.8312190077        0.4876423832 C             0.9203827123        0.6688719658        0.4876539348 C             0.9203980636        0.8312048364        0.0123599333 C             0.8312189977        0.5796323772        0.0123574320 C             0.5796153428        0.6688635280        0.0123507776 C             0.6688720266        0.9203827096        0.0123458485  MB2C2 paper_MDR supporting information_MDR