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[Wataru Hayami](https://orcid.org/0000-0003-0497-8690), Takaho Tanaka

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Superconductivity of alkali-metal intercalated BC2AIP Advances 10, 065213 (2020); https://doi.org/10.1063/5.0008280 10, 065213© 2020 Author(s).Superconductivity of alkali-metalintercalated BC2Cite as: AIP Advances 10, 065213 (2020); https://doi.org/10.1063/5.0008280Submitted: 21 March 2020 . Accepted: 23 May 2020 . Published Online: 10 June 2020Wataru Hayami , and Takaho Tanakahttps://images.scitation.org/redirect.spark?MID=176720&plid=1196622&setID=378289&channelID=0&CID=402214&banID=519926094&PID=0&textadID=0&tc=1&type=tclick&mt=1&hc=c4884d7d2e427dae0699656497e58840013d02e6&location=https://doi.org/10.1063/5.0008280https://doi.org/10.1063/5.0008280https://aip.scitation.org/author/Hayami%2C+Wataruhttp://orcid.org/0000-0003-0497-8690https://aip.scitation.org/author/Tanaka%2C+Takahohttps://doi.org/10.1063/5.0008280https://aip.scitation.org/action/showCitFormats?type=show&doi=10.1063/5.0008280http://crossmark.crossref.org/dialog/?doi=10.1063%2F5.0008280&domain=aip.scitation.org&date_stamp=2020-06-09AIP Advances ARTICLE scitation.org/journal/advSuperconductivity of alkali-metalintercalated BC2Cite as: AIP Advances 10, 065213 (2020); doi: 10.1063/5.0008280Submitted: 21 March 2020 • Accepted: 23 May 2020 •Published Online: 9 June 2020Wataru Hayamia) and Takaho TanakaAFFILIATIONSInternational Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba,Ibaraki 305-0044, Japana)Author to whom correspondence should be addressed: HAYAMI.Wataru@nims.go.jpABSTRACTThe superconductivity of alkali-metal intercalated BC2, MxBC2 (M = Li, Na, and K; x = 0.5–1.5), has been studied using first-principlescalculations. The calculated critical temperature (Tc) values are substantially high at x = 0.5 (49.8–57.1 K), which are higher than those forMgB2 and close to those predicted for LixByCz compounds. The Tc values at x = 1.5 are comparatively low (0.6–5.6 K) and close to those forgraphite intercalation compounds. No superconductivity is observed at x = 1.0 for all alkali metals. An analysis of the electronic structuresreveals that at x = 0.5, the state at the Fermi energy includes the σ bond character. In contrast, at x = 1.5, the state includes only π bondscomprising pz orbitals of B and C atoms. The σ bond character is essential for attaining high Tc values because the σ bond couples stronglywith the bending-like phonon modes of the BC2 layer. However, the π bond couples weakly with the stretching-like phonon modes due to thesmall overlap of the pz orbitals, which results in a relatively low Tc for the material.© 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0008280., sI. INTRODUCTIONGraphite and graphite-related materials have been studied andutilized for centuries. Since a technique for exfoliating single-layergraphene was developed,1 graphite and graphite-related materialshave been attracting more attention than ever. Most of the uniqueproperties of these substances derive from two-dimensional atomicstructures and semi-metallic electronic structures that distinguishthem from three-dimensional bulk materials.Based on the B–C binary phase diagram,2 the substitution ofcarbon in graphite with boron is allowed only by a few atomicpercent, which means that graphite-like (g-) BxCy is thermody-namically unfavorable. However, syntheses of g-BCx (x = 3–9) viachemical vapor deposition,3–7 the arc-discharge method,8 and seg-regation onto a metal diboride surface9 have been reported as ametastable phase. It appears that experimentally, the value of x can-not be smaller than three, i.e., the composition ratio of B is limited to25 at. %. This is understandable based on the fact that the electronicstructure of graphite has the Fermi level in the middle of the pseu-dogap (semi-metallic); hence, the substitution with B atoms reduceselectrons in the bonding orbitals.Consequently, g-BC and g-BC2 are yet to be synthesized. How-ever, these structures appear in compounds such as MxByCz inwhich the metal atoms M stabilize the BCx layer by donating elec-trons. It has been established that g-BC is formed in LiBC andMgB2C2,10,11 whereas g-BC2 was only recently recognized.A compound comprising the g-BC2 structure, Sc2B1.1C3.2, wasdiscovered by Shi et al.12 In Sc2B1.1C3.2, the g-BC2 layers and Sc2Clayers are stacked alternatingly.12,13 The Sc2C layer is the sameas MXene, a single layer of the MAX phases.14,15 Sc2B1.1C3.2 can,thus, be regarded as a graphene–MXene complex compound. Anincommensurate structure is formed by stacking the BC2 and Sc2Clayers because they have slightly different unit cell sizes, whichgives the compound a large lattice parameter a = 23.710 Å. Notethat Sc2B1.1C3.2 is thermodynamically stable because it was syn-thesized via the conventional solid-state reaction and floating zonemethods.Although the precise structure of g-BC2 was unclear in theexperiments,12,13 our theoretical study16 has revealed it to be asshown in Fig. 1, with boron atoms arranged to form a√3 ×√3-R30○ superlattice. BC2 may appear to be merely a derivative of theBCx group. However, in contrast to BC and BC3, BC2 had not beenAIP Advances 10, 065213 (2020); doi: 10.1063/5.0008280 10, 065213-1© Author(s) 2020https://scitation.org/journal/advhttps://doi.org/10.1063/5.0008280https://www.scitation.org/action/showCitFormats?type=show&doi=10.1063/5.0008280https://crossmark.crossref.org/dialog/?doi=10.1063/5.0008280&domain=pdf&date_stamp=2020-June-9https://doi.org/10.1063/5.0008280https://orcid.org/0000-0003-0497-8690mailto:HAYAMI.Wataru@nims.go.jphttp://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0008280AIP Advances ARTICLE scitation.org/journal/advFIG. 1. Structure of BC2 with alkali metals (M) intercalated (MxBC2). B, C, and Mare denoted by blue, green, and yellow spheres, respectively.discovered until our discovery of the Sc2B1.1C3.2 compound in1999.12 Even after the discovery, the importance of BC2 had not beenrecognized until our recent theoretical study.16 Therefore, BC2 is asort of “missing link” between BC and BC3 and there have been fewother studies on it.The most stable structure of BC2, i.e., the arrangement of Batoms, varies depending on the electric charge of the BC2 layeritself.17 When the BC2 layer has sufficient negative charge, as inSc2B1.1C3.2, the structure shown in Fig. 1 becomes the most stable. Inanalogy to graphite intercalation compounds (GICs), we have inves-tigated Li intercalation into g-BC2.17 Because alkali metals donateelectrons to BC2, it is reasonable to study the properties of BC2on the basis of the structure in Fig. 1. Intercalated alkali atoms aremost stably settled at the hexagonal sites. The calculated intercala-tion potential for Li indicates that the composition ratio of Li hardlyexceeds 1.5 (Li1.5BC2) when the hexagonal sites are fully occupied(Fig. 1).17GICs containing alkali and alkali-earth metals often exhibitsuperconductivity at critical temperature (Tc) values in the rangeof 0.02–11.5 K.18 In contrast, MgB2 comprising a graphite-likeboron layer has a much higher Tc of 39 K.19 The higher Tc derivesfrom the fact that the electronic state at the Fermi level has aσ bond component, which couples strongly with bond-stretchingphonons.20 Inspired by this, Rosner et al. theoretically proposedhole-doped LixBC (x < 1.0),21 and later, Bazhirov et al. also reportedon Li4B5C3 and Li2B3C22 as a potential candidate for high Tcsuperconductivity. These theoretical studies predicted that the Tcof LixByCz compounds could be as high or higher than those ofMgB2.Considering these two studies, it is natural to ask whether inter-calated g-BC2 becomes a superconductor as well. In this study, weconducted first-principles calculations to evaluate the Tc values ofMxBC2 (M = Li, Na, and K) at x = 0.5, 1.0, and 1.5, as shown inFig. 1. We assumed that Na and K atoms behave like Li, i.e., settle atthe hexagonal sites at values of x up to 1.5.Interestingly, the electronic structure changes substantiallywith the value of x. The density of states (DOS) calculated for LixBC2had a pseudogap, and the Fermi level was located at the bottom ofthe pseudogap at x = 1.0.17 This suggests that the dominant carrierchanges from holes to electrons as x increases from 0.5 to 1.5, whichwould affect how superconductivity emerges in this material. It hasbeen found that Tc for MxBC2 depends considerably on x, the mech-anism of which will be discussed in detail along with their electronicand phononic structures in Secs. II–IV.II. COMPUTATIONAL DETAILSThe electronic structures, phonon dispersion curves, and Tcvalues were calculated using the Quantum ESPRESSO code,23based on the density functional theory (DFT) with plane wavesand pseudopotentials. The ultrasoft pseudopotentials24 for alkalimetals, boron, and carbon were adopted from the libraryat http://www.quantum-espresso.org. The generalized-gradient-approximation (GGA) functional of Perdew–Burke–Ernzerhof(PBE) was employed.25 The energy cutoffs for plain waves were 50Ry for Li and K and 70 Ry for Na. The cutoffs for the electron den-sity were 400 Ry for Li and 350 Ry for Na and K. These cutoffs wereconfirmed to provide good convergence of the total energy.The unit cell used for the calculations was√3×√3-R30○ of thegraphite unit cell for all the structures. While having alkali metalsintercalated, the stacking of the BC2 layer was aligned in the z direc-tion, i.e., the xy positions of the B and C atoms were the same inall the BC2 layers. Thus, the unit cell for the calculations compriseda BC2 layer and an alkali metal layer, which in total contained twoB atoms, four C atoms, and one to three alkali metal atoms corre-sponding to x = 0.5–1.5. k-point sampling was implemented usingthe Monkhorst–Pack scheme.26 An (8 × 8 × 8) mesh was adoptedfor calculating the electronic structures.Phonon dispersion curves and Eliashberg spectral functions(α2F) were calculated using the PHonon package in the Quan-tum ESPRESSO suite. For the calculation of electron–phonon (EP)coupling coefficients, coarse meshes of (6 × 6 × 6)–(8 × 8 × 8)were adopted for the phonon k-point grid and fine meshes of (30× 30 × 30)–(32 × 32 × 32) were adopted for the Fermi surface cal-culations. The sum at the Fermi energy was conducted using theinterpolation method.27 The Tc values were estimated using theAllen–Dynes formula,28Tc =ωlog1.2exp[− 1.04(1 + λ)λ − μ∗(1 + 0.62λ)], (1)ωlog = exp[2λ ∫∞0dωα2F(ω)ωlogω], (2)λ = 2∫∞0dωα2F(ω)ω, (3)where μ∗ is the Coulomb repulsion parameter and was taken as0.1 in this study.III. RESULTS AND DISCUSSIONThe calculated Tc values for MxBC2 (M = Li, Na, and K) arelisted in Table I. The Tc values are notably high at x = 0.5 for allalkali metals and are much higher than those for GICs such as KC8(0.15 K),29,30 CaC6 (11.5 K),31 YbC6 (6.5 K),31 LiC2 (high pressure,1.9 K),32 and a few-layer graphene intercalate LiC6 (7.4 K).33 The TcAIP Advances 10, 065213 (2020); doi: 10.1063/5.0008280 10, 065213-2© Author(s) 2020https://scitation.org/journal/advhttp://www.quantum-espresso.orgAIP Advances ARTICLE scitation.org/journal/advTABLE I. Calculated Tc (K) for MxBC2 (M = Li, Na, and K).M x = 0.5 x = 1.0 x = 1.5Li 49.8 0.0 0.6Na 57.1 0.0 5.6K 51.6 0.0 1.9values are rather close to those of MgB2 (39 K).19 The emergenceof high Tc in graphite-like materials was predicted by Rosner et al.,who theoretically demonstrated that the Tc for hole-doped LixBC (x< 1.0) could rise as high as 100 K.21 Bazhirov et al. also calculated theTc values for the LixByCz compound and obtained 36.8 K for Li2B3Cand 16.8 K for Li4B5C3.22The Tc values for MxBC2 vary significantly as x increases from0.5 to 1.5, during which the materials continue to be metallic, witha finite DOS. The comparison of the Tc values for MxBC2, GICs,and LixByCz suggests that the mechanism of superconductivity forMxBC2 at x = 0.5 may be the same as that for LixByCz21,22 and maybe the same as that for the GICs at x = 1.5.29–33To elucidate how superconductivity is achieved, the electronicDOSs, phonon dispersion curves, and Eliashberg spectral functionsfor MxBC2 were calculated. Because the electronic structures ofMxBC2 (M = Li, Na, and K) are similar to each other, the resultsof the Li case are shown in Figs. 2–5.Figure 2 shows the total and partial DOSs of LixBC2 (x = 0.5–1.5). As mentioned earlier, the total DOSs (top left) have a pseudo-gap. As x increases from 0.5 to 1.5, the Fermi level (Ef) shifts frombelow to above the pseudogap. Therefore, the carrier is hole-like at x= 0.5, as in the case of LixByCz ,21,22 and it is electron-like at x = 1.5, asin the case of GICs.29–33 The partial DOSs arising from the B and Catoms are shown in Fig. 2, while those from the Li atoms are omittedbecause they have little contribution to the DOS. At x = 0.5, the stateat Ef consists of px and py orbitals of the B and C atoms along withpz orbitals. The px and py orbitals in the plane form sp2 hybridizedorbitals that yield σ bonds between atoms. Thus, the state at Ef hasthe σ bond character, which plays a crucial role in achieving a highTc, as is the case with LixByCz21,22 and MgB2.20 In contrast, at x = 1.0and 1.5, it is seen that the state at Ef consists of only pz orbitals, whichindicates that the state has the π bond character as in GICs,29–33 andhigh Tc cannot be expected. Note that at x = 0.5, the Ef is located justat the upper end of the px and py states of B and C. This means that0.5 is the critical value of x for LixBC2 to have the σ bond characterin the state at Ef.To clarify how the σ and π bond characters appear in the stateat Ef, the spatial distributions of DOS at Ef are plotted in Fig. 3.The isosurfaces are plotted in orange, along with the B (blue), C(green), and Li (yellow) atoms. At x = 0.5, the state at Ef extendsbetween B and C atoms, exhibiting the σ bond character, and theisosurface also has traits of the pz orbitals showing that the π bondcharacter is partially mixed, as shown in Fig. 2 (top). In contrast,at x = 1.0 and 1.5, the state at Ef has only the π bond characterand the overlap between component pz orbitals is comparativelysmall. This suggests that the energy of the state at Ef is sensitive tothe atomic positions when x = 0.5 and much less sensitive whenx = 1.0 and 1.5, which explains the difference in the strength ofFIG. 2. Total and partial densities of states of LixBC2. Top: x = 0.5, middle: x = 1.0,and bottom: x = 1.5. The Fermi level is set to zero. C center is the carbon atomcoordinated with three C atoms, and C side is the carbon atom coordinated to twoB atoms and a C atom (see Fig. 1).AIP Advances 10, 065213 (2020); doi: 10.1063/5.0008280 10, 065213-3© Author(s) 2020https://scitation.org/journal/advAIP Advances ARTICLE scitation.org/journal/advFIG. 3. Spatial distributions of DOS at Ef for LixBC2. The isosurfaces at 0.05[states/(Ry cell bohr3)] are plotted in orange. B, C, and Li atoms are denoted byblue, green, and yellow spheres, respectively.EP coupling. The area of the isosurface at x = 0.5 is larger thanin the cases of x = 1.0 and 1.5, which would also be favorable forenhancing Tc.Figure 4 shows the calculated phonon dispersion curves, theDOSs (red), and the Eliashberg spectral functions (α2F, blue) forLixBC2. As expected, based on Fig. 3, α2F is very small at x = 1.0,which explains why the material cannot be superconducting at thiscomposition ratio. The Debye frequency at x = 1.0 (1340 cm−1) ishigher than those at x = 0.5 (1295 cm−1) and x = 1.5 (1208 cm−1),suggesting that the structure is most stable at x = 1.0 because Efis located at the bottom of the pseudogap. The difference in α2Fbetween x = 0.5 and 1.5 is remarkable. At x = 0.5, α2F is enhancedin the frequency range of 890–970 cm−1, whereas at x = 1.5, α2Fin the range of 1050–1200 cm−1 is dominant. A qualitative expla-nation of this is provided based on the analysis of vibrationalmodes.Figure 5 illustrates some examples of the vibrational modes ofLixBC2 at x = 0.5 and 1.5. These were selected from the region offrequency for each x, where α2F is enhanced, as mentioned ear-lier. Frequencies denoted under each figure were calculated at theΓ point. At x = 0.5 (left), the vibrations appear to be in the bendingmodes. This is probably because the σ bond character in the stateat Ef (Figs. 2 and 3) originates from sp2 hybridized orbitals and thebond angle particularly prefers to be 120○. Hence, the change in thebond angle significantly influences the energy of the state leadingto strong EP coupling. In contrast, at x = 1.5 (right), the vibrationsappear to be in the stretching modes. This is understandable becausethe state at Ef consists of only pz orbitals of B and C (Figs. 2 and 3),which makes its energy more sensitive to interatomic distance thanto bond angle. The small overlap of the pz orbitals keeps the energyof the state rather unaffected by the atomic positions and causesrelatively weak EP coupling.Thus far, we have theoretically investigated superconductiv-ity in BC2. Concerning experiments, Mori et al. reported onthe electrical resistivity of Sc2B1.1C3.2,34 the compound compris-ing the BC2 layer (see Sec. I). Although the compound is metal-lic, no superconductivity was observed at temperatures down to4 K. Based on our previous study,16 the state at Ef in Sc2B1.1C3.2FIG. 4. Phonon dispersion curves, densities of states (DOSs, red), and Eliashbergspectral functions (α2F, blue) for LixBC2. Top: x = 0.5, middle: x = 1.0, and bottom:x = 1.5.mostly consists of Sc 3d states. Therefore, the discussion of BC2in this paper cannot be applied to superconductivity in Sc2B1.1C3.2.Instead, the superconductivity of the Sc2C layer (MXene) should beconsidered.Another problem that may affect superconductivity is struc-tural disorder. The resistivity of Sc2B1.1C3.2 increased slightly afterreaching a minimum at about 75 K, which is interpreted as weaklocalization due to configurational disorder in the BC2 layer.34 Asimilar situation occurred with hole-doped LixBC. After Rosneret al.’s proposition,21 Bharathi et al. experimentally searched forAIP Advances 10, 065213 (2020); doi: 10.1063/5.0008280 10, 065213-4© Author(s) 2020https://scitation.org/journal/advAIP Advances ARTICLE scitation.org/journal/advFIG. 5. Examples of vibrational modes for LixBC2. Left: x = 0.5 and right: x =1.5. Red arrows indicate the directions of atomic motion. B, C, and Li atoms aredenoted by blue, green, and yellow spheres, respectively.superconductivity in LixBC (x = 0.4–1.0) but was unsuccessful.35They concluded that the structural disorder in the B–C stackingobstructed the emergence of superconductivity. These experimen-tal findings suggest that B and C atoms can exchange their positionsin the BCx layers without a large increase in the total free energy.Hence, it is crucial to prepare a sample crystal with well-ordered BCxlayers to achieve superconductivity.In principle, disorder in the BCx layers increases entropy andaccordingly lowers free energy at high temperatures. If the reactiontemperature for the synthesis is lowered by choosing appropriatestarting materials and catalysts, disorder may be suppressed greatly.As an example, the synthesis of well-ordered α-tetragonal boron hasbeen achieved by using decaborane (B10B14) as a starting material.36In this case, hydrogen in decaborane may act as a catalyst that low-ers the reaction temperature. Thus, it may be possible to develop animproved method to synthesize well-ordered BCx.IV. CONCLUSIONSThe superconductivity of alkali-metal intercalated BC2, MxBC2(M = Li, Na, and K; x = 0.5–1.5), has been investigated using first-principles calculations. The calculated Tc values were substantiallyhigh at x = 0.5 (49.8–57.1 K), which were higher than those for MgB2and close to those predicted for LixByCz compounds. The Tc valuesat x = 1.5 were comparatively low and close to those for GICs. Theanalysis of the partial DOSs revealed that at x = 0.5, the state at Efincludes the σ bond character, whereas at x = 1.5, the state includesonly the π bonds comprising pz orbitals. The value of 0.5 is the crit-ical value for MxBC2 to have a σ bond component. The σ bondcharacter is essential to achieve high Tc values because the σ bondcouples strongly with the bending phonon modes of the BC2 layer.In contrast, the π bond couples weakly with the stretching phononmodes due to the small overlap of the component pz orbitals, whichresults in relatively low Tc at x = 1.0 and 1.5.From an experimental point of view, the superconductivity inBCx layers tends to be suppressed by the configurational disorder ofits constituent atoms. Consequently, it is essential to find a way togrow a crystal with well-ordered BCx layers.DATA AVAILABILITYThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.REFERENCES1K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos,I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).2P. 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