Evolution of crystal and electronic structures of magnesium dicarbide at high pressure

Carbon-based compounds exhibit unexpected structures and electronic behavior at high pressure arising from various bonding features of carbon (e.g., sp, sp2 and sp3 C-C bonds). Here we report evolution of crystal structures of MgC2 in a wide pressure range of 0–200 GPa as predicted through ab-initio calculations in combination with an unbiased swarm structure search. Three pressure-induced structural transformations are unraveled, following the phase sequence of ambient-pressure P42/mnm (α-phase) → Cmcm (β-phase) → C2m (γ-phase) → EuGe2-type P-3m1 (δ-phase), where significant C-C bonding modifications from C-C dimer to quasi 1-dimensionzigzag chain, to polymerized ribbon and then to winkled quasi 2- dimension graphite sheet are evident. The predicted β- and γ-phases with sp2 C-C hybridization are metals, while the δ- phase characterized by a sp3C-C hybridization is a narrow-gap semiconductor with a band gap of 0.667 eV. Strong electron-phonon couplings in the compressed β- and γ- phases arepredicted with β-phase showing a high superconducting critical temperature of 11.2 K. The current results indicate that pressure is effective in tuning the crystal and electronic structures of MgC2, which is expected to have impact on physical properties for potential applications.

A systematic analysis of the electronic properties shows that the overlap between the conduction and the valence bands makes the β -and γ -phases metal, while the δ -phase is a narrow-gap semiconductor. Phonon-mediated superconducting behavior of two new metallic phases of MgC 2 was revealed by exploring the electron-phonon coupling.

Results and Discussions
Crystal structures of MgC 2 . We performed variable-cell structure predictions with the simulation cell size of 1-4 formula at pressure of 0-200 GPa. At ambient pressure, our simulations revealed the experimental observed P4 2 /mnm phase (denoted as α-structure/phase) has a lower enthalpy than all other candidates, indicating that it is the thermodynamic ground state 12 . This proved the reliability of our method for application to this dicarbide system. Interestingly, with in the whole pressure range studied, three new low-enthalpy structures with space group of orthorhombic Cmcm (β -phase), monoclinic C2/m (γ -phase) and EuGe 2 -type hexagonal P-3m1 (δ -phase) were explored.
The enthalpies of these new structures with respected to the experimental structure are shown as a function of pressure in Fig. 1. In order to investigate the phase transition pressure clearly, the enthalpy differences vs. pressure for the β -and γ -phases are given in insert of Fig. 1(a). As can be seen that, for compressed MgC 2 , the ambient-pressure α-phase is the most stable structure below 3.4 GPa, and the β -phase become more favorable at the pressure range from 3.4 to 9.4 GPa, and then the γ-phase is stable from 9.4 to 66.2 GPa, above which δ-phase is the energetically much superior to the γ-phase from 66.2 to 200 GPa. The current experimental techniques are readily accessible to these extreme conditions. The pressure evolution of the unite cell volume of MgC 2 in the α -, β -, γ -and δ -structures are depicted in insert of Fig. 1(b). The abrupt volumecollapses of about 19.7%, 9.6% and 4.8% around 3.4, 9.4 and 66.2 GPa, respectively, indicating the first-order nature of these phase transitions in MgC 2 . No imaginary frequencies are observed throughout the whole Brillouin zone, declaring that the three novel phases are dynamically stable at studied pressure region.
The optimized structure parameters at related pressures are listed in Table 1. The atomic arrangements of competing structures are shown in Fig. 2. The calculated lattice constants of the ambient-pressure have been widely demonstrated, consistent results with power X-ray and neutron powder diffraction measurements 12 . For the β -phase, the equilibrium lattices are a = 3.183 Å, b = 8.536 Å and c = 4.410 Å at 3.7 GPa. Four Mg atoms occupy the wyckoff 4c site and eight C atoms lie in 8f site in the unit cell. The β -structure is similar to the recently predicted of CaC 2 for Cmcm phase 20 . Figure 3 shows the simulated X-ray diffraction data of these structures, indicating that their structures are differenr from each other.
In this structure, one-dimension carbon chain along z direction lies in the center of the structure, in which the Mg atoms construct cylinder with hexagon cross-section. With increasing pressure, the γ -structure contains four molecules per unite cell. The optimized structural parameters are a = 8.321 Å, b = 2.609 Å and c = 9.304 Å. Four Mg atoms hold the wyckoff 4i site and the in-equivalent of two C atoms also lie in 4i site in the unit cell, respectively. The results show that carbon atoms are polymerized into ribbon with a six-membered ring. A carbon quasi 1-dimension ribbon lies in the center of cylinder constructed by Mg atoms. For the δ -phase with a EuGe 2 -type structure, including one molecule in unite cell, the equilibrium lattice are a = b = 2.525 Å and c = 3.623 Å at 66.2 GPa. One Mg atom occupies the wyckoff 1b site and two C atoms at 2d site. The plans of Mg atoms separate the hexagonal honeycombed layers of carbon atoms. It is obviously that the δ -phase consists of the bulking honeycomb-layered of carbon atoms separate by planes of Mg atoms. We investigate the nature of carbon-carbon bonding in MgC 2 with increasing pressure. The carbon-carbon bonding behavior reveals significant change with the external pressure and chemical precompression. At ambient pressure, the length of isolated dumbbell C-C bond in the α -phase (P4 2 /mnm) is 1.253 Å, which is nearly identical to the experimental value of 1.215 Å 12 . With increasing pressure, the distance between the isolated dumbbell decreases, resulting in carbon atomic chain formed in the β -phase (Cmcm), consistent with the increase in the C-C distance (1.458 Å and 1.401 Å). Under further compressed, the carbon atomic chains polymerize to a well-organized arrangement, transforming to the monoclinic (C/2m) γ -phase. It is obviously that the carbon nanoribbons appear between neighboring Mg atomic layers. The two types of in-equivalent C-C bond lengths in the γ -structure referred as d 1 and d 2 as a function of the pressure is plotted as a function of pressure in Fig. 4. The difference (∆d) between d 1 and d 2 in ribbon with six-membered carbon ring is also explored. At higher pressure, the difference ∆d begins to decrease more smoothly and reaches 0.009 Å at 66.2 GPa. The C-C bond lengths are 1.445 Å and 1.454 Å close to that of graphite (1.420 Å). However, the C-C bond lengths in honeycomb layer is 1.544 Å in the δ -phase, larger than those of the γ -structure at 66.2 GPa. The increased bond length induced the well organized carbon six-ring collapse into the winkled quasi 2-dimension graphite sheet. Due to the occurrence of graphite sheet between neighboring Mg atomic layer, the γ -phase can be regarded as one of folded graphite intercalation compounds.
Electronic structuresof MgC 2 . The calculated band structure and projected density of states are shown in Fig. 5. The ambient-pressure α -phase is an insulator with a larger indirect band gap of ~2.643 eV. The predicted overlap between the conduction and the valence bands shows the β -and γ -phases with sp 2 hybridization are metallic with C-p orbital dominating the density of states at the Fermi level. However, there are few C-s electrons and Mg-s, p electrons near the Fermi level, showing a pressure-induced charge transfer from C-s and Mg-s, p to C-p electron. In the α -phase, the value of the band gap decreases with the increasing pressures as the molar volume decreases along with the van der Walls gap reduces, the orbital overlaps across the gap are enhanced and this would reduce the energy separation between bonding and anti-bonding interactions. The reduction of the band gap is a promising signal for reaching a metallic state. At 66.2 GPa, the δ -phase characterized by sp 3 hybridization is most thermodynamically stable and is semiconductor with an indirect band gap of 0.667 eV. The significant evolution of electronic structures from sp 2 to sp 3 hybridization of carbon atoms between the γ -and δ -phases is similar to the fact of graphite transforms to diamond under sufficient compression. The pressure-induced insulator-metallization-semiconductor and related propertiesincent us to calculate the electron localization behavior of MgC 2 . Therefore, we have performed a chemical bonding analysis via calculation of the electron localization function (ELF) 22 . The calculated ELF isosurface (0.86) for the α -structure shows that two C atoms bond together to form a double bonded C 2 dimer with a stable and localized lone-pair nonbonding state, as shown in Fig. 6. With increasing pressure, the distance between the isolated dumbbell decreases, constructing carbon atomic chain with armchair-type carbon chains in the β -phase. One can see that each C has one lone pair of electrons. In the γ -structure, the ribbon with a six-member carbon ring has the feature of sp 2 -like nature with each inner C atoms forming three C-C covalent bonds, while each outer C atoms has one electron lone pair and two C-C covalent bonds, while the remaining 2p z electrons of the C 6 ring form a delocalized π system. In the δ -phase, the winkled honeycomb-layered structure lacks the system of delocalized π bonds with mobile electrons and has than that of values at 4 GPa. The calculated results show that ω log has positive pressure dependence, and coupling parameter λ decreases with pressure. For the γ -phase, the estimated superconducting critical T c is 7.1 K at 9.6 GPa, which is comparable with that of β -phase due to the similar of electron-phonon coupling integral (λ ) 0.472.

Conclusion
In summary, we have reported three high-pressure phases of MgC 2 , Cmcm ( β -phase), C2m ( γ -phase), P-3m1( δ -phase), which are stable in the pressure ranges of 3.4-9.4 GPa, 9.4-66.2 GPa and 66.2-200 GPa, respectively. The structural, dynamical, and electronic properties of high-pressure MgC 2 were systemically investigated up to 200 GPa. The predicted α -to β -phase structural transition is accompanied with a metallization by band gap closure. The γ -phase transfers to the δ -phase with a narrow band gap characterized by C-C sp 3 hybridized. Strong electron-phonon coupling in the compressed β -and γ -phases is found, in particular for the β -phase with carbon sp 2 -hybridization, which has the highest λ 0.558 value, leading to its high superconducting critical temperature Tc of 11.3 K, which is comparable with the 11.5 K value of CaC 6 . These results show that pressure has a strong influence on the fundamental crystal and electronic structure of MgC 2 , and as a result, the sensitive pressure tuning of the electronic properties offers an effective tool to modulate a wide range of physical properties for its potential applications.

Methods
The search for the stable structures is based on the CALYPSO (Crystal structure Analysis by Particle Swarm Optimization) methodology [25][26][27] and the first-principles calculations using a global minimization of free energy surfaces. The remarkable feature of this methodology is the ability of predicting the stable  structure with the knowledge of chemical composition under given external pressures 28,29 . Enthalpy calculations and geometry optimizations were performed within the framework of the Perdew-Burke-Ernzerhof parametrization for the exchange-correlation functional as implemented in the VASP (Vienna ab initio simulation package) code 30 . The projector augmented wave method 31,32 has been adopted, with 2p 6 3s 2 and 2s 2 2p 2 treated as valence electrons for Mg and C atoms, respectively. For Brillouin zone integration, we used the Monkhorst− Pack scheme 33 and checked convergence of ground state calculations with uniformly increasing k-point meshes for each structure. We used cutoff energy of 900 eV for the expansion of the wave function into the plane-wave basis-set. Monkhorst-Pack k-pointmeshes with a grid of 0.03 Å −1 for Brillouin zonesampling were chosen to achieve the total energy convergence of less than 1meV/atom. The phonon calculations were carried out by using a supercell approach as implemented in the PHONOPY code 34 . Electron-phonon coupling calculations were performed using the planewave pseudopotential method and density-functional perturbation theory as implemented in the QUANTUM ESPRESSO with a kinetic energy cutoff of 70 Ry 35 . 4 × 4 × 3 and 4 × 4 × 2 q-meshes in the first Brillouin zones were used in the EPC calculations for the β -and γ -structures, respectively.