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One-dimensional carbon chains are expected to show outstanding optical and mechanical properties. But synthesis of the compounds containing one-dimensional carbon chains is a challenging work, because of the difficulty in saturating the dangling bonds of carbon atoms. Recently, the transition from the Immm phase to the Cmcm one at a transition pressure 5 GPa has been predicted for Li2C2 by density-functional theory calculations. In Cmcm-Li2C2, there are one-dimensional zigzag carbon chains caged by lithium atoms. Under ambient pressure, the electronic structure of Cmcm-Li2C2 is as follows: The hybridization among 2s, 2py, and 2pz orbitals of carbon atoms results in three sp2-hybridized orbitals that are coplanar with the zigzag chains of these carbon atoms, denoted as the y-z plane. The sp2-hybridized orbitals along y-axis (perpendicular to the zigzag chain) overlap with each other and form one πup-bonding band and one πup ^*-antibonding band. Likewise, the 2p_x orbitals of carbon atoms will provide also one πup-bonding band and one π*-antibonding band. These two π*-antibonding bands cross the Fermi level and contribute to the metallicity of Cmcm-Li2C2. The other two sp2-hybridized orbitals will give two σ-bonding bands, whose band tops are about 5 eV below the Fermi energy level. These two fully occupied σ bands are the framework of the zigzag carbon chains. The changes in electronic structure of Cmcm-Li2C2 under 5 GPa are negligible, compared with that in case of ambient pressure. To our best knowledge, there is no report upon the superconductivity for compounds containing one dimensional carbon chains. We choose Cmcm-Li2C2 as a model system to investigate its electron-phonon coupling and phonon-mediated superconductivity. To determine the phonon-mediated superconductivity, the electron-phonon coupling constant λ and logarithmic average frequency ωlog are calculated based on density functional perturbation theory and Eliashberg equations. We find that λ and ωlog are equal to 0.63 and 53.8 meV respectively at ambient pressure for Cmcm-Li2C2. In comparison, both the phonon density of states and the Eliashberg spectral function α2F(ω) are slightly blue-shifted at a pressure of 5 GPa. Correspondingly, λ and ωlog are calculated to be 0.56 and 58.2 meV at 5 GPa. Utilizing McMillian-Allen-Dynes formula, we find that the superconducting transition temperatures (Tc) for Cmcm-Li2C2 are 13.2 K and 9.8 K, respectively, at ambient pressure and 5 GPa. We also find that two phonon modes B1g and Ag at Γ point have strong coupling with π* electrons. Among lithium carbide compounds, the superconductivity is only observed in LiC2 below 1.9 K. Besides LiC2, theoretical calculations also predicted superconductivity in mono-layer LiC6, with Tc being 8.1 K. So if the superconductivity of Cmcm-Li2C2 is confirmed by experiment, it will be the first superconducting compound containing one dimensional carbon chains and its Tc will be the highest one among lithium carbide compounds. Thus experimental research to explore the possible superconductivity in Cmcm-Li2C2 is called for.
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[24] Rappe A M, Rabe K M, Kaxiras E, Joannopoulos J D 1990 Phys. Rev. B 41 1227
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[26] Eliashberg G M 1960 Zh. Eksp. Teor. Fiz. 38 966
[27] Allen P B 1972 Phys. Rev. B 6 2577
[28] Richardson C F, Ashcroft N W 1997 Phys. Rev. Lett. 78 118
[29] Lee K H, Chang K J, Cohen M L 1995 Phys. Rev. B 52 1425
[30] Wierzbowska M, Gironcoli S de, Giannozzi P 2005 arXiv:cond-mat 0504077
[31] An J M, Pickett W E 2001 Phys. Rev. Lett. 86 4366
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[1] Allen P B, Dynes R C 1975 Phys. Rev. B 12 905
[2] McMahon J M, Ceperley D M 2011 Phys. Rev. Lett. 106 165302
[3] McMahon J M, Ceperley D M 2011 Phys. Rev. B 84 144515
[4] Drozdov A P, Eremets M I, Troyan I A 2014 arXiv:1412.0460
[5] Duan D et al. 2014 Sci. Reports 4 6968
[6] Gao M, Lu Z Y, Xiang T 2015 Phys. Rev. B 91 045132
[7] Ekimov E A et al. 2004 Nature 428 542
[8] Takano Y et al. 2007 Diamond Relat. Mater. 16 911
[9] Moussa J E, Cohen M L 2008 Phys. Rev. B 77 064518
[10] Solozhenko V L, Kurakevych O O, Andrault D, Godec Y Le, Mezouar M 2009 Phys. Rev. Lett. 102 015506
[11] Hannay N B, Geballe T H, Matthias B T, Andres K, Schmidt P, MacNair D 1965 Phys. Rev. Lett. 14 225
[12] Weller T E, Ellerby M, Saxena S S, Smith R P, Skipper N T 2005 Nature Phys. 1 39
[13] Emery N et al. 2005 Phys. Rev. Lett. 95 087003
[14] Profeta G, Calandra M, Mauri F 2012 Nature Phys. 8 131
[15] Pan Z H, Camacho J, Upton M H, Fedorov A V, Howard C A, Ellerby M, Valla T 2011 Phys. Rev. Lett. 106 187002
[16] Hebard A F et al. 1991 Nature 350 600
[17] Varma C M, Zaanen J, Raghavachari K 1991 Science 254 989
[18] Juza R, Wehle V, Schuster H U 1967 Z. Anorg. Allg. Chem. 352 252
[19] Ruschewitz U, Pöttgen R 1999 Z. Anorg. Allg. Chem. 625 1599
[20] Chen X Q, Fu C L, Franchini C 2010 J. Phys.: Condens. Matter 22 292201
[21] Belash I T, Bronnikov A D, Zharikov O V, Pal'nichenko A V 1989 Solid State Commun. 69 921
[22] Giannozzi P et al. 2009 J. Phys.: Condens. Matter 21 395502
[23] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[24] Rappe A M, Rabe K M, Kaxiras E, Joannopoulos J D 1990 Phys. Rev. B 41 1227
[25] Baroni S, de Gironcoli S, Corso A Dal, Giannozzi P 2001 Rev. Mod. Phys. 73 515
[26] Eliashberg G M 1960 Zh. Eksp. Teor. Fiz. 38 966
[27] Allen P B 1972 Phys. Rev. B 6 2577
[28] Richardson C F, Ashcroft N W 1997 Phys. Rev. Lett. 78 118
[29] Lee K H, Chang K J, Cohen M L 1995 Phys. Rev. B 52 1425
[30] Wierzbowska M, Gironcoli S de, Giannozzi P 2005 arXiv:cond-mat 0504077
[31] An J M, Pickett W E 2001 Phys. Rev. Lett. 86 4366
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