With the motivation of searching for new superconductors in the Mg-B system, we performed ab initio evolutionary searches for all the stable compounds in this binary system in the pressure range of 0-200 GPa. We found previously unknown, yet thermodynamically stable, compositions MgB3 and Mg3B10. Experimentally known MgB2 is stable in the entire pressure range 0-200 GPa, while MgB7 and MgB12 are stable at pressures below 90 GPa and 35 GPa, respectively. We predict a reentrant behavior for MgB4, which becomes unstable against decomposition into MgB2 and MgB7 at 4 GPa and then becomes stable above 61 GPa. We find ubiquity of phases with boron sandwich structures analogous to the AlB2-type structure. However, with the exception of MgB2, all other magnesium borides have low electron-phonon coupling constants λ of 0.32 to 0.39 and are predicted to have Tc below 3 K.
INTRODUCTIONTremendous efforts have been put to design conventional superconductors with higher and higher critical temperatures [1][2][3][4][5] . It is also the main focus of theoretical and experimental studies to determine that how high the superconducting transition temperature T c can be pushed in binary and ternary boron-compounds. For instance, theoretical works predicted thermodynamically unstable CaB 2 to be superconducting at ∼50 K 1 and hole-doped LiBC to have T c of 65 K 2 . Ternary Mo 2 Re 3 B with T c = 8.5 K 3 , CuB 2−x C x (T c ∼ 50 K) 4 and multiple-phase bulk sample of yttrium-palladium-boroncarbon (T c = 23 K 5 ) are important boron-based superconductors.The unexpected discovery of superconductivity in MgB 2 with high T c = 39 K 6 has triggered a flurry of publications. In previous studies, superconductivity in MgB 2 has been thoroughly investigated [7][8][9][10][11] . The isotope effect demonstrated the phonon-mediated nature of superconductivity in this compound 12 . Although doping is usually expressed as a hope to enhance the desired properties, carbon-doped MgB 2 (Mg(B 0.8 C 0.2 ) 2 ) has a lower T c = 21.9 K 13 . Aluminum, with one more electron than magnesium, was reported to be an unfit candidate for partial substitution for magnesium14 . This shows that increasing electron concentration suppresses superconductivity of magnesium diboride.Elemental magnesium 15 and boron 16 have been shown to exhibit unexpected chemistry under high pressure, raising the motivation of studying their compounds. Moreover, materials composed of light atoms could make good conventional superconductors. The Mg-B system was subject to some explorations of superconductivity [17][18][19] 36 . Phonon frequencies and electron-phonon coupling (EPC) were calculated using QUANTUM ESPRESSO 37 . PBE-GGA functional is used for this part. A plane-wave basis set with a cutoff of 60 Ry gave a convergence in energy with a precision of 1 meV/atom. For electron-phonon coupling, a 6×6×2, 6×6×4 and a 4×4×4 q-point meshes were used for C2/mMgB 3 , Amm2-Mg 3 B 10 and C2/m-MgB 4 , respectively. Denser k-point meshes, 12×12×4, 12×12×8 and 8×8×8 were used for the convergence ...