Electron-phonon coupling superconductivity in two-dimensional orthorhombic M B6 (M =Mg ,Ca ,Ti ,Y ) and hexagonal M B6 (M =Mg ,Ca ,Sc ,Ti )

Combining crystal structure search and first-principles calculations, we report a series of two-dimensional (2D) metal borides including orthorhombic (ort-)M B₆ (M =Mg ,Ca ,Ti ,Y ) and hexagonal (hex-)M B₆ (M =Mg ,Ca ,Sc ,Ti ) . Then, we investigate their geometrical structures, bonding properties, electronic structures, mechanical properties, phonon dispersions, thermal stability, dynamic stability, charge density wave (CDW) phase transition, electron-phonon coupling (EPC), superconducting properties, and so on. Our ab initio molecular dynamics simulation results show that these M B₆ can maintain their original configurations up to about 1000 or 700 K (only for hex-MgB₆), indicating their excellent thermal stability. All their elastic constants satisfy the Born mechanically stable criteria and no imaginary frequencies are observed in their phonon dispersions. Interestingly, there may exist a CDW phase transition for ort-TiB₆ from type-I to type-II 2 ×1 supercell structure and for ort-YB₆ from type-I to type-III 2 ×1 supercell structure. Besides, these 2D M B₆ are all predicted to be intrinsic phonon-mediated superconductors. By analytically solving the McMillan-Allen-Dynes formula derived from the microscopic theory of Bardeen, Cooper, and Schrieffer, we obtain the superconducting transition temperature (T_c) for these materials, which are in the range of 1.4-22.6 K. Among our studied M B₆ , the highest T_c (22.6 K) appears in hex-CaB₆, whose EPC constant (λ ) is 0.87. By applying tensile/compressive strains on ort-/hex-CaB₆, we find that the compressive strain can obviously soften the acoustic-phonon branch and enhance the EPC as well as T_c. The T_c of the hex-CaB₆ can be increased from 22.6 to 28.4 K under compressive strain of 3%. These findings enrich the database of 2D superconductors and should stimulate experimental synthesizing and characterizing of 2D superconducting metal borides.