Combining crystal structure search and first-principles calculations, we report a series of two-dimensional (2D) metal borides including orthorhombic (ort-)$M{\mathrm{B}}_6$ $(M=\mathrm{Mg},\mathrm{Ca},\mathrm{Ti},\mathrm{Y})$ and hexagonal (hex-)$M{\mathrm{B}}_6$ $(M=\mathrm{Mg},\mathrm{Ca},\mathrm{Sc},\mathrm{Ti})$. 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 $M{\mathrm{B}}_6$ can maintain their original configurations up to about 1000 or 700 K (only for hex-${\mathrm{MgB}}_6$), 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-${\mathrm{TiB}}_6$ from type-I to type-II $2\times 1$ supercell structure and for ort-${\mathrm{YB}}_6$ from type-I to type-III $2\times 1$ supercell structure. Besides, these 2D $M{\mathrm{B}}_6$ 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 ($T_{\mathrm{c}}$) for these materials, which are in the range of 1.4–22.6 K. Among our studied $M{\mathrm{B}}_6$, the highest $T_{\mathrm{c}}$ (22.6 K) appears in hex-${\mathrm{CaB}}_6$, whose EPC constant $\left(\lambda \right)$ is 0.87. By applying tensile/compressive strains on ort-/hex-${\mathrm{CaB}}_6$, we find that the compressive strain can obviously soften the acoustic-phonon branch and enhance the EPC as well as $T_{\mathrm{c}}$. The $T_{\mathrm{c}}$ of the hex-${\mathrm{CaB}}_6$ 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.

中文翻译：

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二维正交MB6（M = Mg，Ca，Ti，Y）和六角形MB6（M = Mg，Ca，Sc，Ti）中的电子-声子耦合超导

结合晶体结构搜索和第一性原理计算，我们报告了一系列二维（2D）金属硼化物，包括正交晶（ort-）$\mathrm{中号}{\mathrm{乙}}_6$ $（\mathrm{中号}=镁，钙，钛，\mathrm{ÿ}）$ 和六角形（十六进制）$\mathrm{中号}{\mathrm{乙}}_6$ $（\mathrm{中号}=镁，钙，\mathrm{SC}，钛）$。然后，我们研究了它们的几何结构，键合特性，电子结构，机械特性，声子色散，热稳定性，动态稳定性，电荷密度波（CDW）相变，电子-声子耦合（EPC），超导特性等。我们的从头算分子动力学模拟结果表明，这些$\mathrm{中号}{\mathrm{乙}}_6$ 最多可以维持其原始配置约1000或700 K（仅适用于十六进制-${\mathrm{镁硼}}_6$），说明它们具有出色的热稳定性。它们的所有弹性常数都满足Born机械稳定标准，并且在其声子色散中未观察到虚数频率。有趣的是，对于ort-${钛}_6$ 从I型到II型 $2\times \mathrm{1个}$ 超级单元结构和$B_6$ 从I型到III型 $2\times \mathrm{1个}$超级单元结构。此外，这些2D$\mathrm{中号}{\mathrm{乙}}_6$都被认为是固有的声子介导的超导体。通过解析求解从Bardeen，Cooper和Schrieffer的微观理论得出的McMillan-Allen-Dynes公式，我们得出超导转变温度（${Ť}_{\mathrm{C}}$），这些材料的范围在1.4–22.6 K之间。 $\mathrm{中号}{\mathrm{乙}}_6$最高 ${Ť}_{\mathrm{C}}$ （22.6 K）以十六进制显示-${\mathrm{出租车}}_6$，其EPC常数 $（\lambda ）$是0.87。通过在ort / hex-上施加拉伸/压缩应变${\mathrm{出租车}}_6$，我们发现压缩应变可以明显地软化声子的声子分支并增强EPC以及 ${Ť}_{\mathrm{C}}$。的${Ť}_{\mathrm{C}}$ 十六进制的${\mathrm{出租车}}_6$在3％的压缩应变下可以从22.6 K增加到28.4K。这些发现丰富了二维超导体的数据库，并应促进二维超导金属硼化物的实验合成和表征。